Finite Group Databasebeta

← C2×C3×#88907 #72244461

Subgroups — C2×C3×#88907 #72244461

Order 2592.

3892 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 3892 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#88907C211yesmaximal, characteristic, direct product factor
2C25×C33C311yesmaximal, characteristic
3C2×#88907C319yesmaximal, direct product factor
4C2×C3×C22⋊(C22⋊C9)C313yesmaximal, complemented
5C2×C3×#1094—41nomaximal
6C2×C3×#1094—41nomaximal
7C2×C3×#1094—41nomaximal
8C2×C3×#1094—41nomaximal
9C2×C3×#1094—41nomaximal
10C24×C33—31no—
11C24×C33—31no—
12C24×C33—31no—
13C24×C33—31no—
14C24×C33—31no—
15C24×C33—31no—
16C24×C33—31no—
17C24×C33—31no—
18C24×C33—31no—
19C24×C33—31no—
20C24×C33C2×C311yescharacteristic
21#88907C2×C319yesdirect product factor
22C3×C22⋊(C22⋊C9)C2×C313yescomplemented
23C3×#1094—41no—
24C3×#1094—41no—
25C3×#1094—41no—
26C3×#1094—41no—
27C3×#1094—41no—
28C25×C32—33no—
29C25×C32C3213yes—
30C25×C32C3211yescharacteristic
31C2×C22⋊(C22⋊C9)C3219yescomplemented
32C23×C33—31no—
33C23×C33—31no—
34C23×C33—31no—
35C23×C33—31no—
36C23×C33—31no—
37C23×C33—31no—
38C23×C33—31no—
39C23×C33—31no—
40C23×C33—31no—
41C23×C33—31no—
42C23×C33—31no—
43C23×C33—31no—
44C23×C33—31no—
45C23×C33—31no—
46C23×C33—31no—
47C23×C33—31no—
48C23×C33—31no—
49C23×C33—31no—
50C23×C33—31no—
51C23×C33—31no—
52C23×C33—31no—
53C23×C33—31no—
54C23×C33—31no—
55C23×C33—31no—
56C23×C33—31no—
57C23×C33—31no—
58C23×C33—31no—
59C23×C33—31no—
60C23×C33—31no—
61C23×C33—31no—
62C23×C33—31no—
63C23×C33—31no—
64C23×C33—31no—
65C23×C33—31no—
66C23×C33—31no—
67C23×C33—31no—
68C23×C33—31no—
69C23×C33—31no—
70C23×C33—31no—
71C23×C33—31no—
72C23×C33—31no—
73C23×C33—31no—
74C23×C33—31no—
75C23×C33—31no—
76C23×C33—31no—
77C23×C33—31no—
78C23×C33—31no—
79C23×C33—31no—
80C23×C33—31no—
81C23×C33—31no—
82C23×C33A411yescharacteristic
83C23×C33A411yescharacteristic
84C23×C33A411yescharacteristic
85C23×C33A411yescharacteristic
86C23×C33A411yescharacteristic
87C2×#1094—49no—
88C2×#1094—49no—
89C2×#1094—49no—
90C2×#1094—49no—
91C2×#1094—49no—
92C2×C3×C22⋊C9—43no—
93C2×C3×C22⋊C9—43no—
94C2×C3×C22⋊C9—43no—
95C2×C3×C22⋊C9—43no—
96C2×C3×C22⋊C9—43no—
97C2×C3×3−1+2—161no—
98C24×C32—33no—
99C24×C32—33no—
100C24×C32—33no—
101C24×C32—33no—
102C24×C32—33no—
103C24×C32—33no—
104C24×C32—33no—
105C24×C32—33no—
106C24×C32—33no—
107C24×C32—33no—
108C24×C32—33no—
109C24×C32—33no—
110C24×C32—33no—
111C24×C32—33no—
112C24×C32—33no—
113C24×C32—33no—
114C24×C32—33no—
115C24×C32—33no—
116C24×C32—33no—
117C24×C32—33no—
118C24×C32—33no—
119C24×C32—33no—
120C24×C32—33no—
121C24×C32—33no—
122C24×C32—33no—
123C24×C32—33no—
124C24×C32—33no—
125C24×C32—33no—
126C24×C32—33no—
127C24×C32—33no—
128C24×C32—33no—
129C24×C32—33no—
130C24×C32—33no—
131C24×C32—33no—
132C24×C32—33no—
133C24×C32—33no—
134C24×C32—31no—
135C24×C32—31no—
136C24×C32—31no—
137C24×C32—31no—
138C24×C32—31no—
139C24×C32—33no—
140C24×C32—33no—
141C24×C32—33no—
142C24×C32—33no—
143C24×C32—33no—
144C24×C32—31no—
145C24×C32—31no—
146C24×C32—31no—
147C24×C32—31no—
148C24×C32—31no—
149C24×C32C2×C3213yes—
150C24×C32C2×C3211yescharacteristic
151C22⋊(C22⋊C9)C2×C3219yescomplemented
152C22×C33—31no—
153C22×C33—31no—
154C22×C33—31no—
155C22×C33—31no—
156C22×C33—31no—
157C22×C33—31no—
158C22×C33—31no—
159C22×C33—31no—
160C22×C33—31no—
161C22×C33—31no—
162C22×C33—31no—
163C22×C33—31no—
164C22×C33—31no—
165C22×C33—31no—
166C22×C33—31no—
167C22×C33—31no—
168C22×C33—31no—
169C22×C33—31no—
170C22×C33—31no—
171C22×C33—31no—
172C22×C33—31no—
173C22×C33—31no—
174C22×C33—31no—
175C22×C33—31no—
176C22×C33—31no—
177C22×C33—31no—
178C22×C33—31no—
179C22×C33—31no—
180C22×C33—31no—
181C22×C33—31no—
182C22×C33—31no—
183C22×C33—31no—
184C22×C33—31no—
185C22×C33—31no—
186C22×C33—31no—
187C22×C33—31no—
188C22×C33—31no—
189C22×C33—31no—
190C22×C33—31no—
191C22×C33—31no—
192C22×C33—31no—
193C22×C33—31no—
194C22×C33—31no—
195C22×C33—31no—
196C22×C33—31no—
197C22×C33—31no—
198C22×C33—31no—
199C22×C33—31no—
200C22×C33—31no—
201C22×C33—31no—
202C22×C33C2×A411yescharacteristic
203C22×C33C2×A411yescharacteristic
204C22×C33C2×A411yescharacteristic
205C22×C33C2×A411yescharacteristic
206C22×C33C2×A411yescharacteristic
207#1094—49no—
208#1094—49no—
209#1094—49no—
210#1094—49no—
211#1094—49no—
212C3×C22⋊C9—43no—
213C3×C22⋊C9—43no—
214C3×C22⋊C9—43no—
215C3×C22⋊C9—43no—
216C3×C22⋊C9—43no—
217C25×C3—33no—
218C25×C33−1+213yescomplemented
219C25×C3C3311yescharacteristic
220C3×3−1+2—161noSylow
221C23×C32—33no—
222C23×C32—33no—
223C23×C32—33no—
224C23×C32—33no—
225C23×C32—33no—
226C23×C32—33no—
227C23×C32—33no—
228C23×C32—33no—
229C23×C32—33no—
230C23×C32—33no—
231C23×C32—33no—
232C23×C32—33no—
233C23×C32—33no—
234C23×C32—33no—
235C23×C32—33no—
236C23×C32—33no—
237C23×C32—33no—
238C23×C32—33no—
239C23×C32—33no—
240C23×C32—33no—
241C23×C32—33no—
242C23×C32—33no—
243C23×C32—33no—
244C23×C32—33no—
245C23×C32—33no—
246C23×C32—33no—
247C23×C32—33no—
248C23×C32—33no—
249C23×C32—33no—
250C23×C32—33no—
251C23×C32—33no—
252C23×C32—33no—
253C23×C32—33no—
254C23×C32—33no—
255C23×C32—33no—
256C23×C32—33no—
257C23×C32—33no—
258C23×C32—33no—
259C23×C32—33no—
260C23×C32—33no—
261C23×C32—33no—
262C23×C32—33no—
263C23×C32—33no—
264C23×C32—33no—
265C23×C32—33no—
266C23×C32—33no—
267C23×C32—33no—
268C23×C32—33no—
269C23×C32—33no—
270C23×C32—33no—
271C23×C32—33no—
272C23×C32—33no—
273C23×C32—33no—
274C23×C32—33no—
275C23×C32—33no—
276C23×C32—33no—
277C23×C32—33no—
278C23×C32—33no—
279C23×C32—33no—
280C23×C32—33no—
281C23×C32—33no—
282C23×C32—33no—
283C23×C32—33no—
284C23×C32—33no—
285C23×C32—33no—
286C23×C32—33no—
287C23×C32—33no—
288C23×C32—33no—
289C23×C32—33no—
290C23×C32—33no—
291C23×C32—33no—
292C23×C32—33no—
293C23×C32—33no—
294C23×C32—33no—
295C23×C32—33no—
296C23×C32—33no—
297C23×C32—33no—
298C23×C32—33no—
299C23×C32—33no—
300C23×C32—33no—
301C23×C32—33no—
302C23×C32—33no—
303C23×C32—33no—
304C23×C32—33no—
305C23×C32—33no—
306C23×C32—33no—
307C23×C32—33no—
308C23×C32—33no—
309C23×C32—33no—
310C23×C32—33no—
311C23×C32—33no—
312C23×C32—33no—
313C23×C32—33no—
314C23×C32—33no—
315C23×C32—33no—
316C23×C32—33no—
317C23×C32—33no—
318C23×C32—33no—
319C23×C32—33no—
320C23×C32—33no—
321C23×C32—31no—
322C23×C32—31no—
323C23×C32—31no—
324C23×C32—31no—
325C23×C32—31no—
326C23×C32—31no—
327C23×C32—31no—
328C23×C32—31no—
329C23×C32—31no—
330C23×C32—31no—
331C23×C32—31no—
332C23×C32—31no—
333C23×C32—31no—
334C23×C32—31no—
335C23×C32—31no—
336C23×C32—31no—
337C23×C32—31no—
338C23×C32—31no—
339C23×C32—31no—
340C23×C32—31no—
341C23×C32—31no—
342C23×C32—31no—
343C23×C32—31no—
344C23×C32—31no—
345C23×C32—31no—
346C23×C32—31no—
347C23×C32—31no—
348C23×C32—31no—
349C23×C32—31no—
350C23×C32—31no—
351C23×C32—33no—
352C23×C32—33no—
353C23×C32—33no—
354C23×C32—33no—
355C23×C32—33no—
356C23×C32—33no—
357C23×C32—33no—
358C23×C32—33no—
359C23×C32—31no—
360C23×C32—31no—
361C23×C32—31no—
362C23×C32—31no—
363C23×C32—31no—
364C23×C32—31no—
365C23×C32—31no—
366C23×C32—31no—
367C23×C32—31no—
368C23×C32—31no—
369C23×C32—33no—
370C23×C32—33no—
371C23×C32—33no—
372C23×C32—33no—
373C23×C32—33no—
374C23×C32—33no—
375C23×C32—33no—
376C23×C32—33no—
377C23×C32—33no—
378C23×C32—33no—
379C23×C32—33no—
380C23×C32—33no—
381C23×C32—33no—
382C23×C32—33no—
383C23×C32—33no—
384C23×C32—33no—
385C23×C32—33no—
386C23×C32—33no—
387C23×C32—33no—
388C23×C32—33no—
389C23×C32—33no—
390C23×C32—33no—
391C23×C32—33no—
392C23×C32—33no—
393C23×C32—33no—
394C23×C32—33no—
395C23×C32—33no—
396C23×C32—33no—
397C23×C32—33no—
398C23×C32—33no—
399C23×C32—33no—
400C23×C32—33no—
401C23×C32—33no—
402C23×C32—33no—
403C23×C32—33no—
404C23×C32—33no—
405C23×C32—33no—
406C23×C32—33no—
407C23×C32—33no—
408C23×C32—33no—
409C23×C32—33no—
410C23×C32—33no—
411C23×C32—31no—
412C23×C32—31no—
413C23×C32—31no—
414C23×C32—31no—
415C23×C32—31no—
416C23×C32—31no—
417C23×C32—31no—
418C23×C32—31no—
419C23×C32—31no—
420C23×C32—31no—
421C23×C32—33no—
422C23×C32—33no—
423C23×C32—33no—
424C23×C32—33no—
425C23×C32—33no—
426C23×C32—33no—
427C23×C32—33no—
428C23×C32—33no—
429C23×C32—33no—
430C23×C32—33no—
431C23×C32—33no—
432C23×C32—33no—
433C23×C32—33no—
434C23×C32—33no—
435C23×C32—33no—
436C23×C32—33no—
437C23×C32—33no—
438C23×C32—33no—
439C23×C32—33no—
440C23×C32—33no—
441C23×C32—33no—
442C23×C32—33no—
443C23×C32—33no—
444C23×C32—33no—
445C23×C32—33no—
446C23×C32—33no—
447C23×C32—33no—
448C23×C32—33no—
449C23×C32—33no—
450C23×C32—33no—
451C23×C32—33no—
452C23×C32—33no—
453C23×C32—33no—
454C23×C32—33no—
455C23×C32—33no—
456C23×C32—33no—
457C23×C32—33no—
458C23×C32—33no—
459C23×C32—33no—
460C23×C32—33no—
461C23×C32—33no—
462C23×C32—33no—
463C23×C32—33no—
464C23×C32—33no—
465C23×C32—33no—
466C23×C32—33no—
467C23×C32—33no—
468C23×C32—33no—
469C23×C32—33no—
470C23×C32—33no—
471C23×C32—33no—
472C23×C32—33no—
473C23×C32—33no—
474C23×C32—33no—
475C23×C32—33no—
476C23×C32C3×A413yes—
477C23×C32C3×A413yes—
478C23×C32C3×A413yes—
479C23×C32C3×A413yes—
480C23×C32C3×A413yes—
481C23×C32C3×A411yescharacteristic
482C23×C32C3×A411yescharacteristic
483C23×C32C3×A411yescharacteristic
484C23×C32C3×A411yescharacteristic
485C23×C32C3×A411yescharacteristic
486C2×C22⋊C9—49no—
487C2×C22⋊C9—49no—
488C2×C22⋊C9—49no—
489C2×C22⋊C9—49no—
490C2×C22⋊C9—49no—
491C2×C33—31no—
492C2×C33—31no—
493C2×C33—31no—
494C2×C33—31no—
495C2×C33—31no—
496C2×C33—31no—
497C2×C33—31no—
498C2×C33—31no—
499C2×C33—31no—
500C2×C33—31no—
501C2×C33C22⋊A411yescharacteristic
502C2×3−1+2—169no—
503C2×C3×C9—163no—
504C24×C3—33no—
505C24×C3—33no—
506C24×C3—33no—
507C24×C3—33no—
508C24×C3—33no—
509C24×C3—31no—
510C24×C3—31no—
511C24×C3—31no—
512C24×C3—31no—
513C24×C3—31no—
514C24×C3—33no—
515C24×C3—33no—
516C24×C3—33no—
517C24×C3—33no—
518C24×C3—33no—
519C24×C3—33no—
520C24×C3—33no—
521C24×C3—33no—
522C24×C3—33no—
523C24×C3—33no—
524C24×C3—33no—
525C24×C3—33no—
526C24×C3—33no—
527C24×C3—33no—
528C24×C3—33no—
529C24×C3—33no—
530C24×C3—33no—
531C24×C3—33no—
532C24×C3—33no—
533C24×C3—33no—
534C24×C3—33no—
535C24×C3—33no—
536C24×C3—33no—
537C24×C3—33no—
538C24×C3—33no—
539C24×C3—33no—
540C24×C3—33no—
541C24×C3—33no—
542C24×C3—33no—
543C24×C3—33no—
544C24×C3—33no—
545C24×C3—33no—
546C24×C3—33no—
547C24×C3—33no—
548C24×C3—33no—
549C24×C3—31no—
550C24×C3—31no—
551C24×C3—31no—
552C24×C3—31no—
553C24×C3—31no—
554C24×C3—33no—
555C24×C3C2×3−1+213yescomplemented
556C24×C3C2×C3311yescharacteristic
557C22×C32—31no—
558C22×C32—31no—
559C22×C32—31no—
560C22×C32—31no—
561C22×C32—31no—
562C22×C32—33no—
563C22×C32—33no—
564C22×C32—33no—
565C22×C32—33no—
566C22×C32—33no—
567C22×C32—33no—
568C22×C32—33no—
569C22×C32—33no—
570C22×C32—33no—
571C22×C32—33no—
572C22×C32—33no—
573C22×C32—33no—
574C22×C32—33no—
575C22×C32—33no—
576C22×C32—33no—
577C22×C32—33no—
578C22×C32—33no—
579C22×C32—33no—
580C22×C32—33no—
581C22×C32—33no—
582C22×C32—33no—
583C22×C32—33no—
584C22×C32—33no—
585C22×C32—33no—
586C22×C32—33no—
587C22×C32—33no—
588C22×C32—33no—
589C22×C32—33no—
590C22×C32—33no—
591C22×C32—33no—
592C22×C32—33no—
593C22×C32—33no—
594C22×C32—33no—
595C22×C32—33no—
596C22×C32—33no—
597C22×C32—33no—
598C22×C32—33no—
599C22×C32—33no—
600C22×C32—33no—
601C22×C32—33no—
602C22×C32—33no—
603C22×C32—33no—
604C22×C32—33no—
605C22×C32—33no—
606C22×C32—33no—
607C22×C32—31no—
608C22×C32—31no—
609C22×C32—31no—
610C22×C32—31no—
611C22×C32—31no—
612C22×C32—31no—
613C22×C32—31no—
614C22×C32—31no—
615C22×C32—31no—
616C22×C32—31no—
617C22×C32—31no—
618C22×C32—31no—
619C22×C32—31no—
620C22×C32—31no—
621C22×C32—31no—
622C22×C32—31no—
623C22×C32—31no—
624C22×C32—31no—
625C22×C32—31no—
626C22×C32—31no—
627C22×C32—31no—
628C22×C32—31no—
629C22×C32—31no—
630C22×C32—31no—
631C22×C32—31no—
632C22×C32—31no—
633C22×C32—31no—
634C22×C32—31no—
635C22×C32—31no—
636C22×C32—31no—
637C22×C32—31no—
638C22×C32—31no—
639C22×C32—31no—
640C22×C32—31no—
641C22×C32—31no—
642C22×C32—31no—
643C22×C32—31no—
644C22×C32—31no—
645C22×C32—31no—
646C22×C32—31no—
647C22×C32—33no—
648C22×C32—33no—
649C22×C32—33no—
650C22×C32—33no—
651C22×C32—33no—
652C22×C32—33no—
653C22×C32—33no—
654C22×C32—33no—
655C22×C32—33no—
656C22×C32—33no—
657C22×C32—33no—
658C22×C32—33no—
659C22×C32—33no—
660C22×C32—33no—
661C22×C32—33no—
662C22×C32—33no—
663C22×C32—33no—
664C22×C32—33no—
665C22×C32—33no—
666C22×C32—33no—
667C22×C32—33no—
668C22×C32—33no—
669C22×C32—33no—
670C22×C32—33no—
671C22×C32—33no—
672C22×C32—33no—
673C22×C32—33no—
674C22×C32—33no—
675C22×C32—33no—
676C22×C32—33no—
677C22×C32—33no—
678C22×C32—33no—
679C22×C32—33no—
680C22×C32—33no—
681C22×C32—33no—
682C22×C32—33no—
683C22×C32—33no—
684C22×C32—33no—
685C22×C32—33no—
686C22×C32—33no—
687C22×C32—33no—
688C22×C32—33no—
689C22×C32—33no—
690C22×C32—33no—
691C22×C32—33no—
692C22×C32—33no—
693C22×C32—33no—
694C22×C32—33no—
695C22×C32—33no—
696C22×C32—33no—
697C22×C32—33no—
698C22×C32—33no—
699C22×C32—33no—
700C22×C32—33no—
701C22×C32—33no—
702C22×C32—33no—
703C22×C32—33no—
704C22×C32—33no—
705C22×C32—33no—
706C22×C32—33no—
707C22×C32—33no—
708C22×C32—33no—
709C22×C32—33no—
710C22×C32—33no—
711C22×C32—33no—
712C22×C32—33no—
713C22×C32—33no—
714C22×C32—33no—
715C22×C32—33no—
716C22×C32—33no—
717C22×C32—33no—
718C22×C32—33no—
719C22×C32—33no—
720C22×C32—33no—
721C22×C32—33no—
722C22×C32—33no—
723C22×C32—33no—
724C22×C32—33no—
725C22×C32—33no—
726C22×C32—33no—
727C22×C32—33no—
728C22×C32—33no—
729C22×C32—33no—
730C22×C32—33no—
731C22×C32—33no—
732C22×C32—33no—
733C22×C32—33no—
734C22×C32—33no—
735C22×C32—33no—
736C22×C32—33no—
737C22×C32—33no—
738C22×C32—33no—
739C22×C32—33no—
740C22×C32—33no—
741C22×C32—33no—
742C22×C32—33no—
743C22×C32—33no—
744C22×C32—33no—
745C22×C32—33no—
746C22×C32—33no—
747C22×C32—33no—
748C22×C32—33no—
749C22×C32—33no—
750C22×C32—33no—
751C22×C32—33no—
752C22×C32—31no—
753C22×C32—31no—
754C22×C32—31no—
755C22×C32—31no—
756C22×C32—31no—
757C22×C32—33no—
758C22×C32—33no—
759C22×C32—33no—
760C22×C32—33no—
761C22×C32—33no—
762C22×C32—33no—
763C22×C32—33no—
764C22×C32—33no—
765C22×C32—33no—
766C22×C32—33no—
767C22×C32—33no—
768C22×C32—33no—
769C22×C32—33no—
770C22×C32—33no—
771C22×C32—33no—
772C22×C32—33no—
773C22×C32—33no—
774C22×C32—33no—
775C22×C32—33no—
776C22×C32—33no—
777C22×C32—33no—
778C22×C32—33no—
779C22×C32—33no—
780C22×C32—33no—
781C22×C32—33no—
782C22×C32—33no—
783C22×C32—33no—
784C22×C32—33no—
785C22×C32—33no—
786C22×C32—33no—
787C22×C32—33no—
788C22×C32—33no—
789C22×C32—33no—
790C22×C32—33no—
791C22×C32—33no—
792C22×C32—33no—
793C22×C32—33no—
794C22×C32—33no—
795C22×C32—33no—
796C22×C32—33no—
797C22×C32—33no—
798C22×C32—33no—
799C22×C32—33no—
800C22×C32—33no—
801C22×C32—33no—
802C22×C32—33no—
803C22×C32—33no—
804C22×C32—33no—
805C22×C32—33no—
806C22×C32—33no—
807C22×C32—33no—
808C22×C32—33no—
809C22×C32—33no—
810C22×C32—33no—
811C22×C32—33no—
812C22×C32C2×C3×A413yes—
813C22×C32C2×C3×A413yes—
814C22×C32C2×C3×A413yes—
815C22×C32C2×C3×A413yes—
816C22×C32C2×C3×A413yes—
817C22×C32C2×C3×A411yescharacteristic
818C22×C32C2×C3×A411yescharacteristic
819C22×C32C2×C3×A411yescharacteristic
820C22×C32C2×C3×A411yescharacteristic
821C22×C32C2×C3×A411yescharacteristic
822C22⋊C9—49no—
823C22⋊C9—49no—
824C22⋊C9—49no—
825C22⋊C9—49no—
826C22⋊C9—49no—
827C25C3×3−1+211yescharacteristic, complemented, Sylow
828C33C2×C22⋊A411yescharacteristic
8293−1+2—169no—
830C3×C9—163no—
831C23×C3—33no—
832C23×C3—33no—
833C23×C3—33no—
834C23×C3—33no—
835C23×C3—33no—
836C23×C3—33no—
837C23×C3—33no—
838C23×C3—33no—
839C23×C3—33no—
840C23×C3—33no—
841C23×C3—33no—
842C23×C3—33no—
843C23×C3—33no—
844C23×C3—33no—
845C23×C3—33no—
846C23×C3—33no—
847C23×C3—33no—
848C23×C3—33no—
849C23×C3—33no—
850C23×C3—33no—
851C23×C3—33no—
852C23×C3—33no—
853C23×C3—33no—
854C23×C3—33no—
855C23×C3—33no—
856C23×C3—33no—
857C23×C3—33no—
858C23×C3—33no—
859C23×C3—33no—
860C23×C3—33no—
861C23×C3—31no—
862C23×C3—31no—
863C23×C3—31no—
864C23×C3—31no—
865C23×C3—31no—
866C23×C3—31no—
867C23×C3—31no—
868C23×C3—31no—
869C23×C3—31no—
870C23×C3—31no—
871C23×C3—31no—
872C23×C3—31no—
873C23×C3—31no—
874C23×C3—31no—
875C23×C3—31no—
876C23×C3—31no—
877C23×C3—31no—
878C23×C3—31no—
879C23×C3—31no—
880C23×C3—31no—
881C23×C3—31no—
882C23×C3—31no—
883C23×C3—31no—
884C23×C3—31no—
885C23×C3—31no—
886C23×C3—31no—
887C23×C3—31no—
888C23×C3—31no—
889C23×C3—31no—
890C23×C3—31no—
891C23×C3—33no—
892C23×C3—33no—
893C23×C3—33no—
894C23×C3—33no—
895C23×C3—33no—
896C23×C3—33no—
897C23×C3—33no—
898C23×C3—33no—
899C23×C3—33no—
900C23×C3—33no—
901C23×C3—33no—
902C23×C3—33no—
903C23×C3—33no—
904C23×C3—33no—
905C23×C3—33no—
906C23×C3—33no—
907C23×C3—33no—
908C23×C3—33no—
909C23×C3—33no—
910C23×C3—33no—
911C23×C3—33no—
912C23×C3—33no—
913C23×C3—33no—
914C23×C3—33no—
915C23×C3—33no—
916C23×C3—33no—
917C23×C3—33no—
918C23×C3—33no—
919C23×C3—33no—
920C23×C3—33no—
921C23×C3—33no—
922C23×C3—33no—
923C23×C3—33no—
924C23×C3—33no—
925C23×C3—33no—
926C23×C3—33no—
927C23×C3—33no—
928C23×C3—33no—
929C23×C3—33no—
930C23×C3—33no—
931C23×C3—31no—
932C23×C3—31no—
933C23×C3—31no—
934C23×C3—31no—
935C23×C3—31no—
936C23×C3—31no—
937C23×C3—31no—
938C23×C3—31no—
939C23×C3—31no—
940C23×C3—31no—
941C23×C3—33no—
942C23×C3—33no—
943C23×C3—33no—
944C23×C3—33no—
945C23×C3—33no—
946C23×C3—33no—
947C23×C3—33no—
948C23×C3—33no—
949C23×C3—33no—
950C23×C3—33no—
951C23×C3—33no—
952C23×C3—33no—
953C23×C3—33no—
954C23×C3—33no—
955C23×C3—33no—
956C23×C3—33no—
957C23×C3—33no—
958C23×C3—33no—
959C23×C3—33no—
960C23×C3—33no—
961C23×C3—33no—
962C23×C3—33no—
963C23×C3—33no—
964C23×C3—33no—
965C23×C3—33no—
966C23×C3—33no—
967C23×C3—33no—
968C23×C3—33no—
969C23×C3—33no—
970C23×C3—33no—
971C23×C3—33no—
972C23×C3—33no—
973C23×C3—33no—
974C23×C3—33no—
975C23×C3—33no—
976C23×C3—33no—
977C23×C3—33no—
978C23×C3—33no—
979C23×C3—33no—
980C23×C3—33no—
981C23×C3—33no—
982C23×C3—33no—
983C23×C3—33no—
984C23×C3—33no—
985C23×C3—33no—
986C23×C3—33no—
987C23×C3—33no—
988C23×C3—33no—
989C23×C3—33no—
990C23×C3—33no—
991C23×C3—33no—
992C23×C3—33no—
993C23×C3—33no—
994C23×C3—33no—
995C23×C3—33no—
996C23×C3—33no—
997C23×C3—33no—
998C23×C3—33no—
999C23×C3—33no—
1000C23×C3—33no—
1001C23×C3—33no—
1002C23×C3—33no—
1003C23×C3—33no—
1004C23×C3—33no—
1005C23×C3—33no—
1006C23×C3—33no—
1007C23×C3—33no—
1008C23×C3—33no—
1009C23×C3—33no—
1010C23×C3—33no—
1011C23×C3—33no—
1012C23×C3—33no—
1013C23×C3—33no—
1014C23×C3—33no—
1015C23×C3—33no—
1016C23×C3—33no—
1017C23×C3—33no—
1018C23×C3—33no—
1019C23×C3—33no—
1020C23×C3—33no—
1021C23×C3—33no—
1022C23×C3—33no—
1023C23×C3—33no—
1024C23×C3—33no—
1025C23×C3—33no—
1026C23×C3—33no—
1027C23×C3—33no—
1028C23×C3—33no—
1029C23×C3—33no—
1030C23×C3—33no—
1031C23×C3—33no—
1032C23×C3—33no—
1033C23×C3—33no—
1034C23×C3—33no—
1035C23×C3—33no—
1036C23×C3—33no—
1037C23×C3—33no—
1038C23×C3—33no—
1039C23×C3—33no—
1040C23×C3—33no—
1041C23×C3—33no—
1042C23×C3—33no—
1043C23×C3—33no—
1044C23×C3—33no—
1045C23×C3—33no—
1046C23×C3—33no—
1047C23×C3—33no—
1048C23×C3—33no—
1049C23×C3—33no—
1050C23×C3—33no—
1051C23×C3—33no—
1052C23×C3—33no—
1053C23×C3—33no—
1054C23×C3—33no—
1055C23×C3—33no—
1056C23×C3—33no—
1057C23×C3—33no—
1058C23×C3—33no—
1059C23×C3—33no—
1060C23×C3—33no—
1061C23×C3—33no—
1062C23×C3—33no—
1063C23×C3—33no—
1064C23×C3—33no—
1065C23×C3—33no—
1066C23×C3—33no—
1067C23×C3—33no—
1068C23×C3—33no—
1069C23×C3—33no—
1070C23×C3—33no—
1071C23×C3—31no—
1072C23×C3—31no—
1073C23×C3—31no—
1074C23×C3—31no—
1075C23×C3—31no—
1076C23×C3—31no—
1077C23×C3—31no—
1078C23×C3—31no—
1079C23×C3—31no—
1080C23×C3—31no—
1081C23×C3—33no—
1082C23×C3—33no—
1083C23×C3—33no—
1084C23×C3—33no—
1085C23×C3—33no—
1086C23×C3#109413yescomplemented
1087C23×C3#109413yescomplemented
1088C23×C3#109413yescomplemented
1089C23×C3#109413yescomplemented
1090C23×C3#109413yescomplemented
1091C23×C3C32×A411yescharacteristic
1092C23×C3C32×A411yescharacteristic
1093C23×C3C32×A411yescharacteristic
1094C23×C3C32×A411yescharacteristic
1095C23×C3C32×A411yescharacteristic
1096C2×C32—33no—
1097C2×C32—33no—
1098C2×C32—33no—
1099C2×C32—33no—
1100C2×C32—33no—
1101C2×C32—33no—
1102C2×C32—33no—
1103C2×C32—33no—
1104C2×C32—33no—
1105C2×C32—33no—
1106C2×C32—33no—
1107C2×C32—33no—
1108C2×C32—33no—
1109C2×C32—33no—
1110C2×C32—33no—
1111C2×C32—33no—
1112C2×C32—33no—
1113C2×C32—33no—
1114C2×C32—33no—
1115C2×C32—33no—
1116C2×C32—33no—
1117C2×C32—33no—
1118C2×C32—33no—
1119C2×C32—33no—
1120C2×C32—33no—
1121C2×C32—33no—
1122C2×C32—33no—
1123C2×C32—33no—
1124C2×C32—33no—
1125C2×C32—33no—
1126C2×C32—31no—
1127C2×C32—31no—
1128C2×C32—31no—
1129C2×C32—31no—
1130C2×C32—31no—
1131C2×C32—31no—
1132C2×C32—31no—
1133C2×C32—31no—
1134C2×C32—31no—
1135C2×C32—31no—
1136C2×C32—33no—
1137C2×C32—33no—
1138C2×C32—33no—
1139C2×C32—33no—
1140C2×C32—33no—
1141C2×C32—33no—
1142C2×C32—33no—
1143C2×C32—33no—
1144C2×C32—33no—
1145C2×C32—33no—
1146C2×C32—33no—
1147C2×C32C3×C22⋊A413yes—
1148C2×C32C3×C22⋊A411yescharacteristic
1149C2×C9—169no—
1150C24—31no—
1151C24—31no—
1152C24—31no—
1153C24—31no—
1154C24—31no—
1155C24—31no—
1156C24—31no—
1157C24—31no—
1158C24—31no—
1159C24—31no—
1160C24C2×C3×3−1+211yescharacteristic, complemented
1161C22×C3—33no—
1162C22×C3—33no—
1163C22×C3—33no—
1164C22×C3—33no—
1165C22×C3—33no—
1166C22×C3—31no—
1167C22×C3—31no—
1168C22×C3—31no—
1169C22×C3—31no—
1170C22×C3—31no—
1171C22×C3—33no—
1172C22×C3—33no—
1173C22×C3—33no—
1174C22×C3—33no—
1175C22×C3—33no—
1176C22×C3—33no—
1177C22×C3—33no—
1178C22×C3—33no—
1179C22×C3—33no—
1180C22×C3—33no—
1181C22×C3—33no—
1182C22×C3—33no—
1183C22×C3—33no—
1184C22×C3—33no—
1185C22×C3—33no—
1186C22×C3—33no—
1187C22×C3—33no—
1188C22×C3—33no—
1189C22×C3—33no—
1190C22×C3—33no—
1191C22×C3—33no—
1192C22×C3—33no—
1193C22×C3—33no—
1194C22×C3—33no—
1195C22×C3—33no—
1196C22×C3—33no—
1197C22×C3—33no—
1198C22×C3—33no—
1199C22×C3—33no—
1200C22×C3—33no—
1201C22×C3—33no—
1202C22×C3—33no—
1203C22×C3—33no—
1204C22×C3—33no—
1205C22×C3—33no—
1206C22×C3—33no—
1207C22×C3—33no—
1208C22×C3—33no—
1209C22×C3—33no—
1210C22×C3—33no—
1211C22×C3—33no—
1212C22×C3—33no—
1213C22×C3—33no—
1214C22×C3—33no—
1215C22×C3—33no—
1216C22×C3—33no—
1217C22×C3—33no—
1218C22×C3—33no—
1219C22×C3—33no—
1220C22×C3—33no—
1221C22×C3—33no—
1222C22×C3—33no—
1223C22×C3—33no—
1224C22×C3—33no—
1225C22×C3—33no—
1226C22×C3—33no—
1227C22×C3—33no—
1228C22×C3—33no—
1229C22×C3—33no—
1230C22×C3—33no—
1231C22×C3—33no—
1232C22×C3—33no—
1233C22×C3—33no—
1234C22×C3—33no—
1235C22×C3—33no—
1236C22×C3—33no—
1237C22×C3—33no—
1238C22×C3—33no—
1239C22×C3—33no—
1240C22×C3—33no—
1241C22×C3—33no—
1242C22×C3—33no—
1243C22×C3—33no—
1244C22×C3—33no—
1245C22×C3—33no—
1246C22×C3—33no—
1247C22×C3—33no—
1248C22×C3—33no—
1249C22×C3—33no—
1250C22×C3—33no—
1251C22×C3—33no—
1252C22×C3—33no—
1253C22×C3—33no—
1254C22×C3—33no—
1255C22×C3—33no—
1256C22×C3—33no—
1257C22×C3—33no—
1258C22×C3—33no—
1259C22×C3—33no—
1260C22×C3—33no—
1261C22×C3—33no—
1262C22×C3—33no—
1263C22×C3—33no—
1264C22×C3—33no—
1265C22×C3—33no—
1266C22×C3—33no—
1267C22×C3—33no—
1268C22×C3—33no—
1269C22×C3—33no—
1270C22×C3—33no—
1271C22×C3—33no—
1272C22×C3—33no—
1273C22×C3—33no—
1274C22×C3—33no—
1275C22×C3—33no—
1276C22×C3—33no—
1277C22×C3—33no—
1278C22×C3—33no—
1279C22×C3—33no—
1280C22×C3—33no—
1281C22×C3—33no—
1282C22×C3—33no—
1283C22×C3—33no—
1284C22×C3—33no—
1285C22×C3—33no—
1286C22×C3—33no—
1287C22×C3—33no—
1288C22×C3—33no—
1289C22×C3—33no—
1290C22×C3—33no—
1291C22×C3—33no—
1292C22×C3—33no—
1293C22×C3—33no—
1294C22×C3—33no—
1295C22×C3—33no—
1296C22×C3—33no—
1297C22×C3—33no—
1298C22×C3—33no—
1299C22×C3—33no—
1300C22×C3—33no—
1301C22×C3—33no—
1302C22×C3—33no—
1303C22×C3—33no—
1304C22×C3—33no—
1305C22×C3—33no—
1306C22×C3—33no—
1307C22×C3—33no—
1308C22×C3—33no—
1309C22×C3—33no—
1310C22×C3—33no—
1311C22×C3—33no—
1312C22×C3—33no—
1313C22×C3—33no—
1314C22×C3—33no—
1315C22×C3—33no—
1316C22×C3—33no—
1317C22×C3—33no—
1318C22×C3—33no—
1319C22×C3—33no—
1320C22×C3—33no—
1321C22×C3—33no—
1322C22×C3—33no—
1323C22×C3—33no—
1324C22×C3—33no—
1325C22×C3—33no—
1326C22×C3—33no—
1327C22×C3—33no—
1328C22×C3—33no—
1329C22×C3—33no—
1330C22×C3—33no—
1331C22×C3—33no—
1332C22×C3—33no—
1333C22×C3—33no—
1334C22×C3—33no—
1335C22×C3—33no—
1336C22×C3—33no—
1337C22×C3—33no—
1338C22×C3—33no—
1339C22×C3—33no—
1340C22×C3—33no—
1341C22×C3—33no—
1342C22×C3—33no—
1343C22×C3—33no—
1344C22×C3—33no—
1345C22×C3—33no—
1346C22×C3—33no—
1347C22×C3—33no—
1348C22×C3—33no—
1349C22×C3—33no—
1350C22×C3—33no—
1351C22×C3—33no—
1352C22×C3—33no—
1353C22×C3—33no—
1354C22×C3—33no—
1355C22×C3—33no—
1356C22×C3—31no—
1357C22×C3—31no—
1358C22×C3—31no—
1359C22×C3—31no—
1360C22×C3—31no—
1361C22×C3—31no—
1362C22×C3—31no—
1363C22×C3—31no—
1364C22×C3—31no—
1365C22×C3—31no—
1366C22×C3—31no—
1367C22×C3—31no—
1368C22×C3—31no—
1369C22×C3—31no—
1370C22×C3—31no—
1371C22×C3—31no—
1372C22×C3—31no—
1373C22×C3—31no—
1374C22×C3—31no—
1375C22×C3—31no—
1376C22×C3—31no—
1377C22×C3—31no—
1378C22×C3—31no—
1379C22×C3—31no—
1380C22×C3—31no—
1381C22×C3—31no—
1382C22×C3—31no—
1383C22×C3—31no—
1384C22×C3—31no—
1385C22×C3—31no—
1386C22×C3—31no—
1387C22×C3—31no—
1388C22×C3—31no—
1389C22×C3—31no—
1390C22×C3—31no—
1391C22×C3—31no—
1392C22×C3—31no—
1393C22×C3—31no—
1394C22×C3—31no—
1395C22×C3—31no—
1396C22×C3—33no—
1397C22×C3—33no—
1398C22×C3—33no—
1399C22×C3—33no—
1400C22×C3—33no—
1401C22×C3—31no—
1402C22×C3—31no—
1403C22×C3—31no—
1404C22×C3—31no—
1405C22×C3—31no—
1406C22×C3—33no—
1407C22×C3—33no—
1408C22×C3—33no—
1409C22×C3—33no—
1410C22×C3—33no—
1411C22×C3—33no—
1412C22×C3—33no—
1413C22×C3—33no—
1414C22×C3—33no—
1415C22×C3—33no—
1416C22×C3C2×#109413yescomplemented
1417C22×C3C2×#109413yescomplemented
1418C22×C3C2×#109413yescomplemented
1419C22×C3C2×#109413yescomplemented
1420C22×C3C2×#109413yescomplemented
1421C22×C3C2×C32×A411yescharacteristic
1422C22×C3C2×C32×A411yescharacteristic
1423C22×C3C2×C32×A411yescharacteristic
1424C22×C3C2×C32×A411yescharacteristic
1425C22×C3C2×C32×A411yescharacteristic
1426C32—33no—
1427C32C2×C3×C22⋊A413yes—
1428C32C2×C3×C22⋊A411yescharacteristic
1429C9—169no—
1430C23—31no—
1431C23—31no—
1432C23—31no—
1433C23—31no—
1434C23—31no—
1435C23—31no—
1436C23—31no—
1437C23—31no—
1438C23—31no—
1439C23—31no—
1440C23—31no—
1441C23—31no—
1442C23—31no—
1443C23—31no—
1444C23—31no—
1445C23—31no—
1446C23—31no—
1447C23—31no—
1448C23—31no—
1449C23—31no—
1450C23—31no—
1451C23—31no—
1452C23—31no—
1453C23—31no—
1454C23—31no—
1455C23—31no—
1456C23—31no—
1457C23—31no—
1458C23—31no—
1459C23—31no—
1460C23—31no—
1461C23—31no—
1462C23—31no—
1463C23—31no—
1464C23—31no—
1465C23—31no—
1466C23—31no—
1467C23—31no—
1468C23—31no—
1469C23—31no—
1470C23—31no—
1471C23—31no—
1472C23—31no—
1473C23—31no—
1474C23—31no—
1475C23—31no—
1476C23—31no—
1477C23—31no—
1478C23—31no—
1479C23—31no—
1480C23C3×#109411yescharacteristic, complemented
1481C23C3×#109411yescharacteristic, complemented
1482C23C3×#109411yescharacteristic, complemented
1483C23C3×#109411yescharacteristic, complemented
1484C23C3×#109411yescharacteristic, complemented
1485C2×C3—33no—
1486C2×C3—33no—
1487C2×C3—33no—
1488C2×C3—33no—
1489C2×C3—33no—
1490C2×C3—33no—
1491C2×C3—33no—
1492C2×C3—33no—
1493C2×C3—33no—
1494C2×C3—33no—
1495C2×C3—33no—
1496C2×C3—33no—
1497C2×C3—33no—
1498C2×C3—33no—
1499C2×C3—33no—
1500C2×C3—33no—
1501C2×C3—33no—
1502C2×C3—33no—
1503C2×C3—33no—
1504C2×C3—33no—
1505C2×C3—33no—
1506C2×C3—33no—
1507C2×C3—33no—
1508C2×C3—33no—
1509C2×C3—33no—
1510C2×C3—33no—
1511C2×C3—33no—
1512C2×C3—33no—
1513C2×C3—33no—
1514C2×C3—33no—
1515C2×C3—33no—
1516C2×C3—33no—
1517C2×C3—33no—
1518C2×C3—33no—
1519C2×C3—33no—
1520C2×C3—33no—
1521C2×C3—33no—
1522C2×C3—33no—
1523C2×C3—33no—
1524C2×C3—33no—
1525C2×C3—31no—
1526C2×C3—31no—
1527C2×C3—31no—
1528C2×C3—31no—
1529C2×C3—31no—
1530C2×C3—31no—
1531C2×C3—31no—
1532C2×C3—31no—
1533C2×C3—31no—
1534C2×C3—31no—
1535C2×C3—33no—
1536C2×C3#8890713yesdirect product factor
1537C2×C3C32×C22⋊A411yescharacteristic
1538C22—31no—
1539C22—31no—
1540C22—31no—
1541C22—31no—
1542C22—31no—
1543C22—31no—
1544C22—31no—
1545C22—31no—
1546C22—31no—
1547C22—31no—
1548C22—31no—
1549C22—31no—
1550C22—31no—
1551C22—31no—
1552C22—31no—
1553C22—31no—
1554C22—31no—
1555C22—31no—
1556C22—31no—
1557C22—31no—
1558C22—31no—
1559C22—31no—
1560C22—31no—
1561C22—31no—
1562C22—31no—
1563C22—31no—
1564C22—31no—
1565C22—31no—
1566C22—31no—
1567C22—31no—
1568C22—31no—
1569C22—31no—
1570C22—31no—
1571C22—31no—
1572C22—31no—
1573C22—31no—
1574C22—31no—
1575C22—31no—
1576C22—31no—
1577C22—31no—
1578C22—31no—
1579C22—31no—
1580C22—31no—
1581C22—31no—
1582C22—31no—
1583C22—31no—
1584C22—31no—
1585C22—31no—
1586C22—31no—
1587C22—31no—
1588C22C2×C3×#109411yescharacteristic, complemented
1589C22C2×C3×#109411yescharacteristic, complemented
1590C22C2×C3×#109411yescharacteristic, complemented
1591C22C2×C3×#109411yescharacteristic, complemented
1592C22C2×C3×#109411yescharacteristic, complemented
1593C3—33no—
1594C3C2×#8890713yesdirect product factor
1595C3C2×C32×C22⋊A411yescharacteristic
1596C2—31no—
1597C2—31no—
1598C2—31no—
1599C2—31no—
1600C2—31no—
1601C2—31no—
1602C2—31no—
1603C2—31no—
1604C2—31no—
1605C2—31no—
1606C2C3×#8890711yescharacteristic, direct product factor
subgroupG/H
centerC2×C32C3×C22⋊A4
commutator, cosocleC24×C3C2×C33
FrattiniC3C2×C32×C22⋊A4
Fitting, prime radicalC25×C33C3
socleC25×C32C32
hypercenterC2×C33C22⋊A4
hypocenterC24C2×C3×3−1+2
LCSG ▷ C24×C3 ▷ C24
UCSC1 ◁ C2×C32 ◁ C2×C33

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#88907C2direct (N × H)
3. C2×#88907C3direct (N × H)
4. C2×C3×C22⋊(C22⋊C9)C3semidirect
21. #88907C2×C3direct (N × H)
22. C3×C22⋊(C22⋊C9)C2×C3semidirect
31. C2×C22⋊(C22⋊C9)C32semidirect
151. C22⋊(C22⋊C9)C2×C32semidirect
218. C25×C33−1+2semidirect
555. C24×C3C2×3−1+2semidirect
827. C25C3×3−1+2semidirect
1086. C23×C3#1094semidirect
1087. C23×C3#1094semidirect
1088. C23×C3#1094semidirect
1089. C23×C3#1094semidirect
1090. C23×C3#1094semidirect
1160. C24C2×C3×3−1+2semidirect
1416. C22×C3C2×#1094semidirect
1417. C22×C3C2×#1094semidirect
1418. C22×C3C2×#1094semidirect
1419. C22×C3C2×#1094semidirect
1420. C22×C3C2×#1094semidirect
1480. C23C3×#1094semidirect
1481. C23C3×#1094semidirect
1482. C23C3×#1094semidirect
1483. C23C3×#1094semidirect
1484. C23C3×#1094semidirect
1536. C2×C3#88907direct (N × H)
1588. C22C2×C3×#1094semidirect
1589. C22C2×C3×#1094semidirect
1590. C22C2×C3×#1094semidirect
1591. C22C2×C3×#1094semidirect
1592. C22C2×C3×#1094semidirect
1594. C3C2×#88907direct (N × H)
1606. C2C3×#88907direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#889072
C25×C333
C2×#889073
C2×C3×C22⋊(C22⋊C9)3
C2×C3×#10944