Finite Group Databasebeta

← #11790846

Subgroups — #11790846

Order 1152.

921 conjugacy classes of subgroups.

The subgroup lattice has 819 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#939C211yesmaximal, characteristic
2C2×#63661C211yesmaximal, characteristic, complemented
3C2×C3×#834C211yesmaximal, characteristic, complemented
4#10591716C211yesmaximal, characteristic, complemented
5Dic3×#217C211yesmaximal, characteristic, complemented
6C2×#63580C211yesmaximal, characteristic, complemented
7C2×#63580C211yesmaximal, characteristic, complemented
8#71686—31nomaximal
9#70030—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×C3×#67C411yescharacteristic, complemented
12C22×C3×#67C2211yescharacteristic
13C23×C3×Dic3C2211yescharacteristic
14C2×#3757C2211yescharacteristic
15C2×#3757C2211yescharacteristic
16C2×C3×#217C411yescharacteristic, complemented
17C2×C3×#217C2211yescharacteristic
18C2×C3×#217C2211yescharacteristic
19C3×#939—21no—
20C3×#939—21no—
21C3×#939—21no—
22C3×#939—21no—
23C2×C3×(C2×D3)⋊C4C411yescharacteristic, complemented
24C2×C3×Dic3⋊C4C411yescharacteristic, complemented
25C2×Dic3⋊Dic3—21no—
26C2×Dic32—21no—
27#63661—22no—
28C3×#834—22no—
29#63580—22no—
30#63580—22no—
31#63579—21no—
32#63579—21no—
33C2×C3×#121—31no—
34C2×#939D311yescharacteristic
35C2×C3×#99—31no—
36C2×#834—31no—
37C2×#834—31no—
38C2×#834—31no—
39C2×#834—31no—
40C2×#834—61no—
41C2×#834D311yescharacteristic, complemented
42#5212—31no—
43C4×#217—31no—
44C2×#806—31no—
45C2×#806—31no—
46#4942—31no—
47Dic3×C22⋊C4—31no—
48C24×C32C2×C411yescharacteristic
49C24×C32C2311yescharacteristic
50C23×C3×D3C2×C411yescharacteristic
51C2×C32×D4—21no—
52C2×C32×D4—21no—
53C2×C32×D4—21no—
54C2×C32×D4—21no—
55C2×C32×D4—21no—
56C2×C32×D4—21no—
57C22×C32×C4C2×C411yescharacteristic
58C22×C3⋊Dic3—21no—
59C22×C3⋊Dic3—21no—
60C2×C3×#67—21no—
61C2×C3×#67—21no—
62C2×C3×#67—21no—
63C2×C3×#67—21no—
64C2×C3×#67—21no—
65C2×C3×#67—21no—
66C2×C3×#67—21no—
67C2×C3×#67—21no—
68C2×C3×#67—42no—
69C22×C3×Dic3—21no—
70C22×C3×Dic3—21no—
71C22×C3×Dic3—42no—
72C22×C3×Dic3C2×C411yescharacteristic
73C22×C3×Dic3C2×C411yescharacteristic
74C22×C3×Dic3C2×C411yescharacteristic
75C22×C3×Dic3D411yescharacteristic
76C22×C3×Dic3D411yescharacteristic
77C22×C3×Dic3D411yescharacteristic
78C22×C3×Dic3D411yescharacteristic
79#3757—21no—
80#3757—21no—
81#3757—21no—
82#3757D412yescomplemented
83C3×#217—21no—
84C3×#217—21no—
85C3×#217—21no—
86C3×#217—21no—
87C3×#217—21no—
88C3×#217D412yescomplemented
89C3×(C2×D3)⋊C4—21no—
90C3×(C2×D3)⋊C4—21no—
91C3×Dic3⋊C4—21no—
92C3×Dic3⋊C4—21no—
93Dic3⋊Dic3—42no—
94Dic32—42no—
95#1964—91noSylow
96C22×C3×D4—21no—
97C22×C3×D4—31no—
98C22×C3×D4—31no—
99C22×C3×D4C2×D311yescharacteristic
100C22×C3×D4C2×D311yescharacteristic
101C23×C3×C4—31no—
102C22×#67Dic311yescharacteristic, complemented
103C22×#67C2×D311yescharacteristic
104C23×Dic3C2×D311yescharacteristic
105C3×#121—61no—
106C3×#121—61no—
107C3×#121—61no—
108C3×#121—61no—
109C2×C3×C4⋊C4—31no—
110C2×C3×C22⋊C4—31no—
111C2×C3×C22⋊C4—31no—
112C2×C3×C22⋊C4—31no—
113C2×C3×C22⋊C4—31no—
114C2×#217—31no—
115C2×#217—31no—
116C2×#217—31no—
117C2×#217—31no—
118C2×#217—61no—
119C2×#217—61no—
120C2×#217Dic311yescharacteristic, complemented
121C2×#217C2×D311yescharacteristic
122C2×#217C2×D311yescharacteristic
123#939—21no—
124#939—21no—
125#939—21no—
126#939—21no—
127C2×(C2×D3)⋊C4Dic311yescharacteristic, complemented
128C2×C4⋊Dic3—61no—
129C2×Dic3⋊C4—61no—
130C2×Dic3⋊C4Dic311yescharacteristic, complemented
131C2×C4×Dic3—61no—
132C2×C4×Dic3—61no—
133C3×#99—62no—
134#834—22no—
135#834—62no—
136#834—62no—
137#834—62no—
138#834—64no—
139#834—62no—
140C3⋊#95—61no—
141C3⋊#95—61no—
142C3⋊#95—61no—
143C3⋊#95—61no—
144#806—62no—
145#806—62no—
146C23×C32—21no—
147C23×C32—21no—
148C23×C32—21no—
149C23×C32—41no—
150C23×C32—41no—
151C23×C32—41no—
152C23×C32—41no—
153C23×C32C22×C411yescharacteristic
154C23×C32C2×D411yescharacteristic
155C23×C32C2×D411yescharacteristic
156C23×C32C2×D411yescharacteristic
157C23×C32C2×D411yescharacteristic
158C23×C32#4111yescharacteristic
159C23×C32#4111yescharacteristic
160C22×C3×D3—21no—
161C22×C3×D3—21no—
162C22×C3×D3—21no—
163C22×C3×D3—41no—
164C22×C3×D3—41no—
165C32×D4—41no—
166C32×D4—41no—
167C32×D4—41no—
168C32×D4—41no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3—41no—
174C2×C3⋊Dic3—41no—
175C2×C3⋊Dic3—41no—
176C2×C3⋊Dic3—41no—
177C2×C3⋊Dic3—41no—
178C3×#67—42no—
179C3×#67—41no—
180C3×#67—41no—
181C3×#67—41no—
182C3×#67—41no—
183C3×#67—42no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—41no—
192C2×C3×Dic3—41no—
193C2×C3×Dic3—41no—
194C2×C3×Dic3—41no—
195C2×C3×Dic3—41no—
196C2×C3×Dic3—41no—
197C2×C3×Dic3—41no—
198C2×C3×Dic3—41no—
199C2×C3×Dic3C22⋊C411yescharacteristic
200C2×C3×Dic3C22⋊C411yescharacteristic
201C2×C3×Dic3C22⋊C411yescharacteristic
202C2×C3×Dic3C22⋊C411yescharacteristic
203C2×#121—31no—
204C2×#99—31no—
205C2×#99—91no—
206C2×#99—91no—
207C2×#99—91no—
208#380—91no—
209C4×C22⋊C4—91no—
210C24×C3—21no—
211C24×C3—21no—
212C24×C3—31no—
213C24×C3C4×D311yescharacteristic
214C24×C3C2×Dic311yescharacteristic
215C24×C3C22×D311yescharacteristic
216C24×C3C22×D311yescharacteristic
217C23×D3C2×Dic311yescharacteristic
218C2×C3×D4—22no—
219C2×C3×D4—22no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—41no—
233C2×C3×D4—41no—
234C2×C3×D4—41no—
235C2×C3×D4—41no—
236C2×C3×D4—61no—
237C2×C3×D4—61no—
238C2×C3×D4—61no—
239C2×C3×D4—61no—
240C2×C3×D4—61no—
241C2×C3×D4—61no—
242C2×C3×D4—61no—
243C2×C3×D4—61no—
244C2×C3×D4—122no—
245C22×C3×C4—21no—
246C22×C3×C4—31no—
247C22×C3×C4—31no—
248C22×C3×C4—31no—
249C22×C3×C4—31no—
250C22×C3×C4—31no—
251C22×C3×C4—31no—
252C22×C3×C4—31no—
253C22×C3×C4—61no—
254C22×C3×C4—61no—
255C22×C3×C4—122no—
256C22×C3×C4C4×D311yescharacteristic
257C22×C3×C4C2×Dic311yescharacteristic
258C2×#67—21no—
259C2×#67—21no—
260C2×#67—21no—
261C2×#67—21no—
262C2×#67—21no—
263C2×#67—21no—
264C2×#67—21no—
265C2×#67—21no—
266C2×#67—42no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3—42no—
270C22×Dic3—61no—
271C22×Dic3—61no—
272C22×Dic3—61no—
273C22×Dic3—61no—
274C22×Dic3—121no—
275C22×Dic3—121no—
276C22×Dic3C2×Dic311yescharacteristic
277C22×Dic3C2×Dic311yescharacteristic
278C22×Dic3C2×Dic311yescharacteristic
279C22×Dic3#6711yescharacteristic
280C22×Dic3#6711yescharacteristic
281C22×Dic3#6711yescharacteristic
282C22×Dic3#6711yescharacteristic
283C3×C4⋊C4—61no—
284C3×C4⋊C4—61no—
285C3×C22⋊C4—32no—
286C3×C22⋊C4—61no—
287C3×C22⋊C4—61no—
288C3×C22⋊C4—61no—
289C3×C22⋊C4—61no—
290C3×C22⋊C4—61no—
291C3×C22⋊C4—61no—
292C3×C22⋊C4—61no—
293#217—21no—
294#217—21no—
295#217—21no—
296#217—21no—
297#217—21no—
298#217—32no—
299#217—32no—
300#217—62no—
301#217—61no—
302#217—61no—
303#217—62no—
304#217—61no—
305#217—61no—
306#217—61no—
307#217—61no—
308#217—121no—
309#217—121no—
310#217#6712yescomplemented
311(C2×D3)⋊C4—21no—
312(C2×D3)⋊C4—21no—
313C4⋊Dic3—122no—
314Dic3⋊C4—21no—
315Dic3⋊C4—21no—
316Dic3⋊C4—122no—
317C4×Dic3—122no—
318C4×Dic3—122no—
319C22×C32—21no—
320C22×C32—21no—
321C22×C32—21no—
322C22×C32—21no—
323C22×C32—21no—
324C22×C32—21no—
325C22×C32—41no—
326C22×C32—41no—
327C22×C32—41no—
328C22×C32—41no—
329C22×C32—41no—
330C22×C32—41no—
331C22×C32—41no—
332C22×C32—81no—
333C22×C32—81no—
334C22×C32C2×C22⋊C411yescharacteristic
335C22×C32C4×D411yescharacteristic
336C22×C32C4×D411yescharacteristic
337C22×C32#12111yescharacteristic
338C22×C32#12111yescharacteristic
339C22×C32#12411yescharacteristic
340C22×C32#12711yescharacteristic
341C2×C3×D3—41no—
342C2×C3×D3—41no—
343C2×C3×D3—41no—
344C2×C3×D3—81no—
345C2×C3×D3—81no—
346C32×C4—41no—
347C3⋊Dic3—42no—
348C3⋊Dic3—81no—
349C3×Dic3—21no—
350C3×Dic3—21no—
351C3×Dic3—21no—
352C3×Dic3—42no—
353C3×Dic3—41no—
354C3×Dic3—81no—
355C3×Dic3#9912yescomplemented
356C22×D4—31no—
357C22×D4—31no—
358C22×D4D3211yescharacteristic
359C23×C4—31no—
360#121—61no—
361#121—61no—
362#121—61no—
363#121—61no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—181no—
366C2×C22⋊C4—31no—
367C2×C22⋊C4—31no—
368C2×C22⋊C4—31no—
369C2×C22⋊C4—31no—
370C2×C22⋊C4—91no—
371C2×C22⋊C4—91no—
372C2×C42—181no—
373#99—62no—
374#99—182no—
375#99—182no—
376#99—182no—
377#95—181no—
378#95—181no—
379C23×C3—22no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—21no—
393C23×C3—41no—
394C23×C3—41no—
395C23×C3—41no—
396C23×C3—41no—
397C23×C3—41no—
398C23×C3—41no—
399C23×C3—41no—
400C23×C3—41no—
401C23×C3—41no—
402C23×C3—41no—
403C23×C3—61no—
404C23×C3—61no—
405C23×C3—61no—
406C23×C3—81no—
407C23×C3—81no—
408C23×C3—81no—
409C23×C3—81no—
410C23×C3—121no—
411C23×C3—121no—
412C23×C3C2×C4×D311yescharacteristic
413C23×C3#23511yescharacteristic
414C23×C3D3×D411yescharacteristic
415C23×C3D3×D411yescharacteristic
416C23×C3D3×D411yescharacteristic
417C23×C3D3×D411yescharacteristic
418C23×C3D3×D411yescharacteristic
419C23×C3#23711yescharacteristic
420C23×C3#23711yescharacteristic
421C23×C3#23711yescharacteristic
422C23×C3C22×Dic311yescharacteristic
423C23×C3C2×#6711yescharacteristic
424C23×C3C2×#6711yescharacteristic
425C23×C3C2×#6711yescharacteristic
426C22×D3—21no—
427C22×D3—21no—
428C22×D3—21no—
429C22×D3—41no—
430C22×D3—41no—
431C3×D4—42no—
432C3×D4—42no—
433C3×D4—42no—
434C3×D4—42no—
435C3×D4—41no—
436C3×D4—41no—
437C3×D4—41no—
438C3×D4—41no—
439C3×D4—41no—
440C3×D4—41no—
441C3×D4—41no—
442C3×D4—41no—
443C3×D4—122no—
444C3×D4—122no—
445C3×D4—121no—
446C3×D4—121no—
447C3×D4—121no—
448C3×D4—121no—
449C2×C3×C4—22no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—31no—
457C2×C3×C4—31no—
458C2×C3×C4—31no—
459C2×C3×C4—31no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—62no—
463C2×C3×C4—62no—
464C2×C3×C4—62no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4—62no—
469C2×C3×C4—121no—
470C2×C3×C4—121no—
471C2×C3×C4—121no—
472C2×C3×C4—121no—
473C2×C3×C4—121no—
474C2×C3×C4—121no—
475C2×C3×C4—121no—
476C2×C3×C4—121no—
477#67—42no—
478#67—41no—
479#67—41no—
480#67—41no—
481#67—41no—
482#67—42no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—22no—
489C2×Dic3—21no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—62no—
499C2×Dic3—62no—
500C2×Dic3—122no—
501C2×Dic3—121no—
502C2×Dic3—121no—
503C2×Dic3—121no—
504C2×Dic3—121no—
505C2×Dic3—121no—
506C2×Dic3—121no—
507C2×Dic3—122no—
508C2×Dic3—121no—
509C2×Dic3—121no—
510C2×Dic3—121no—
511C2×Dic3—121no—
512C2×Dic3—241no—
513C2×Dic3—241no—
514C2×Dic3—241no—
515C2×Dic3—241no—
516C2×Dic3#21711yescharacteristic
517C2×Dic3#21711yescharacteristic
518C2×Dic3#21711yescharacteristic
519C2×Dic3#21711yescharacteristic
520C2×C32—21no—
521C2×C32—21no—
522C2×C32—21no—
523C2×C32—21no—
524C2×C32—21no—
525C2×C32—21no—
526C2×C32—81no—
527C2×C32#39011yescharacteristic
528C2×C32C2×#9911yescharacteristic
529C2×C32#41011yescharacteristic
530C3×D3—81no—
531C24—31no—
532C24D3×Dic311yescharacteristic
533C24C2×D3211yescharacteristic
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—61no—
541C2×D4—61no—
542C2×D4—61no—
543C2×D4—61no—
544C2×D4—61no—
545C2×D4—61no—
546C2×D4—61no—
547C2×D4—61no—
548C2×D4—122no—
549C22×C4—31no—
550C22×C4—31no—
551C22×C4—31no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—31no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—122no—
559C22×C4—181no—
560C22×C4—181no—
561C22×C4D3×Dic311yescharacteristic
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—362no—
565C22⋊C4—32no—
566C22⋊C4—61no—
567C22⋊C4—61no—
568C22⋊C4—61no—
569C22⋊C4—61no—
570C22⋊C4—61no—
571C22⋊C4—61no—
572C22⋊C4—61no—
573C22⋊C4—92no—
574C22⋊C4—181no—
575C22⋊C4—181no—
576C22⋊C4—181no—
577C42—362no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—41no—
606C22×C3—41no—
607C22×C3—41no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—42no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—81no—
619C22×C3—81no—
620C22×C3—81no—
621C22×C3—81no—
622C22×C3—81no—
623C22×C3—81no—
624C22×C3—81no—
625C22×C3—81no—
626C22×C3—81no—
627C22×C3—81no—
628C22×C3—82no—
629C22×C3—82no—
630C22×C3—121no—
631C22×C3—121no—
632C22×C3—121no—
633C22×C3—241no—
634C22×C3—241no—
635C22×C3D3×C22⋊C411yescharacteristic
636C22×C3#67⋊C411yescharacteristic
637C22×C3#88411yescharacteristic
638C22×C3#88511yescharacteristic
639C22×C3C4×#6711yescharacteristic
640C22×C3D4×Dic311yescharacteristic
641C22×C3D4×Dic311yescharacteristic
642C22×C3#93611yescharacteristic
643C22×C3#93811yescharacteristic
644C22×C3#93811yescharacteristic
645C22×C3#93911yescharacteristic
646C22×C3#94011yescharacteristic
647C22×C3#94011yescharacteristic
648C22×C3C2×#21711yescharacteristic
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—81no—
653C2×D3—81no—
654C3×C4—32no—
655C3×C4—42no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—61no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—122no—
662C3×C4—121no—
663C3×C4—241no—
664Dic3—21no—
665Dic3—21no—
666Dic3—21no—
667Dic3—42no—
668Dic3—41no—
669Dic3—81no—
670Dic3—122no—
671Dic3—122no—
672Dic3—242no—
673Dic3—241no—
674Dic3—241no—
675Dic3—242no—
676Dic3#83412yescomplemented
677C32#196411yescharacteristic, complemented, Sylow
678C23—21no—
679C23—21no—
680C23—21no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—61no—
686C23—61no—
687C23—61no—
688C23—121no—
689C23—121no—
690C23C2×D3×Dic311yescharacteristic
691C23#380411yescharacteristic
692C23#380511yescharacteristic
693C23D3×#6711yescharacteristic
694C23D3×#6711yescharacteristic
695C23D3×#6711yescharacteristic
696C23#381111yescharacteristic
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—122no—
702D4—122no—
703D4—121no—
704D4—121no—
705D4—121no—
706D4—121no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—31no—
711C2×C4—31no—
712C2×C4—31no—
713C2×C4—31no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—61no—
718C2×C4—62no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—121no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—182no—
730C2×C4—361no—
731C2×C4—361no—
732C2×C4—361no—
733C2×C4—361no—
734C2×C4—361no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—41no—
751C2×C3—41no—
752C2×C3—41no—
753C2×C3—41no—
754C2×C3—41no—
755C2×C3—41no—
756C2×C3—82no—
757C2×C3—81no—
758C2×C3—81no—
759C2×C3—241no—
760C2×C3#474011yescharacteristic
761C2×C3D3×#9911yescharacteristic
762C2×C3#495711yescharacteristic
763C2×C3C2×#83411yescharacteristic
764C2×C3#522111yescharacteristic
765C2×C3#524011yescharacteristic
766D3—81no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—81no—
781C22—81no—
782C22—121no—
783C22—121no—
784C22—121no—
785C22—241no—
786C22—241no—
787C22#6395811yescharacteristic
788C22#6395911yescharacteristic
789C22D3×#21711yescharacteristic
790C22#6397011yescharacteristic
791C22Dic3×#6711yescharacteristic
792C22#67⋊Dic311yescharacteristic
793C22#6397911yescharacteristic
794C4—32no—
795C4—41no—
796C4—61no—
797C4—61no—
798C4—61no—
799C4—122no—
800C4—121no—
801C4—241no—
802C4—362no—
803C4—721no—
804C3—21no—
805C3#7003011yescharacteristic, complemented
806C3#7168611yescharacteristic, complemented
807C2—21no—
808C2—21no—
809C2—21no—
810C2—21no—
811C2—21no—
812C2—21no—
813C2—81no—
814C2—241no—
815C2D3×#83411yescharacteristic
816C2#1059152811yescharacteristic
817C2#1059170711yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC22×C32×D4C22
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#939C2
cosocleC24×C32C23
hypercenterC22×D4D32
hypocenterC32#1964
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63661C2semidirect
3. C2×C3×#834C2semidirect
4. #10591716C2semidirect
5. Dic3×#217C2semidirect
6. C2×#63580C2semidirect
7. C2×#63580C2semidirect
11. C22×C3×#67C4semidirect
16. C2×C3×#217C4semidirect
23. C2×C3×(C2×D3)⋊C4C4semidirect
24. C2×C3×Dic3⋊C4C4semidirect
41. C2×#834D3semidirect
82. #3757D4semidirect
88. C3×#217D4semidirect
102. C22×#67Dic3semidirect
120. C2×#217Dic3semidirect
127. C2×(C2×D3)⋊C4Dic3semidirect
130. C2×Dic3⋊C4Dic3semidirect
310. #217#67semidirect
355. C3×Dic3#99semidirect
676. Dic3#834semidirect
677. C32#1964semidirect
805. C3#70030semidirect
806. C3#71686semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9392
C2×#636612
C2×C3×#8342
#105917162
Dic3×#2172
C2×#635802
#716863
#700303