Finite Group Databasebeta

← #11790841

Subgroups — #11790841

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×#63978C211yesmaximal, characteristic
2C2×#63633C211yesmaximal, characteristic, complemented
3C2×C3×#806C211yesmaximal, characteristic, complemented
4C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
5#10591716C211yesmaximal, characteristic, complemented
6C2×#63581C211yesmaximal, characteristic, complemented
7C2×#63580C211yesmaximal, characteristic, complemented
8#70030—31nomaximal
9#69456—31nomaximal
10C22×#638C2211yescharacteristic
11C22×C3×#67C2211yescharacteristic
12C23×C3×Dic3C2211yescharacteristic
13C22×#626C411yescharacteristic, complemented
14C2×C32×C22⋊C4C2211yescharacteristic
15C2×#3757C2211yescharacteristic
16C2×C3×#217C2211yescharacteristic
17C2×C3×#217C2211yescharacteristic
18C2×C3×C4×Dic3—21no—
19#63978—21no—
20#63978—21no—
21#63978—21no—
22#63978—21no—
23C2×Dic3⋊Dic3—21no—
24C2×Dic3⋊Dic3C411yescharacteristic, complemented
25C2×#3722C411yescharacteristic, complemented
26C2×(C2×D3)⋊Dic3C411yescharacteristic, complemented
27#63633—22no—
28C3×C3⋊#95—21no—
29C3×#806—22no—
30#63581—22no—
31#63580—22no—
32#63579—21no—
33C2×#939—31no—
34C2×#930—31no—
35C2×C3×#99—31no—
36C3×C4×C22⋊C4—31no—
37C2×#834—31no—
38#5212—31no—
39C2×#806—31no—
40C2×#806—31no—
41C2×#806—31no—
42C2×#806—31no—
43C2×#806—31no—
44C2×#806—61no—
45C2×#806D311yescharacteristic, complemented
46#4942—31no—
47Dic3×C22⋊C4D311yescharacteristic, complemented
48C24×C32C2311yescharacteristic
49C23×C3⋊D3C2×C411yescharacteristic
50C23×C3×D3C2×C411yescharacteristic
51C22×C32×C4—21no—
52C2×#638—21no—
53C2×#638—21no—
54C2×#638—21no—
55C2×#638—21no—
56C2×#638—21no—
57C2×#638—21no—
58C22×C3⋊Dic3—21no—
59C22×C3⋊Dic3C2×C411yescharacteristic
60C2×C3×#67—21no—
61C2×C3×#67—21no—
62C2×C3×#67—21no—
63C2×C3×#67—21no—
64C2×C3×#67—21no—
65C2×C3×#67—21no—
66C22×C3×Dic3—21no—
67C22×C3×Dic3—21no—
68C22×C3×Dic3—42no—
69C22×C3×Dic3C2×C411yescharacteristic
70C22×C3×Dic3C2×C411yescharacteristic
71C22×C3×Dic3C2×C411yescharacteristic
72C22×C3×Dic3D411yescharacteristic
73C22×C3×Dic3D411yescharacteristic
74C22×C3×Dic3D411yescharacteristic
75C22×C3×Dic3D411yescharacteristic
76C2×#626—21no—
77C2×#626—21no—
78C2×#626—42no—
79C32×C22⋊C4—21no—
80C32×C22⋊C4D412yescomplemented
81#3757—21no—
82#3757—21no—
83C3×#217—21no—
84C3×#217—21no—
85C3×#217—21no—
86C3×#217D412yescomplemented
87C3×C4×Dic3—42no—
88Dic3⋊Dic3—21no—
89Dic3⋊Dic3—21no—
90Dic3⋊Dic3—42no—
91#3722—21no—
92#3722—21no—
93(C2×D3)⋊Dic3—21no—
94(C2×D3)⋊Dic3—21no—
95#1964—91noSylow
96C22×C3×D4—31no—
97C23×C3×C4—31no—
98C22×#67—31no—
99C22×#67—31no—
100C22×#67—31no—
101C22×#67—61no—
102C22×#67C2×D311yescharacteristic
103C23×Dic3C2×D311yescharacteristic
104C22×D12—31no—
105C2×C3×C22⋊C4—21no—
106C2×C3×C22⋊C4—31no—
107C2×C3×C22⋊C4—31no—
108C2×C3×C22⋊C4C2×D311yescharacteristic
109C2×C3×C22⋊C4C2×D311yescharacteristic
110C2×C3×C42—61no—
111C2×#217—31no—
112C2×#217—31no—
113C2×#217—31no—
114C2×#217—61no—
115C2×#217C2×D311yescharacteristic
116C2×#217C2×D311yescharacteristic
117#939—61no—
118#939—61no—
119#939—61no—
120#939—61no—
121#930—61no—
122#930—61no—
123#930—61no—
124#930—61no—
125C2×(C2×D3)⋊C4—31no—
126C2×(C2×D3)⋊C4—31no—
127C2×(C2×D3)⋊C4—31no—
128C2×C4⋊Dic3—31no—
129C2×C4⋊Dic3—61no—
130C2×Dic3⋊C4—31no—
131C2×Dic3⋊C4—61no—
132C2×C4×Dic3—21no—
133C3×#99—62no—
134C3×#95—61no—
135#834—62no—
136C3⋊#95—21no—
137C3⋊#95—61no—
138C3⋊#95—61no—
139#806—22no—
140#806—62no—
141#806—64no—
142#806—62no—
143#806—62no—
144#806—62no—
145#806—62no—
146C23×C32—41no—
147C23×C32—41no—
148C23×C32C22×C411yescharacteristic
149C23×C32C2×D411yescharacteristic
150C23×C32C2×D411yescharacteristic
151C23×C32C2×D411yescharacteristic
152C23×C32C2×D411yescharacteristic
153C23×C32#4111yescharacteristic
154C23×C32#4111yescharacteristic
155C22×C3⋊D3—21no—
156C22×C3⋊D3—21no—
157C22×C3⋊D3—21no—
158C22×C3⋊D3—41no—
159C22×C3⋊D3—41no—
160C22×C3×D3—21no—
161C22×C3×D3—21no—
162C22×C3×D3—21no—
163C22×C3×D3—41no—
164C22×C3×D3—41no—
165C2×C32×C4—22no—
166C2×C32×C4—41no—
167C2×C32×C4—41no—
168#638—41no—
169#638—41no—
170#638—41no—
171#638—41no—
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—41no—
176C2×C3⋊Dic3—41no—
177C2×C3⋊Dic3—41no—
178C3×#67—41no—
179C3×#67—41no—
180C3×#67—41no—
181C3×#67—41no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—41no—
190C2×C3×Dic3—41no—
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×Dic3C22⋊C411yescharacteristic
198C2×C3×Dic3C22⋊C411yescharacteristic
199C2×C3×Dic3C22⋊C411yescharacteristic
200C2×C3×Dic3C22⋊C411yescharacteristic
201#626—42no—
202#626—42no—
203C2×#121—91no—
204C2×#99—31no—
205C2×#99—91no—
206C2×#99—91no—
207C2×#99—91no—
208#380—91no—
209C4×C22⋊C4—31no—
210C24×C3—21no—
211C24×C3—31no—
212C24×C3C22×D311yescharacteristic
213C24×C3C22×D311yescharacteristic
214C23×D3—31no—
215C23×D3—31no—
216C23×D3—61no—
217C23×D3C4×D311yescharacteristic
218C2×C3×D4—61no—
219C2×C3×D4—61no—
220C2×C3×D4—61no—
221C2×C3×D4—61no—
222C2×C3×D4—61no—
223C2×C3×D4—61no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—31no—
227C22×C3×C4—31no—
228C22×C3×C4—31no—
229C22×C3×C4—31no—
230C22×C3×C4—31no—
231C22×C3×C4—31no—
232C22×C3×C4—31no—
233C22×C3×C4—41no—
234C22×C3×C4—61no—
235C22×C3×C4—61no—
236C22×C3×C4—122no—
237C2×#67—21no—
238C2×#67—21no—
239C2×#67—21no—
240C2×#67—21no—
241C2×#67—21no—
242C2×#67—21no—
243C2×#67—62no—
244C2×#67—62no—
245C2×#67—61no—
246C2×#67—61no—
247C2×#67—61no—
248C2×#67—61no—
249C2×#67—61no—
250C2×#67—61no—
251C2×#67—61no—
252C2×#67—61no—
253C2×#67—61no—
254C2×#67—61no—
255C2×#67—61no—
256C2×#67—61no—
257C2×#67—61no—
258C2×#67—61no—
259C2×#67—121no—
260C2×#67—121no—
261C2×#67—121no—
262C2×#67—121no—
263C2×#67—122no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3—31no—
267C22×Dic3—31no—
268C22×Dic3—42no—
269C22×Dic3—61no—
270C22×Dic3—61no—
271C22×Dic3—61no—
272C22×Dic3—121no—
273C22×Dic3C4×D311yescharacteristic
274C22×Dic3C4×D311yescharacteristic
275C22×Dic3C4×D311yescharacteristic
276C22×Dic3D1211yescharacteristic
277C22×Dic3D1211yescharacteristic
278C22×Dic3#6711yescharacteristic
279C22×Dic3#6711yescharacteristic
280C2×D12—61no—
281C2×D12—61no—
282C2×D12—122no—
283C3×C22⋊C4—21no—
284C3×C22⋊C4—21no—
285C3×C22⋊C4—22no—
286C3×C22⋊C4—32no—
287C3×C22⋊C4—41no—
288C3×C22⋊C4—61no—
289C3×C22⋊C4—61no—
290C3×C22⋊C4—61no—
291C3×C22⋊C4D1212yescomplemented
292C3×C22⋊C4#6712yescomplemented
293C3×C42—122no—
294#217—21no—
295#217—21no—
296#217—21no—
297#217—61no—
298#217—61no—
299#217—62no—
300#217—61no—
301#217—61no—
302#217—61no—
303#217—61no—
304#217—121no—
305#217D1212yescomplemented
306(C2×D3)⋊C4—61no—
307(C2×D3)⋊C4—61no—
308(C2×D3)⋊C4—61no—
309(C2×D3)⋊C4—61no—
310(C2×D3)⋊C4—61no—
311(C2×D3)⋊C4—61no—
312C4⋊Dic3—61no—
313C4⋊Dic3—61no—
314C4⋊Dic3—122no—
315Dic3⋊C4—61no—
316Dic3⋊C4—61no—
317Dic3⋊C4—122no—
318C4×Dic3—42no—
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×C32C2×C22⋊C411yescharacteristic
330C22×C32C4×D411yescharacteristic
331C22×C32C4×D411yescharacteristic
332C22×C32#12111yescharacteristic
333C22×C32#12111yescharacteristic
334C22×C32#12411yescharacteristic
335C22×C32#12711yescharacteristic
336C2×C3⋊D3—41no—
337C2×C3⋊D3—41no—
338C2×C3⋊D3—41no—
339C2×C3⋊D3—81no—
340C2×C3⋊D3—81no—
341C2×C3×D3—41no—
342C2×C3×D3—41no—
343C2×C3×D3—41no—
344C2×C3×D3—81no—
345C2×C3×D3—81no—
346C32×C4—42no—
347C3⋊Dic3—41no—
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—91no—
358C22×D4—91no—
359C23×C4—31no—
360#121—181no—
361#121—181no—
362#121—181no—
363#121—181no—
364C2×C4⋊C4—91no—
365C2×C4⋊C4—181no—
366C2×C22⋊C4—31no—
367C2×C22⋊C4—31no—
368C2×C22⋊C4—91no—
369C2×C22⋊C4—91no—
370C2×C22⋊C4—91no—
371C2×C22⋊C4D3211yescharacteristic
372C2×C42—61no—
373#99—62no—
374#99—182no—
375#99—182no—
376#99—182no—
377#95—61no—
378#95—181no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—21no—
386C23×C3—41no—
387C23×C3—41no—
388C23×C3—41no—
389C23×C3—41no—
390C23×C3—61no—
391C23×C3—61no—
392C23×C3—61no—
393C23×C3—81no—
394C23×C3—81no—
395C23×C3—121no—
396C23×C3—121no—
397C23×C3C2×C4×D311yescharacteristic
398C23×C3C2×C4×D311yescharacteristic
399C23×C3C2×D1211yescharacteristic
400C23×C3C2×D1211yescharacteristic
401C23×C3C2×D1211yescharacteristic
402C23×C3#23511yescharacteristic
403C23×C3#23511yescharacteristic
404C23×C3#23511yescharacteristic
405C23×C3D3×D411yescharacteristic
406C23×C3D3×D411yescharacteristic
407C23×C3D3×D411yescharacteristic
408C23×C3#23711yescharacteristic
409C23×C3C2×#6711yescharacteristic
410C23×C3C2×#6711yescharacteristic
411C22×D3—21no—
412C22×D3—21no—
413C22×D3—21no—
414C22×D3—41no—
415C22×D3—41no—
416C22×D3—61no—
417C22×D3—61no—
418C22×D3—62no—
419C22×D3—61no—
420C22×D3—61no—
421C22×D3—61no—
422C22×D3—61no—
423C22×D3—121no—
424C22×D3—121no—
425C22×D3—121no—
426C22×D3—121no—
427C22×D3—121no—
428C22×D3—121no—
429C22×D3—241no—
430C22×D3—241no—
431C3×D4—121no—
432C3×D4—121no—
433C3×D4—121no—
434C3×D4—121no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—31no—
438C2×C3×C4—31no—
439C2×C3×C4—31no—
440C2×C3×C4—31no—
441C2×C3×C4—42no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—62no—
447C2×C3×C4—62no—
448C2×C3×C4—62no—
449C2×C3×C4—61no—
450C2×C3×C4—61no—
451C2×C3×C4—62no—
452C2×C3×C4—61no—
453C2×C3×C4—81no—
454C2×C3×C4—81no—
455C2×C3×C4—121no—
456C2×C3×C4—121no—
457C2×C3×C4—121no—
458C2×C3×C4—121no—
459C2×C3×C4—121no—
460C2×C3×C4—121no—
461C2×C3×C4—121no—
462C2×C3×C4—121no—
463#67—41no—
464#67—41no—
465#67—41no—
466#67—41no—
467#67—122no—
468#67—122no—
469#67—122no—
470#67—122no—
471#67—122no—
472#67—121no—
473#67—121no—
474#67—121no—
475#67—121no—
476#67—121no—
477#67—121no—
478#67—121no—
479#67—121no—
480#67—122no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—22no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3—62no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—61no—
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(C2×D3)⋊C411yescharacteristic
515C2×Dic3(C2×D3)⋊C411yescharacteristic
516C2×Dic3(C2×D3)⋊C411yescharacteristic
517C2×Dic3(C2×D3)⋊C411yescharacteristic
518D12—122no—
519D12—122no—
520C2×C32—21no—
521C2×C32—21no—
522C2×C32—21no—
523C2×C32—21no—
524C2×C32—21no—
525C2×C32—21no—
526C2×C32#39011yescharacteristic
527C2×C32C2×#9911yescharacteristic
528C2×C32#41011yescharacteristic
529C3⋊D3—81no—
530C3×D3—81no—
531C24—31no—
532C24—91no—
533C24C2×D3211yescharacteristic
534C2×D4—61no—
535C2×D4—61no—
536C2×D4—61no—
537C2×D4—61no—
538C2×D4—61no—
539C2×D4—61no—
540C2×D4—181no—
541C2×D4—181no—
542C2×D4—181no—
543C2×D4—181no—
544C2×D4—181no—
545C2×D4—181no—
546C2×D4—181no—
547C2×D4—181no—
548C2×D4—362no—
549C22×C4—21no—
550C22×C4—31no—
551C22×C4—31no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—31no—
556C22×C4—31no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—91no—
560C22×C4—122no—
561C22×C4—181no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—362no—
565C22⋊C4—21no—
566C22⋊C4—32no—
567C22⋊C4—61no—
568C22⋊C4—61no—
569C22⋊C4—61no—
570C22⋊C4—181no—
571C22⋊C4—181no—
572C22⋊C4—181no—
573C22⋊C4—181no—
574C22⋊C4—181no—
575C22⋊C4—181no—
576C22⋊C4#62612yescomplemented
577C42—122no—
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—81no—
612C22×C3—81no—
613C22×C3—81no—
614C22×C3—81no—
615C22×C3—121no—
616C22×C3—121no—
617C22×C3—121no—
618C22×C3—241no—
619C22×C3—241no—
620C22×C3C4×D1211yescharacteristic
621C22×C3C4×D1211yescharacteristic
622C22×C3#87411yescharacteristic
623C22×C3#87511yescharacteristic
624C22×C3D3×C22⋊C411yescharacteristic
625C22×C3#67⋊C411yescharacteristic
626C22×C3#88411yescharacteristic
627C22×C3#88511yescharacteristic
628C22×C3C2×(C2×D3)⋊C411yescharacteristic
629C22×C3C4×#6711yescharacteristic
630C22×C3#93011yescharacteristic
631C22×C3#93011yescharacteristic
632C22×C3#93911yescharacteristic
633C22×C3#94011yescharacteristic
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—81no—
638C2×D3—81no—
639C2×D3—122no—
640C2×D3—121no—
641C2×D3—121no—
642C2×D3—121no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—241no—
647C2×D3—241no—
648C2×D3—242no—
649C2×D3—241no—
650C2×D3—241no—
651C2×D3—241no—
652C2×D3—241no—
653C2×D3—242no—
654C3×C4—32no—
655C3×C4—42no—
656C3×C4—42no—
657C3×C4—61no—
658C3×C4—61no—
659C3×C4—61no—
660C3×C4—82no—
661C3×C4—122no—
662C3×C4—121no—
663C3×C4—241no—
664Dic3—21no—
665Dic3—21no—
666Dic3—21no—
667Dic3—42no—
668Dic3—41no—
669Dic3—81no—
670Dic3—122no—
671Dic3—121no—
672Dic3—121no—
673Dic3—241no—
674Dic3—241no—
675Dic3—242no—
676Dic3#80612yescomplemented
677C32#196411yescharacteristic, complemented, Sylow
678C23—41no—
679C23—41no—
680C23—61no—
681C23—61no—
682C23—61no—
683C23—121no—
684C23—121no—
685C23—181no—
686C23—181no—
687C23—181no—
688C23—361no—
689C23—361no—
690C23#379811yescharacteristic
691C23C4×D3211yescharacteristic
692C23D3×D1211yescharacteristic
693C23D3×D1211yescharacteristic
694C23#380411yescharacteristic
695C23C2×#62611yescharacteristic
696C23D3×#6711yescharacteristic
697D4—121no—
698D4—121no—
699D4—121no—
700D4—121no—
701D4—362no—
702D4—362no—
703D4—361no—
704D4—361no—
705D4—361no—
706D4—361no—
707C2×C4—22no—
708C2×C4—31no—
709C2×C4—31no—
710C2×C4—31no—
711C2×C4—31no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—62no—
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—181no—
730C2×C4—181no—
731C2×C4—181no—
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—241no—
757C2×C3#474011yescharacteristic
758C2×C3D3×#9911yescharacteristic
759C2×C3#493911yescharacteristic
760C2×C3C2×#80611yescharacteristic
761C2×C3#495711yescharacteristic
762C2×C3#500611yescharacteristic
763D3—81no—
764D3—242no—
765D3—241no—
766D3—241no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—121no—
778C22—121no—
779C22—121no—
780C22—241no—
781C22—241no—
782C22—361no—
783C22—361no—
784C22—361no—
785C22—721no—
786C22—721no—
787C22#6385211yescharacteristic
788C22#6388011yescharacteristic
789C22C4×#62611yescharacteristic
790C22#6390611yescharacteristic
791C22#6391111yescharacteristic
792C22D3×(C2×D3)⋊C411yescharacteristic
793C22#6397811yescharacteristic
794C4—32no—
795C4—42no—
796C4—61no—
797C4—61no—
798C4—61no—
799C4—122no—
800C4—121no—
801C4—241no—
802C4—361no—
803C4—721no—
804C3—21no—
805C3#6945611yescharacteristic, complemented
806C3#7003011yescharacteristic, complemented
807C2—21no—
808C2—21no—
809C2—21no—
810C2—21no—
811C2—21no—
812C2—21no—
813C2—241no—
814C2—721no—
815C2D3×#80611yescharacteristic
816C2#1059040511yescharacteristic
817C2#1059138311yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#63978C2
cosocleC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#1964
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63633C2semidirect
3. C2×C3×#806C2semidirect
4. C3×Dic3×C22⋊C4C2semidirect
5. #10591716C2semidirect
6. C2×#63581C2semidirect
7. C2×#63580C2semidirect
13. C22×#626C4semidirect
24. C2×Dic3⋊Dic3C4semidirect
25. C2×#3722C4semidirect
26. C2×(C2×D3)⋊Dic3C4semidirect
45. C2×#806D3semidirect
47. Dic3×C22⋊C4D3semidirect
80. C32×C22⋊C4D4semidirect
86. C3×#217D4semidirect
291. C3×C22⋊C4D12semidirect
292. C3×C22⋊C4#67semidirect
305. #217D12semidirect
355. C3×Dic3#99semidirect
576. C22⋊C4#626semidirect
676. Dic3#806semidirect
677. C32#1964semidirect
805. C3#69456semidirect
806. C3#70030semidirect

Maximal subgroups

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

subgroupindex
C2×#639782
C2×#636332
C2×C3×#8062
C3×Dic3×C22⋊C42
#105917162
C2×#635812
C2×#635802
#700303
#694563