Finite Group Databasebeta

← #11867790

Subgroups — #11867790

Order 1152.

1004 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5608C211yesmaximal, characteristic
2C2×#63929C211yesmaximal, characteristic, complemented
3#10594884C211yesmaximal, characteristic, complemented
4C2×#63814C211yesmaximal, characteristic, complemented
5#10592741C211yesmaximal, characteristic, complemented
6C3×#5041C211yesmaximal, characteristic, complemented
7#10591502C211yesmaximal, characteristic, complemented
8#10591460C211yesmaximal, characteristic, complemented
9#10591420C211yesmaximal, characteristic, complemented
10#10591189C211yesmaximal, characteristic, complemented
11#10591187C211yesmaximal, characteristic, complemented
12D3×#810C211yesmaximal, characteristic, complemented
13#10590587C211yesmaximal, characteristic, complemented
14#10590581C211yesmaximal, characteristic, complemented
15#10590518C211yesmaximal, characteristic, complemented
16#83423—31nomaximal
17#80662—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C32×#121C2211yescharacteristic
22C2×#3754C2211yescharacteristic
23#64133C2211yescharacteristic
24C2×#3748C2211yescharacteristic
25C3×#939—21no—
26C3×#938—21no—
27C3×#938C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic
29C3×#924C2211yescharacteristic
30C3×#924C2211yescharacteristic
31C22×C3×C3⋊C8C2211yescharacteristic
32C3×#897C2211yescharacteristic
33C3×D3×C4⋊C4C2211yescharacteristic
34C3×#884—21no—
35C3×#878—21no—
36#63969—21no—
37#63959—21no—
38#63929—24no—
39#63884—21no—
40#63857C2211yescharacteristic
41#63856C2211yescharacteristic
42#63841C2211yescharacteristic
43#63839—21no—
44C2×#3719C2211yescharacteristic
45C2×#3718C2211yescharacteristic
46C2×#3711C2211yescharacteristic
47C2×#3711C2211yescharacteristic
48#63814—24no—
49C2×D3×C3⋊C8C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63659C2211yescharacteristic
52#63637C2211yescharacteristic
53#63634C2211yescharacteristic
54C3×#832C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#808C2211yescharacteristic
57#63575C2211yescharacteristic
58#63574C2211yescharacteristic
59#63567C2211yescharacteristic
60#63566C2211yescharacteristic
61#63565C2211yescharacteristic
62#63565C2211yescharacteristic
63C3×#537—31no—
64#5825—31no—
65C2×#951—31no—
66C2×#948—31no—
67C2×#915—31no—
68C2×#901—31no—
69#5628—31no—
70#5608D311yescharacteristic
71C3×#465—31no—
72#5233—31no—
73#5174—31no—
74#5116—31no—
75#5052—31no—
76#5052—31no—
77#5052—31no—
78#5051—31no—
79#5051—31no—
80#5042—31no—
81#5042—31no—
82#5042—31no—
83#5042—61no—
84#5041—31no—
85#5041D311yescharacteristic, complemented
86C2×#810—31no—
87#4964—31no—
88#4867—31no—
89#4861—31no—
90#4813—31no—
91D3×#103—31no—
92#4778—31no—
93#4772—31no—
94C2×C32×D4—21no—
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67D411yescharacteristic
101C2×C3×#67D411yescharacteristic
102C22×C3×Dic3—21no—
103C3×#237—22no—
104C3×#237—22no—
105C3×#235—22no—
106C3×#235—22no—
107C2×C3×D12D411yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6D411yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×C3×Dic6C2311yescharacteristic
114C2×#627—21no—
115C2×D3×Dic3—21no—
116D3×Dic6—22no—
117D3×Dic6—22no—
118C32×C4⋊C4C2311yescharacteristic
119C32×C22⋊C4—21no—
120#3757—21no—
121#3754—22no—
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123#3750—21no—
124#3748—22no—
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C3×#217—21no—
128C3×#217—21no—
129C3×#217—21no—
130C3×#214—22no—
131C3×(C2×D3)⋊C4—21no—
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C2×C3×C3⋊C8—22no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3724—21no—
142Dic3⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146Dic32—21no—
147#3719—22no—
148#3718—22no—
149#3711—22no—
150#3711D414yescomplemented
151D3×C3⋊C8—22no—
152D3×C3⋊C8—22no—
153#3063—91noSylow
154C2×C3×#41—31no—
155C2×C3×#41—31no—
156C2×D3×Q8—31no—
157C2×#237C2×D311yescharacteristic
158C2×#235C2×D311yescharacteristic
159C22×Dic6—31no—
160C2×C3×SD16—31no—
161C22×C3×C8—31no—
162C3×C22⋊Q8—31no—
163C3×C22⋊Q8—31no—
164C3×C22⋊Q8—31no—
165C3×C22⋊Q8—61no—
166C3×#121—21no—
167C3×#121—31no—
168C3×#121—61no—
169C3×#121—61no—
170C3×#121—61no—
171C3×#121C2×D311yescharacteristic
172C3×#121C2×D311yescharacteristic
173C2×C3×C4⋊C4—31no—
174#951—64no—
175#948—64no—
176#946—31no—
177#944—61no—
178C2×#216—31no—
179C2×#216—31no—
180C2×#216—31no—
181#939—21no—
182#938—21no—
183#938C2×D311yescharacteristic
184#936—61no—
185#935—61no—
186#935—61no—
187C2×#214—31no—
188C2×#214—31no—
189C2×#214—61no—
190C2×#214C2×D311yescharacteristic
191#926—31no—
192#924—31no—
193#924—31no—
194#924—31no—
195#924—31no—
196#924—61no—
197#924C2×D311yescharacteristic
198#924C2×D311yescharacteristic
199C2×#208—31no—
200C2×#208—31no—
201C2×#208—31no—
202C2×#208—31no—
203C2×#208—61no—
204C22×C3⋊C8—31no—
205C22×C3⋊C8—31no—
206C22×C3⋊C8C2×D311yescharacteristic
207#915—64no—
208C2×Dic12—31no—
209#901—64no—
210C2×ΓL(1,𝔽25)—31no—
211C2×ΓL(1,𝔽25)—31no—
212C2×D3×C8—31no—
213C2×D3×C8—31no—
214#897—31no—
215#897C2×D311yescharacteristic
216#894—61no—
217#892—31no—
218D3×C4⋊C4C2×D311yescharacteristic
219#888—61no—
220#885—61no—
221#884—21no—
222#883—61no—
223#878—21no—
224C3×#106—31no—
225C3×#103—31no—
226C3×#102—31no—
227#835—31no—
228#835—31no—
229#835—31no—
230#832—31no—
231#832—31no—
232#832—61no—
233#832C2×D311yescharacteristic
234#818—31no—
235#816—31no—
236#816—31no—
237#810—31no—
238#810—31no—
239#810—31no—
240#810—31no—
241#810—31no—
242#810—61no—
243#810C2×D311yescharacteristic
244#808—31no—
245#808—31no—
246#808C2×D311yescharacteristic
247#807—31no—
248#807—31no—
249#807—31no—
250#807—61no—
251C23×C32—21no—
252C23×C32C2×D411yescharacteristic
253C22×C3×D3C2×D411yescharacteristic
254C22×C3×D3C2×D411yescharacteristic
255C32×D4—21no—
256C32×D4—21no—
257C32×D4—81no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4C2×D411yescharacteristic
262C2×C32×C4C2411yescharacteristic
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265#634—21no—
266#634—21no—
267C3×#67—22no—
268C3×#67—22no—
269C3×#67—42no—
270C3×#67—81no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—42no—
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C3×D12—22no—
279C3×C4×D3—21no—
280C3×C4×D3—21no—
281C3×C4×D3—81no—
282C3×C4×D3C2×D412yes—
283C3×C4×D3#4112yes—
284C3×Dic6—22no—
285C3×Dic6—21no—
286C3×Dic6—21no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289#627—42no—
290D3×Dic3—42no—
291C3⋊(C3⋊C8)—21no—
292C3⋊(C3⋊C8)C2×D412yes—
293C3×C3⋊C8—21no—
294C3×C3⋊C8C2×D412yes—
295C2×#137—91no—
296C2×#131—91no—
297#537—31no—
298#536—91no—
299#470—91no—
300#470—91no—
301#468—91no—
302#468—91no—
303#467—91no—
304#467—91no—
305#465—31no—
306#465—91no—
307#428—91no—
308#416—91no—
309C2×#103—91no—
310C3×#41—62no—
311C3×#41—62no—
312C3×#41—62no—
313C3×#41—62no—
314C2×C3×Q8—31no—
315C2×C3×Q8—31no—
316C2×C3×Q8—31no—
317C2×C3×D4—21no—
318C2×C3×D4—21no—
319C2×C3×D4—21no—
320C2×C3×D4—31no—
321C2×C3×D4—31no—
322C2×C3×D4—31no—
323C2×C3×D4—41no—
324C2×C3×D4—61no—
325C2×C3×D4—61no—
326C2×C3×D4C22×D311yescharacteristic
327C2×C3×D4C22×D311yescharacteristic
328C22×C3×C4—21no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—61no—
332C22×C3×C4—61no—
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C2×#67—21no—
336C2×#67—21no—
337C2×#67#6711yescharacteristic
338C2×#67#6711yescharacteristic
339C22×Dic3—21no—
340C22×Dic3—61no—
341D3×Q8—62no—
342D3×Q8—62no—
343#237—22no—
344#237—22no—
345#235—22no—
346#235—22no—
347C2×D12#6711yescharacteristic
348C2×C4×D3—21no—
349C2×C4×D3—61no—
350C2×C4×D3C22×D311yescharacteristic
351C2×C4×D3C22×D311yescharacteristic
352C2×Dic6—31no—
353C2×Dic6—31no—
354C2×Dic6—61no—
355C2×Dic6—62no—
356C2×Dic6—62no—
357C2×Dic6—61no—
358C2×Dic6—61no—
359C2×Dic6#6711yescharacteristic
360C2×Dic6C22×D311yescharacteristic
361C2×Dic6C22×D311yescharacteristic
362C3×SD16—62no—
363C2×C3×C8—31no—
364C2×C3×C8—31no—
365C2×C3×C8—62no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4—61no—
372C3×C4⋊C4—61no—
373C3×C4⋊C4C22×D311yescharacteristic
374C3×C4⋊C4C22×D311yescharacteristic
375C3×C22⋊C4—21no—
376C3×C22⋊C4—21no—
377C3×C22⋊C4—41no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382#217—21no—
383#217—21no—
384#217—21no—
385#217—61no—
386#217—61no—
387#217—61no—
388#217—61no—
389#217—61no—
390#217—121no—
391#216—62no—
392#216—62no—
393#216—62no—
394#214—22no—
395#214—62no—
396#214—62no—
397#214—122no—
398(C2×D3)⋊C4—21no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402C4⋊Dic3—21no—
403C4⋊Dic3—31no—
404C4⋊Dic3—31no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3C22×D311yescharacteristic
408C4⋊Dic3C22×D311yescharacteristic
409Dic3⋊C4—21no—
410Dic3⋊C4—21no—
411Dic3⋊C4—21no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415Dic3⋊C4—61no—
416Dic3⋊C4—61no—
417Dic3⋊C4—121no—
418C4×Dic3—61no—
419C4×Dic3—61no—
420#208—34no—
421#208—62no—
422#208—62no—
423#208—62no—
424#208—122no—
425C2×C3⋊C8—22no—
426C2×C3⋊C8—31no—
427C2×C3⋊C8—31no—
428C2×C3⋊C8—31no—
429C2×C3⋊C8—31no—
430C2×C3⋊C8—61no—
431C2×C3⋊C8—61no—
432C2×C3⋊C8—62no—
433C2×C3⋊C8—62no—
434C2×C3⋊C8C22×D311yescharacteristic
435C2×C3⋊C8C22×D311yescharacteristic
436Dic12—62no—
437ΓL(1,𝔽25)—34no—
438ΓL(1,𝔽25)—62no—
439D3×C8—62no—
440D3×C8—62no—
441C22×C32—21no—
442C22×C32—21no—
443C22×C32—21no—
444C22×C32—41no—
445C22×C32—41no—
446C22×C32—41no—
447C22×C32C22×D411yescharacteristic
448C2×C3×D3—21no—
449C2×C3×D3—21no—
450C2×C3×D3—21no—
451C2×C3×D3—21no—
452C2×C3×D3—21no—
453C2×C3×D3#12112yes—
454C32×C4—21no—
455C32×C4—41no—
456C32×C4C22×D411yescharacteristic
457C32×C4C2×#4111yescharacteristic
458C3⋊Dic3—41no—
459C3⋊Dic3—41no—
460C3×Dic3—21no—
461C3×Dic3—41no—
462C3×Dic3—41no—
463C3×Dic3—41no—
464C3×Dic3—41no—
465C3×Dic3#12112yes—
466C2×#41—31no—
467C2×#41—31no—
468C22×Q8—91no—
469#137—184no—
470C2×Q16—91no—
471C2×Q16—91no—
472C2×SD16—31no—
473C2×SD16—91no—
474#131—184no—
475C2×M16—91no—
476C2×M16—91no—
477C2×M16—91no—
478C22×C8—31no—
479C22×C8—91no—
480C22×C8—91no—
481C4⋊Q8—181no—
482#124—181no—
483#123—181no—
484#123—181no—
485C22⋊Q8—31no—
486C22⋊Q8—31no—
487C22⋊Q8—31no—
488C22⋊Q8—61no—
489C22⋊Q8—91no—
490C22⋊Q8—91no—
491C22⋊Q8—91no—
492#121—31no—
493#121—61no—
494#121—61no—
495#121—61no—
496#121D3211yescharacteristic
497#117—91no—
498C2×C4⋊C4—31no—
499#107—91no—
500#107—91no—
501#106—31no—
502#106—91no—
503#103—31no—
504#103—91no—
505#103—91no—
506#103—91no—
507#103—91no—
508#103—91no—
509#102—31no—
510#102—91no—
511C23×C3—21no—
512C23×C3—21no—
513C23×C3—21no—
514C23×C3—31no—
515C23×C3—31no—
516C23×C3—41no—
517C23×C3D3×D411yescharacteristic
518C23×C3C2×#6711yescharacteristic
519C22×D3C2×#6711yescharacteristic
520C22×D3C2×#6711yescharacteristic
521C3×Q8—62no—
522C3×Q8—61no—
523C3×Q8—61no—
524C3×Q8—61no—
525C3×Q8—61no—
526C3×D4—21no—
527C3×D4—21no—
528C3×D4—21no—
529C3×D4—21no—
530C3×D4—41no—
531C3×D4—41no—
532C3×D4—62no—
533C3×D4—62no—
534C3×D4—62no—
535C3×D4—81no—
536C3×D4—81no—
537C3×D4—82no—
538C3×D4—122no—
539C3×D4—241no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—31no—
549C2×C3×C4—32no—
550C2×C3×C4—32no—
551C2×C3×C4—31no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—122no—
562C2×C3×C4—241no—
563C2×C3×C4D3×D411yescharacteristic
564C2×C3×C4C2×#6711yescharacteristic
565C2×C3×C4C23×D311yescharacteristic
566C2×C3×C4C23×D311yescharacteristic
567#67—22no—
568#67—22no—
569#67—42no—
570#67—81no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—42no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—121no—
581C2×Dic3—121no—
582C2×Dic3—122no—
583C2×Dic3C2×#6711yescharacteristic
584C2×Dic3C2×#6711yescharacteristic
585D12—22no—
586C4×D3—21no—
587C4×D3—21no—
588C4×D3—81no—
589C4×D3—122no—
590C4×D3D3×D412yes—
591C4×D3#23712yes—
592Dic6—22no—
593Dic6—21no—
594Dic6—21no—
595Dic6—21no—
596Dic6—21no—
597Dic6—61no—
598Dic6—61no—
599Dic6—61no—
600Dic6—61no—
601Dic6—121no—
602Dic6—121no—
603Dic6—122no—
604Dic6—122no—
605C3×C8—32no—
606C3×C8—61no—
607C3⋊C8—21no—
608C3⋊C8—32no—
609C3⋊C8—32no—
610C3⋊C8—62no—
611C3⋊C8—61no—
612C3⋊C8—61no—
613C3⋊C8—121no—
614C3⋊C8D3×D412yes—
615C2×C32—41no—
616C2×C32—81no—
617C2×C32C2×#12111yescharacteristic
618C2×C32#57711yescharacteristic
619C2×C32#57811yescharacteristic
620C3×D3—22no—
621C3×D3—41no—
622#41—62no—
623#41—62no—
624#41—62no—
625#41—62no—
626C2×Q8—31no—
627C2×Q8—31no—
628C2×Q8—31no—
629C2×Q8—91no—
630C2×Q8—181no—
631C2×Q8—182no—
632C2×Q8—182no—
633C2×D4—21no—
634C2×D4—31no—
635C2×D4—31no—
636C2×D4—31no—
637C2×D4—61no—
638C2×D4—61no—
639C2×D4C2×D3211yescharacteristic
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—61no—
643C22×C4—61no—
644C22×C4—181no—
645C22×C4C2×D3211yescharacteristic
646Q16—182no—
647Q16—182no—
648SD16—62no—
649SD16—182no—
650M16—94no—
651M16—182no—
652M16—182no—
653C2×C8—31no—
654C2×C8—31no—
655C2×C8—62no—
656C2×C8—91no—
657C2×C8—91no—
658C2×C8—182no—
659C2×C8—182no—
660C4⋊C4—31no—
661C4⋊C4—31no—
662C4⋊C4—61no—
663C4⋊C4—61no—
664C4⋊C4—61no—
665C4⋊C4—61no—
666C4⋊C4—91no—
667C4⋊C4—181no—
668C4⋊C4—181no—
669C4⋊C4—181no—
670C4⋊C4C2×D3211yescharacteristic
671C22⋊C4—21no—
672C22⋊C4—61no—
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C22⋊C4—181no—
680C42—181no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—32no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—61no—
699C22×C3—61no—
700C22×C3—61no—
701C22×C3—61no—
702C22×C3—61no—
703C22×C3—81no—
704C22×C3—81no—
705C22×C3—81no—
706C22×C3C2×D3×D411yescharacteristic
707C22×C3C22×#6711yescharacteristic
708C2×D3—21no—
709C2×D3—21no—
710C2×D3—21no—
711C2×D3—21no—
712C2×D3—21no—
713C2×D3#93912yes—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—32no—
719C3×C4—41no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—61no—
723C3×C4—81no—
724C3×C4—121no—
725C3×C4—121no—
726C3×C4—121no—
727C3×C4—121no—
728C3×C4C2×D3×D411yescharacteristic
729C3×C4C2×D3×D411yescharacteristic
730C3×C4C2×#23711yescharacteristic
731C3×C4D3×#4111yescharacteristic
732Dic3—21no—
733Dic3—41no—
734Dic3—41no—
735Dic3—41no—
736Dic3—41no—
737Dic3—121no—
738Dic3—121no—
739Dic3—121no—
740Dic3—121no—
741Dic3—241no—
742Dic3—241no—
743Dic3#93912yes—
744C32#306311yescharacteristic, complemented, Sylow
745C23—21no—
746C23—31no—
747C23—31no—
748C23D3×#6711yescharacteristic
749Q8—62no—
750Q8—61no—
751Q8—61no—
752Q8—61no—
753Q8—61no—
754Q8—181no—
755Q8—181no—
756Q8—362no—
757D4—21no—
758D4—21no—
759D4—62no—
760D4—62no—
761D4—62no—
762D4—81no—
763D4—122no—
764D4—241no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—31no—
769C2×C4—32no—
770C2×C4—32no—
771C2×C4—31no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—122no—
779C2×C4—181no—
780C2×C4—181no—
781C2×C4—241no—
782C2×C4—362no—
783C2×C4D3×#6711yescharacteristic
784C2×C4C22×D3211yescharacteristic
785C8—32no—
786C8—61no—
787C8—92no—
788C8—181no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—41no—
793C2×C3—41no—
794C2×C3—62no—
795C2×C3—81no—
796C2×C3—81no—
797C2×C3—81no—
798C2×C3—121no—
799C2×C3—161no—
800C2×C3D3×#12111yescharacteristic
801C2×C3#576211yescharacteristic
802C2×C3#577111yescharacteristic
803C2×C3C2×#93911yescharacteristic
804C2×C3#583611yescharacteristic
805C2×C3#583811yescharacteristic
806D3—22no—
807D3—41no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—32no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—61no—
816C22—61no—
817C22—61no—
818C22—61no—
819C22—61no—
820C22C2×D3×#6711yescharacteristic
821C4—21no—
822C4—32no—
823C4—41no—
824C4—61no—
825C4—121no—
826C4—121no—
827C4—121no—
828C4—121no—
829C4—361no—
830C4—361no—
831C4D32×D411yescharacteristic
832C4D3×#23711yescharacteristic
833C3—21no—
834C3#8066211yescharacteristic, complemented
835C3#8342311yescharacteristic, complemented
836C2—41no—
837C2—62no—
838C2—81no—
839C2—121no—
840C2#1059510511yescharacteristic
841C2D3×#93911yescharacteristic
842C2#1059546711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
prime radicalC3×#5608C2
hypercenter#121D32
hypocenterC32#3063
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. C2×#63929C2semidirect
3. #10594884C2semidirect
4. C2×#63814C2semidirect
5. #10592741C2semidirect
6. C3×#5041C2semidirect
7. #10591502C2semidirect
8. #10591460C2semidirect
9. #10591420C2semidirect
10. #10591189C2semidirect
11. #10591187C2semidirect
12. D3×#810C2semidirect
13. #10590587C2semidirect
14. #10590581C2semidirect
15. #10590518C2semidirect
85. #5041D3semidirect
150. #3711D4semidirect
744. C32#3063semidirect
834. C3#80662semidirect
835. C3#83423semidirect

Maximal subgroups

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

subgroupindex
C3×#56082
C2×#639292
#105948842
C2×#638142
#105927412
C3×#50412
#105915022
#105914602
#105914202
#105911892
#105911872
D3×#8102
#105905872
#105905812
#105905182
#834233
#806623