Finite Group Databasebeta

← #11870601

Subgroups — #11870601

Order 1152.

947 conjugacy classes of subgroups.

The subgroup lattice has 783 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C3⋊Dic3C211yesmaximal, characteristic, complemented
2#10594965C211yesmaximal, characteristic, complemented
3C3×#5239C211yesmaximal, characteristic, complemented
4C3×#5238C211yesmaximal, characteristic
5#10591615C211yesmaximal, characteristic, complemented
6#10591612C211yesmaximal, characteristic, complemented
7#10591581C211yesmaximal, characteristic, complemented
8#10591571C211yesmaximal, characteristic, complemented
9#10591479C211yesmaximal, characteristic, complemented
10#10591476C211yesmaximal, characteristic, complemented
11#10591445C211yesmaximal, characteristic, complemented
12#10591435C211yesmaximal, characteristic, complemented
13#10591127C211yesmaximal, characteristic, complemented
14#10591093C211yesmaximal, characteristic, complemented
15#10591061C211yesmaximal, characteristic, complemented
16#80212—31nomaximal
17#80068—31nomaximal
18C2×C32×#41C2211yescharacteristic
19Q8×C3⋊Dic3C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21D4×C3⋊Dic3—21no—
22D4×C3⋊Dic3—21no—
23D4×C3⋊Dic3C2211yescharacteristic
24D4×C3⋊Dic3C2211yescharacteristic
25#64135—21no—
26#64135C2211yescharacteristic
27C2×C4×C3⋊Dic3—21no—
28C2×C4×C3⋊Dic3C2211yescharacteristic
29C2×C3×#216C2211yescharacteristic
30C2×C3×#215C2211yescharacteristic
31C2×C3×#214C2211yescharacteristic
32C2×C3×#213C2211yescharacteristic
33C3×#930C2211yescharacteristic
34C3×#924C2211yescharacteristic
35#67⋊Dic3—21no—
36#63962—21no—
37#63898C2211yescharacteristic
38#63878—21no—
39#63872C2211yescharacteristic
40#63863C2211yescharacteristic
41#63862—21no—
42#63843C2211yescharacteristic
43C3×#835C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#830C2211yescharacteristic
48C3×#830C2211yescharacteristic
49#63575C2211yescharacteristic
50#63575C2211yescharacteristic
51#63573C2211yescharacteristic
52#63573C2211yescharacteristic
53#63572C2211yescharacteristic
54#63572C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63553C2211yescharacteristic
60#63553C2211yescharacteristic
61Dic3×#41—31no—
62Dic3×#41—31no—
63Dic3×#41—61no—
64#5624—31no—
65#5600—31no—
66C3×#452—31no—
67C3×#449—31no—
68#5239D311yescharacteristic, complemented
69#5238D311yescharacteristic
70#5185—31no—
71Dic3×Q16—31no—
72#5166—31no—
73#5165—31no—
74Dic3×SD16—31no—
75Dic3×SD16—31no—
76#5153—31no—
77Dic3×D8—31no—
78#5045—31no—
79#5035—31no—
80#4799—31no—
81#4796—31no—
82#4790—31no—
83#4788—31no—
84#4766—31no—
85#4763—31no—
86#4758—31no—
87#4756—31no—
88#4737—31no—
89#4723—31no—
90#4718—31no—
91#4718—31no—
92C32×#41—22no—
93C32×#41—22no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4C2311yescharacteristic
99C22×C3⋊Dic3—21no—
100C22×C3⋊Dic3—21no—
101C22×C3⋊Dic3D411yescharacteristic
102C22×C3⋊Dic3D411yescharacteristic
103C2×C3×#67—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×D3×Dic3—21no—
107#3757—21no—
108#3757—21no—
109#3757—21no—
110C4⋊(C3⋊Dic3)—21no—
111C4⋊(C3⋊Dic3)—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4×C3⋊Dic3—21no—
115C4×C3⋊Dic3—21no—
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3D411yescharacteristic
118C4×C3⋊Dic3D411yescharacteristic
119C4×C3⋊Dic3C2311yescharacteristic
120C4×C3⋊Dic3C2311yescharacteristic
121C3×#217—21no—
122C3×#216—22no—
123C3×#215—22no—
124C3×#214—22no—
125C3×#213—22no—
126C3×(C2×D3)⋊C4—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141#3102—91noSylow
142C2×C3×#41—21no—
143C2×C3×#41C2×D311yescharacteristic
144C2×C3×#41C2×D311yescharacteristic
145C2×C3×Q16—31no—
146C2×C3×SD16—31no—
147C2×C3×SD16—31no—
148C2×C3×D8—31no—
149C3×C22⋊Q8—31no—
150C3×#121—31no—
151#947—31no—
152Q8×Dic3—31no—
153Q8×Dic3—31no—
154Q8×Dic3—31no—
155Q8×Dic3—31no—
156Q8×Dic3—31no—
157Q8×Dic3—61no—
158Q8×Dic3—61no—
159C2×#216C2×D311yescharacteristic
160C2×#215C2×D311yescharacteristic
161#936—31no—
162#935—61no—
163D4×Dic3—31no—
164D4×Dic3—31no—
165D4×Dic3—31no—
166D4×Dic3—31no—
167D4×Dic3—31no—
168D4×Dic3—61no—
169D4×Dic3—61no—
170D4×Dic3—61no—
171D4×Dic3—61no—
172D4×Dic3—61no—
173D4×Dic3—61no—
174D4×Dic3—61no—
175D4×Dic3—62no—
176D4×Dic3—62no—
177C2×#214C2×D311yescharacteristic
178C2×#213C2×D311yescharacteristic
179#930C2×D311yescharacteristic
180#926—31no—
181#926—31no—
182#926—61no—
183#926—61no—
184#926—61no—
185#926—62no—
186#924C2×D311yescharacteristic
187C2×C4×Dic3—31no—
188C2×C4×Dic3—31no—
189C2×C4×Dic3—61no—
190C2×C4×Dic3—61no—
191C2×C4×Dic3—61no—
192C2×C4×Dic3—62no—
193#898—61no—
194#893—31no—
195#892—61no—
196#890—31no—
197#890—31no—
198#887—31no—
199#886—61no—
200#67⋊C4—61no—
201#879—61no—
202#877—61no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×C22⋊C8—31no—
208C3×C22⋊C8—31no—
209#835—31no—
210#835—31no—
211#835C2×D311yescharacteristic
212#835C2×D311yescharacteristic
213#832—31no—
214#832—31no—
215#832C2×D311yescharacteristic
216#832C2×D311yescharacteristic
217#830C2×D311yescharacteristic
218#830C2×D311yescharacteristic
219#821—31no—
220#821—31no—
221#818—31no—
222#818—31no—
223#817—31no—
224#817—31no—
225#816—31no—
226#816—31no—
227Dic3⋊C8—31no—
228Dic3⋊C8—31no—
229Dic3⋊C8—31no—
230Dic3⋊C8—31no—
231C8×Dic3—31no—
232C8×Dic3—31no—
233C8×Dic3—31no—
234C8×Dic3—31no—
235#808—31no—
236#808—31no—
237#807—31no—
238#807—31no—
239C23×C32—21no—
240C23×C32C2×D411yescharacteristic
241C22×C3×D3—21no—
242C32×Q8—21no—
243C32×Q8#4112yes—
244C32×D4—24no—
245C32×D4—21no—
246C32×D4#4112yes—
247C2×C32×C4—24no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—22no—
256C2×C3⋊Dic3—41no—
257C2×C3⋊Dic3—42no—
258C2×C3⋊Dic3—42no—
259C2×C3⋊Dic3C2×D411yescharacteristic
260C2×C3⋊Dic3C2×D411yescharacteristic
261C2×C3⋊Dic3C2×D411yescharacteristic
262C2×C3⋊Dic3C2×D411yescharacteristic
263C3×#67—42no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C3×D12—21no—
268C3×D12—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271D3×Dic3—42no—
272C3×C3⋊C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#529—91no—
277C4×#41—91no—
278#485—91no—
279#482—91no—
280#479—91no—
281#478—91no—
282#464—91no—
283#463—91no—
284#452—31no—
285#449—31no—
286C4×Q16—91no—
287C4×SD16—91no—
288C4×SD16—91no—
289C4×D8—91no—
290#431—91no—
291C3×#41—24no—
292C3×#41—24no—
293C3×#41—22no—
294C3×#41—22no—
295C3×#41—22no—
296C3×#41—22no—
297C2×C3×Q8—21no—
298C2×C3×Q8—31no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×D4—22no—
302C2×C3×D4—21no—
303C2×C3×D4—21no—
304C2×C3×D4—21no—
305C2×C3×D4—31no—
306C2×C3×D4—61no—
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C22×D311yescharacteristic
309C22×C3×C4—22no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C2×#67—21no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—31no—
319C22×Dic3—31no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—61no—
325C22×Dic3—61no—
326C22×Dic3—61no—
327C22×Dic3—62no—
328C22×Dic3—62no—
329C2×D12C22×D311yescharacteristic
330C2×C4×D3—61no—
331C2×Dic6C22×D311yescharacteristic
332C3×Q16—62no—
333C3×SD16—62no—
334C3×SD16—62no—
335C3×D8—62no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—61no—
343C3×C22⋊C4—61no—
344C3×C22⋊C4—61no—
345#217—21no—
346#217—61no—
347#217—61no—
348#217—61no—
349#217—61no—
350#217—61no—
351#217—61no—
352#217—61no—
353#217—62no—
354#217—62no—
355#217—62no—
356#217—61no—
357#217—61no—
358#216—22no—
359#215—22no—
360#214—22no—
361#213—22no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—62no—
380C4⋊Dic3—62no—
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387C4×Dic3—31no—
388C4×Dic3—31no—
389C4×Dic3—31no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—62no—
406C4×Dic3—62no—
407C4×Dic3—62no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413C2×C3⋊C8C22×D311yescharacteristic
414C22×C32—21no—
415C22×C32—22no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32C22×D411yescharacteristic
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C32×C4—21no—
425C32×C4—22no—
426C32×C4C2×#4111yescharacteristic
427C32×C4C2×#4111yescharacteristic
428C3⋊Dic3—21no—
429C3⋊Dic3—21no—
430C3⋊Dic3—21no—
431C3⋊Dic3—41no—
432C3⋊Dic3—41no—
433C3⋊Dic3#13512yes—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41D3211yescharacteristic
438C2×Q16—31no—
439C2×SD16—31no—
440C2×SD16—31no—
441C2×D8—31no—
442#126—181no—
443#125—91no—
444#124—91no—
445#123—181no—
446C22⋊Q8—31no—
447#121—31no—
448C4×Q8—91no—
449C4×Q8—91no—
450C4×Q8—91no—
451C4×D4—91no—
452C4×D4—91no—
453C4×D4—91no—
454C4×D4—181no—
455C4×D4—181no—
456C4×D4—181no—
457#117—91no—
458#117—181no—
459#117—181no—
460C2×C42—91no—
461C2×C42—181no—
462#107—91no—
463#107—91no—
464#106—91no—
465#106—91no—
466C4⋊C8—91no—
467C4⋊C8—91no—
468#103—31no—
469#103—31no—
470#103—91no—
471#103—91no—
472#102—31no—
473#102—31no—
474#102—91no—
475#102—91no—
476C22⋊C8—31no—
477C22⋊C8—31no—
478C4×C8—91no—
479C4×C8—91no—
480C23×C3—22no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—61no—
485C23×C3D3×D411yescharacteristic
486C23×C3D3×D411yescharacteristic
487C22×D3—21no—
488C3×Q8—22no—
489C3×Q8—21no—
490C3×Q8—21no—
491C3×Q8—22no—
492C3×Q8—61no—
493C3×Q8—61no—
494C3×Q8#23712yes—
495C3×Q8#23712yes—
496C3×D4—28no—
497C3×D4—24no—
498C3×D4—24no—
499C3×D4—22no—
500C3×D4—21no—
501C3×D4—21no—
502C3×D4—22no—
503C3×D4—61no—
504C3×D4—61no—
505C3×D4—122no—
506C3×D4#23712yes—
507C3×D4#23712yes—
508C2×C3×C4—22no—
509C2×C3×C4—28no—
510C2×C3×C4—24no—
511C2×C3×C4—24no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4D3×D411yescharacteristic
526C2×C3×C4D3×D411yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529#67—42no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—62no—
546C2×Dic3—62no—
547C2×Dic3—62no—
548C2×Dic3—62no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—122no—
554C2×Dic3—122no—
555C2×Dic3—122no—
556C2×Dic3—122no—
557C2×Dic3—121no—
558C2×Dic3—121no—
559C2×Dic3—124no—
560C2×Dic3—122no—
561C2×Dic3—124no—
562C2×Dic3—122no—
563C2×Dic3—122no—
564D12—21no—
565D12—21no—
566C4×D3—122no—
567Dic6—21no—
568Dic6—21no—
569C3×C8—61no—
570C3×C8—61no—
571C3×C8—61no—
572C3×C8—61no—
573C3⋊C8—21no—
574C3⋊C8—21no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C2×C32—41no—
578C2×C32—42no—
579C2×C32#52511yescharacteristic
580C2×C32C2×#13511yescharacteristic
581C2×C32#57511yescharacteristic
582C3×D3—81no—
583#41—22no—
584#41—22no—
585C2×Q8—31no—
586C2×Q8C2×D3211yescharacteristic
587C2×D4—21no—
588C2×D4—31no—
589C2×D4—61no—
590C2×D4C2×D3211yescharacteristic
591C22×C4—21no—
592C22×C4—91no—
593C22×C4—91no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4—181no—
597C22×C4C2×D3211yescharacteristic
598Q16—62no—
599SD16—62no—
600SD16—62no—
601D8—62no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—31no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—61no—
609C4⋊C4—91no—
610C4⋊C4—91no—
611C4⋊C4—181no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C42—91no—
625C42—91no—
626C42—91no—
627C42—91no—
628C42—181no—
629C42—181no—
630C42—181no—
631C42—181no—
632C22×C3—22no—
633C22×C3—24no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—22no—
641C22×C3—22no—
642C22×C3—21no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—42no—
646C22×C3—42no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3C2×D3×D411yescharacteristic
655C22×C3C2×D3×D411yescharacteristic
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—41no—
659C3×C4—22no—
660C3×C4—24no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—22no—
664C3×C4—22no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4C2×#23711yescharacteristic
671C3×C4C2×#23711yescharacteristic
672C3×C4C2×#23711yescharacteristic
673C3×C4C2×#23711yescharacteristic
674Dic3—32no—
675Dic3—32no—
676Dic3—41no—
677Dic3—41no—
678Dic3—41no—
679Dic3—62no—
680Dic3—62no—
681Dic3—61no—
682Dic3—61no—
683Dic3—61no—
684Dic3—61no—
685Dic3—61no—
686Dic3—61no—
687Dic3—121no—
688Dic3—121no—
689Dic3—122no—
690Dic3—122no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695C32#310211yescharacteristic, complemented, Sylow
696C23—21no—
697C23—61no—
698C23#381111yescharacteristic
699Q8—21no—
700Q8—61no—
701Q8—61no—
702Q8#380512yes—
703D4—24no—
704D4—21no—
705D4—61no—
706D4—61no—
707D4—122no—
708D4#380512yes—
709C2×C4—24no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—91no—
717C2×C4—91no—
718C2×C4—91no—
719C2×C4—91no—
720C2×C4—182no—
721C2×C4—181no—
722C2×C4—181no—
723C2×C4—362no—
724C2×C4—362no—
725C2×C4—361no—
726C2×C4—362no—
727C2×C4#381111yescharacteristic
728C2×C4C22×D3211yescharacteristic
729C8—61no—
730C8—61no—
731C8—61no—
732C8—61no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—42no—
737C2×C3—44no—
738C2×C3—41no—
739C2×C3—42no—
740C2×C3—41no—
741C2×C3—42no—
742C2×C3—241no—
743C2×C3#558611yescharacteristic
744C2×C3#558611yescharacteristic
745C2×C3D3×#13511yescharacteristic
746C2×C3D3×#13511yescharacteristic
747C2×C3#577311yescharacteristic
748C2×C3#577711yescharacteristic
749D3—81no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—22no—
754C22—41no—
755C22—41no—
756C22—121no—
757C22—121no—
758C22—121no—
759C22C2×#381111yescharacteristic
760C4—21no—
761C4—22no—
762C4—92no—
763C4—121no—
764C4—121no—
765C4—121no—
766C4—181no—
767C4—181no—
768C4—181no—
769C4—361no—
770C4—361no—
771C4C2×#380511yescharacteristic
772C4C2×#380511yescharacteristic
773C3—21no—
774C3#8006811yescharacteristic, complemented
775C3#8021211yescharacteristic, complemented
776C2—41no—
777C2—42no—
778C2—241no—
779C2#1059545911yescharacteristic
780C2#1059547111yescharacteristic
781C2#1059550111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC3×#5238C2
hypercenterC2×#41D32
hypocenterC32#3102
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #41×C3⋊Dic3C2semidirect
2. #10594965C2semidirect
3. C3×#5239C2semidirect
5. #10591615C2semidirect
6. #10591612C2semidirect
7. #10591581C2semidirect
8. #10591571C2semidirect
9. #10591479C2semidirect
10. #10591476C2semidirect
11. #10591445C2semidirect
12. #10591435C2semidirect
13. #10591127C2semidirect
14. #10591093C2semidirect
15. #10591061C2semidirect
68. #5239D3semidirect
695. C32#3102semidirect
774. C3#80068semidirect
775. C3#80212semidirect

Maximal subgroups

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

subgroupindex
#41×C3⋊Dic32
#105949652
C3×#52392
C3×#52382
#105916152
#105916122
#105915812
#105915712
#105914792
#105914762
#105914452
#105914352
#105911272
#105910932
#105910612
#802123
#800683