Finite Group Databasebeta

← #11860435

Subgroups — #11860435

Order 1152.

1027 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63811C211yesmaximal, characteristic
2#10594363C211yesmaximal, characteristic, complemented
3#10594360C211yesmaximal, characteristic
4#10592580C211yesmaximal, characteristic, complemented
5C3×#4889C211yesmaximal, characteristic, complemented
6C3×#4873C211yesmaximal, characteristic, complemented
7#10590812C211yesmaximal, characteristic, complemented
8Dic3×#204C211yesmaximal, characteristic, complemented
9#10590664C211yesmaximal, characteristic, complemented
10#10590612C211yesmaximal, characteristic
11#10590602C211yesmaximal, characteristic, complemented
12#10590478C211yesmaximal, characteristic, complemented
13#10590477C211yesmaximal, characteristic, complemented
14#10590476C211yesmaximal, characteristic, complemented
15#10590453C211yesmaximal, characteristic, complemented
16#79774—31nomaximal
17C4×#918—31nomaximal
18C2×#3797C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×#3743C2211yescharacteristic
21#64101C2211yescharacteristic
22C4⋊C4×C3⋊D3C2211yescharacteristic
23C2×C3×Dic12C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic
25C3×#893C2211yescharacteristic
26C3×#887C2211yescharacteristic
27C3×#887C2211yescharacteristic
28C3×#887C2211yescharacteristic
29#63904—21no—
30Dic3×D12C2211yescharacteristic
31#63883—21no—
32C4×#624—21no—
33C4×#624C2211yescharacteristic
34#63880—21no—
35#63878—21no—
36C4×D3×Dic3—21no—
37Dic3×Dic6C2211yescharacteristic
38Dic3×Dic6C2211yescharacteristic
39Dic3×Dic6C2211yescharacteristic
40#63837—21no—
41#63837—21no—
42C2×#3718C2211yescharacteristic
43C2×#3715C2211yescharacteristic
44C2×#3712C2211yescharacteristic
45#63811C418yescomplemented
46C32×#107C2211yescharacteristic
47#63644C2211yescharacteristic
48#63635C2211yescharacteristic
49#63634C2211yescharacteristic
50C3×#815C2211yescharacteristic
51C3×C8×Dic3C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#810C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#809C2211yescharacteristic
56#63566C2211yescharacteristic
57#63566C2211yescharacteristic
58#63566C2211yescharacteristic
59#63563C2211yescharacteristic
60#63554C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62C2×#918—31no—
63C2×#915—31no—
64C4×#239—31no—
65C4×D3×Q8—31no—
66C4×D3×Q8—31no—
67C4×#237—31no—
68C3×#440—31no—
69C3×C4×Q16—31no—
70#5184—31no—
71Dic3×SD16—31no—
72#5030—31no—
73C4×#216—31no—
74C4×#215—31no—
75#5018—31no—
76#4889D311yescharacteristic, complemented
77#4881—31no—
78#4881—31no—
79#4881—61no—
80#4873D311yescharacteristic, complemented
81#4817—31no—
82#4803—31no—
83#4802—31no—
84#4802—31no—
85#4790—31no—
86#4789—31no—
87#4771—31no—
88#4758—31no—
89#4716—31no—
90#4707—31no—
91C4×#204—31no—
92C4×ΓL(1,𝔽25)—31no—
93C2×C4×C3⋊D3—21no—
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×Dic6C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×#627—21no—
101C2×#626—21no—
102C2×#624—21no—
103C2×#624D411yescharacteristic
104C2×#624D411yescharacteristic
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107#3797—22no—
108#3797C2×C414yescomplemented
109#3796—22no—
110#3796C2×C414yes—
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C4×C3⋊Dic3—21no—
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120#3743C2×C414yescomplemented
121C3×(C2×D3)⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×Dic12C2×C414yescomplemented
133C3×#204C2×C414yescomplemented
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139Dic32—21no—
140Dic32—21no—
141Dic32D411yescharacteristic
142Dic32D411yescharacteristic
143#3718C2×C414yescomplemented
144#3715C2×C414yescomplemented
145#3712—22no—
146C4×#137—91noSylow
147C2×#239—31no—
148C2×D3×Q8—31no—
149C2×D3×Q8—31no—
150C2×#237—31no—
151C2×C3×Q16—31no—
152C2×C3×SD16—31no—
153C3×C4×Q8—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156C3×C4×D4—31no—
157Q8×Dic3—31no—
158Q8×Dic3—31no—
159Q8×Dic3—31no—
160C2×#216—31no—
161C2×#216—31no—
162C2×#215—31no—
163D4×Dic3—31no—
164C2×#214—31no—
165C4×#67—61no—
166C2×C4×Dic3—61no—
167#918—38no—
168#915—38no—
169C2×Dic12C2×D311yescharacteristic
170C2×#204C2×D311yescharacteristic
171C2×ΓL(1,𝔽25)—31no—
172C2×ΓL(1,𝔽25)—31no—
173C2×ΓL(1,𝔽25)—31no—
174C2×ΓL(1,𝔽25)—31no—
175C2×ΓL(1,𝔽25)—61no—
176#893—61no—
177#893C2×D311yescharacteristic
178#892—31no—
179#892—31no—
180#892—61no—
181#892—61no—
182D3×C4⋊C4—31no—
183D3×C4⋊C4—31no—
184D3×C4⋊C4—61no—
185D3×C4⋊C4—61no—
186D3×C4⋊C4—61no—
187#887—61no—
188#887—61no—
189#887C2×D311yescharacteristic
190#887C2×D311yescharacteristic
191#887C2×D311yescharacteristic
192#67⋊C4—61no—
193#877—61no—
194C4×D12—31no—
195C4×D12—61no—
196C42×D3—31no—
197C42×D3—31no—
198C42×D3—61no—
199C42×D3—61no—
200C42×D3—61no—
201C4×Dic6—31no—
202C4×Dic6—31no—
203C4×Dic6—31no—
204C4×Dic6—61no—
205C4×Dic6—61no—
206C3×#107—21no—
207C3×#107C2×D311yescharacteristic
208C3×#107C2×D311yescharacteristic
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#102—31no—
213C3×#97—31no—
214C3×C4×C8—31no—
215#835—31no—
216#835—31no—
217#835—31no—
218#832—31no—
219#821—31no—
220#817—31no—
221#817—31no—
222#817—61no—
223#816—31no—
224#816—31no—
225#816—31no—
226#815—31no—
227#815C2×D311yescharacteristic
228C8×Dic3—31no—
229C8×Dic3C2×D311yescharacteristic
230#810C2×D311yescharacteristic
231#810C2×D311yescharacteristic
232#810C2×D311yescharacteristic
233#809C2×D311yescharacteristic
234#808—31no—
235#808—31no—
236#808—61no—
237#807—31no—
238#807—31no—
239#807—61no—
240#803—31no—
241C4×C3⋊C8—31no—
242C22×C3⋊D3C2×D411yescharacteristic
243C22×C3×D3—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4×C3⋊D3—42no—
251C4×C3⋊D3C22×C412yes—
252C4×C3⋊D3#4112yes—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—21no—
261C3×D12C22×C412yes—
262C3×C4×D3—42no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6C22×C412yes—
267C3×Dic6C22×C412yes—
268C3×Dic6C22×C412yes—
269#627—24no—
270#626—24no—
271#624—24no—
272#624—22no—
273#624—41no—
274D3×Dic3—24no—
275D3×Dic3—42no—
276C32×C8C22×C412yes—
277C3⋊(C3⋊C8)C22×C412yes—
278C3×C3⋊C8—21no—
279C3×C3⋊C8—21no—
280C2×#137—91no—
281C4×#41—91no—
282C2×C4×Q8—91no—
283#441—91no—
284#441—91no—
285#440—31no—
286#440—91no—
287C4×Q16—31no—
288C4×Q16—91no—
289C4×SD16—91no—
290C4×SD16—91no—
291#428—91no—
292#419—91no—
293#417—91no—
294C4×M16—91no—
295C2×C3×Q8—31no—
296C2×C3×Q8—31no—
297C2×C3×Q8—31no—
298C2×C3×D4—31no—
299C22×C3×C4—61no—
300C2×#67—61no—
301C22×Dic3—61no—
302C22×Dic3—61no—
303#239—34no—
304#239—62no—
305D3×Q8—34no—
306D3×Q8—34no—
307D3×Q8—62no—
308D3×Q8—62no—
309#237—34no—
310#237—62no—
311C2×D12—61no—
312C2×D12C22×D311yescharacteristic
313C2×C4×D3—21no—
314C2×C4×D3—31no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—31no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—121no—
328C2×Dic6—61no—
329C2×Dic6—61no—
330C2×Dic6C22×D311yescharacteristic
331C2×Dic6C22×D311yescharacteristic
332C2×Dic6C22×D311yescharacteristic
333C3×Q16—34no—
334C3×SD16—34no—
335C2×C3×C8—21no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C22⋊C4—61no—
350C3×C42—31no—
351C3×C42—31no—
352C3×C42—61no—
353C3×C42—61no—
354C3×C42—61no—
355#217—61no—
356#216—34no—
357#216—34no—
358#215—34no—
359#214—34no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—121no—
365C4⋊Dic3—31no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374Dic3⋊C4—21no—
375Dic3⋊C4—21no—
376Dic3⋊C4—21no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—121no—
383C4×Dic3—21no—
384C4×Dic3—21no—
385C4×Dic3—21no—
386C4×Dic3—31no—
387C4×Dic3—31no—
388C4×Dic3—31no—
389C4×Dic3—31no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—121no—
399C4×Dic3C22×D311yescharacteristic
400C4×Dic3C22×D311yescharacteristic
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406Dic12C4×D314yescomplemented
407#204C4×D314yescomplemented
408ΓL(1,𝔽25)—34no—
409ΓL(1,𝔽25)—34no—
410ΓL(1,𝔽25)—64no—
411ΓL(1,𝔽25)—62no—
412ΓL(1,𝔽25)—62no—
413C22×C32C22×D411yescharacteristic
414C2×C3⋊D3—21no—
415C2×C3⋊D3—21no—
416C2×C3⋊D3C4×D412yes—
417C2×C3×D3—22no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C32×C4—41no—
421C32×C4—41no—
422C32×C4C23×C411yescharacteristic
423C32×C4C2×#4111yescharacteristic
424C3⋊Dic3—41no—
425C3⋊Dic3—41no—
426C3⋊Dic3C4×D412yes—
427C3×Dic3—22no—
428C3×Dic3—22no—
429C3×Dic3—22no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3#13712yescomplemented
434C2×#41—91no—
435C22×Q8—91no—
436#137—98no—
437C2×Q16—31no—
438C2×Q16—91no—
439C2×SD16—31no—
440C2×SD16—91no—
441C2×M16—91no—
442C2×M16—91no—
443C4×Q8—31no—
444C4×Q8—31no—
445C4×Q8—31no—
446C4×Q8—91no—
447C4×Q8—91no—
448C4×Q8—91no—
449C4×Q8—181no—
450C4×Q8—181no—
451C4×D4—31no—
452C4×D4—91no—
453C4×D4—181no—
454C4×D4—181no—
455#117—91no—
456#117—181no—
457C2×C4⋊C4—91no—
458C2×C4⋊C4—181no—
459C2×C42—91no—
460C2×C42—181no—
461C2×C42—181no—
462#107—91no—
463#107D3211yescharacteristic
464#106—91no—
465#106—91no—
466#103—31no—
467#103—31no—
468#103—31no—
469#103—91no—
470#103—91no—
471#103—91no—
472#102—31no—
473#102—91no—
474#97—31no—
475#97—91no—
476C4×C8—31no—
477C4×C8—91no—
478C23×C3—61no—
479C22×D3—21no—
480C22×D3—31no—
481C22×D3—31no—
482C22×D3—61no—
483C3×Q8—32no—
484C3×Q8—32no—
485C3×Q8—32no—
486C3×Q8—61no—
487C3×Q8—61no—
488C3×Q8—61no—
489C3×D4—32no—
490C3×D4—61no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—122no—
506C2×C3×C4C23×D311yescharacteristic
507C2×C3×C4C23×D311yescharacteristic
508#67—64no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—31no—
513C2×Dic3—31no—
514C2×Dic3—61no—
515C2×Dic3—64no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—121no—
521C2×Dic3—121no—
522C2×Dic3—122no—
523C2×Dic3D3×D411yescharacteristic
524C2×Dic3D3×D411yescharacteristic
525C2×Dic3D3×D411yescharacteristic
526C2×Dic3D3×D411yescharacteristic
527D12—21no—
528D12—64no—
529D12C2×C4×D312yes—
530C4×D3—32no—
531C4×D3—32no—
532C4×D3—32no—
533C4×D3—32no—
534C4×D3—42no—
535C4×D3—62no—
536C4×D3—62no—
537C4×D3—62no—
538C4×D3—64no—
539C4×D3—64no—
540C4×D3—64no—
541C4×D3—62no—
542C4×D3—121no—
543C4×D3—121no—
544C4×D3—122no—
545C4×D3—122no—
546C4×D3—122no—
547C4×D3—242no—
548Dic6—21no—
549Dic6—21no—
550Dic6—21no—
551Dic6—64no—
552Dic6—64no—
553Dic6C2×C4×D312yes—
554Dic6C2×C4×D312yes—
555Dic6C2×C4×D312yes—
556C3×C8—22no—
557C3×C8—61no—
558C3×C8—61no—
559C3×C8C2×C4×D312yes—
560C3×C8C2×C4×D312yes—
561C3⋊C8—21no—
562C3⋊C8—21no—
563C3⋊C8—32no—
564C3⋊C8—32no—
565C3⋊C8—62no—
566C2×C32C2×C4×D411yescharacteristic
567C2×C32C2×#13711yescharacteristic
568C2×C32#57511yescharacteristic
569C3⋊D3—22no—
570C3×D3—42no—
571#41—94no—
572#41—182no—
573C2×Q8—31no—
574C2×Q8—31no—
575C2×Q8—31no—
576C2×Q8—94no—
577C2×Q8—181no—
578C2×Q8—182no—
579C2×D4—31no—
580C2×D4—181no—
581C22×C4—61no—
582C22×C4—91no—
583C22×C4—91no—
584C22×C4—91no—
585C22×C4—181no—
586C22×C4—181no—
587C22×C4—181no—
588C22×C4—181no—
589Q16—34no—
590Q16—94no—
591SD16—34no—
592SD16—94no—
593M16—94no—
594M16—182no—
595C2×C8—31no—
596C2×C8—31no—
597C2×C8—91no—
598C2×C8C2×D3211yescharacteristic
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—91no—
603C4⋊C4—91no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4C2×D3211yescharacteristic
609C4⋊C4C2×D3211yescharacteristic
610C22⋊C4—61no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C42—31no—
614C42—31no—
615C42—61no—
616C42—61no—
617C42—61no—
618C42—91no—
619C42—91no—
620C42—181no—
621C42—181no—
622C42—181no—
623C42—181no—
624C22×C3—21no—
625C22×C3—62no—
626C22×C3—121no—
627C22×C3—121no—
628C22×C3C2×D3×D411yescharacteristic
629C22×C3C2×D3×D411yescharacteristic
630C2×D3—22no—
631C2×D3—32no—
632C2×D3—32no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—62no—
636C2×D3—61no—
637C2×D3—61no—
638C2×D3—61no—
639C2×D3—61no—
640C2×D3—121no—
641C2×D3—121no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—32no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—61no—
650C3×C4—61no—
651C3×C4—61no—
652C3×C4—62no—
653C3×C4—62no—
654C3×C4—62no—
655C3×C4—81no—
656C3×C4—81no—
657C3×C4C22×C4×D311yescharacteristic
658C3×C4C22×C4×D311yescharacteristic
659C3×C4D3×#4111yescharacteristic
660C3×C4D3×#4111yescharacteristic
661Dic3—21no—
662Dic3—21no—
663Dic3—21no—
664Dic3—22no—
665Dic3—22no—
666Dic3—22no—
667Dic3—32no—
668Dic3—32no—
669Dic3—62no—
670Dic3—121no—
671Dic3—121no—
672Dic3—121no—
673Dic3—121no—
674Dic3—241no—
675Dic3—241no—
676Dic3#91812yescomplemented
677C32C4×#13711yescharacteristic, complemented, Sylow
678C23—61no—
679C23—91no—
680Q8—32no—
681Q8—32no—
682Q8—32no—
683Q8—61no—
684Q8—61no—
685Q8—61no—
686Q8—184no—
687D4—32no—
688D4—61no—
689D4—184no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—31no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—91no—
700C2×C4—92no—
701C2×C4—92no—
702C2×C4—122no—
703C2×C4—182no—
704C2×C4—184no—
705C2×C4—184no—
706C2×C4—181no—
707C2×C4—181no—
708C2×C4—362no—
709C2×C4—362no—
710C2×C4—361no—
711C2×C4C22×D3211yescharacteristic
712C8—61no—
713C8—61no—
714C8—92no—
715C8C4×D3212yes—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—122no—
720C2×C3C4×D3×D411yescharacteristic
721C2×C3C4×D3×D411yescharacteristic
722C2×C3C2×#91811yescharacteristic
723C2×C3#576811yescharacteristic
724C2×C3#577311yescharacteristic
725C2×C3D3×#13711yescharacteristic
726D3—42no—
727D3—62no—
728D3—62no—
729D3—122no—
730C22—62no—
731C22—92no—
732C22—121no—
733C22—121no—
734C22—181no—
735C22—181no—
736C22D32×D411yescharacteristic
737C4—32no—
738C4—41no—
739C4—41no—
740C4—62no—
741C4—62no—
742C4—62no—
743C4—61no—
744C4—61no—
745C4—61no—
746C4—92no—
747C4—361no—
748C4—361no—
749C4C2×C4×D3211yescharacteristic
750C4#6431911yescharacteristic
751C3—21no—
752C3C4×#91811yescharacteristic, complemented
753C3#7977411yescharacteristic, complemented
754C2—122no—
755C2—182no—
756C2#1059460511yescharacteristic
757C2#1059472911yescharacteristic
758C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC2×#3796C22
cosocleC2×C32×C4C24
hypercenter#107D32
hypocenterC32C4×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #10594363C2semidirect
4. #10592580C2semidirect
5. C3×#4889C2semidirect
6. C3×#4873C2semidirect
7. #10590812C2semidirect
8. Dic3×#204C2semidirect
9. #10590664C2semidirect
11. #10590602C2semidirect
12. #10590478C2semidirect
13. #10590477C2semidirect
14. #10590476C2semidirect
15. #10590453C2semidirect
45. #63811C4semidirect
76. #4889D3semidirect
80. #4873D3semidirect
108. #3797C2×C4semidirect
120. #3743C2×C4semidirect
132. C3×Dic12C2×C4semidirect
133. C3×#204C2×C4semidirect
143. #3718C2×C4semidirect
144. #3715C2×C4semidirect
406. Dic12C4×D3semidirect
407. #204C4×D3semidirect
433. C3×Dic3#137semidirect
676. Dic3#918semidirect
677. C32C4×#137semidirect
752. C3C4×#918semidirect
753. C3#79774semidirect

Maximal subgroups

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

subgroupindex
C2×#638112
#105943632
#105943602
#105925802
C3×#48892
C3×#48732
#105908122
Dic3×#2042
#105906642
#105906122
#105906022
#105904782
#105904772
#105904762
#105904532
#797743
C4×#9183