Finite Group Databasebeta

← #11860548

Subgroups — #11860548

Order 1152.

1073 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63795C211yesmaximal, characteristic
2#10594604C211yesmaximal, characteristic, complemented
3#10594359C211yesmaximal, characteristic, complemented
4#10592551C211yesmaximal, characteristic, complemented
5C3×#4869C211yesmaximal, characteristic, complemented
6C3×#4861C211yesmaximal, characteristic, complemented
7#10590909C211yesmaximal, characteristic, complemented
8#10590777C211yesmaximal, characteristic, complemented
9#10590773C211yesmaximal, characteristic, complemented
10#10590608C211yesmaximal, characteristic, complemented
11D3×#809C211yesmaximal, characteristic, complemented
12#10590479C211yesmaximal, characteristic, complemented
13#10590462C211yesmaximal, characteristic, complemented
14#10590461C211yesmaximal, characteristic, complemented
15#10590456C211yesmaximal, characteristic, complemented
16#79866—31nomaximal
17#79201—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C2×#3744C2211yescharacteristic
21#64102C2211yescharacteristic
22#64096C2211yescharacteristic, complemented
23C2×C3×D24C2211yescharacteristic
24C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
25C3×#893C2211yescharacteristic
26C3×#893C2211yescharacteristic, complemented
27C3×#892C2211yescharacteristic
28C3×D3×C4⋊C4C2211yescharacteristic
29#63921—21no—
30D3×(C2×D3)⋊C4—21no—
31C4×#626—21no—
32C4×#625—21no—
33#63898C2211yescharacteristic
34#63898C2211yescharacteristic, complemented
35#63894C2211yescharacteristic
36#63880—21no—
37#63879—21no—
38#63878—21no—
39D3×Dic3⋊C4—21no—
40#63855C2211yescharacteristic
41#63844C2211yescharacteristic, complemented
42C2×#3716C2211yescharacteristic
43C2×#3714C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45#63795C418yescomplemented
46C32×#106C2211yescharacteristic, complemented
47C8×C3⋊Dic3C2211yescharacteristic, complemented
48#63637C2211yescharacteristic, complemented
49#63636C2211yescharacteristic
50C3×#818C2211yescharacteristic, complemented
51C3×#815C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#809C2211yescharacteristic, complemented
54C3×#808C2211yescharacteristic, complemented
55C3×#807C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic, complemented
60#63555C2211yescharacteristic, complemented
61Dic3×C3⋊C8C2211yescharacteristic, complemented
62C2×#911—31no—
63C2×#908—31no—
64#5546—31no—
65#5545—31no—
66#5521—31no—
67#5504—31no—
68C3×#442—31no—
69C3×#428—31no—
70Dic3×D8—31no—
71#5122—31no—
72C4×#214—31no—
73C4×#213—31no—
74#5002—31no—
75C2×#809—31no—
76#4889—31no—
77#4889—31no—
78#4872—31no—
79#4872—31no—
80#4869—31no—
81#4869D311yescharacteristic, complemented
82#4861D311yescharacteristic, complemented
83#4852—31no—
84#4852—31no—
85#4852—31no—
86#4852—61no—
87#4785—31no—
88#4772—31no—
89D3×#102—31no—
90#4757—31no—
91#4710—31no—
92#4708—31no—
93C22×D32—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×#634C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×#626—21no—
104C2×#625—21no—
105C2×#624—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109D3×D12—22no—
110D3×D12C2×C414yescomplemented
111#3795—22no—
112#3795C2×C414yescomplemented
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116#3752—21no—
117#3750—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121#3744C2×C414yescomplemented
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×D24C2×C414yescomplemented
133C3×ΓL(1,𝔽25)C2×C414yescomplemented
134#3724—21no—
135Dic3⋊Dic3D411yescharacteristic
136Dic3⋊Dic3D411yescharacteristic
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141(C2×D3)⋊Dic3D411yescharacteristic
142Dic32—21no—
143#3716C2×C414yescomplemented
144#3714C2×C414yescomplemented
145D3×C3⋊C8—22no—
146#2946—91noSylow
147C2×#237—31no—
148C2×D3×D4—31no—
149C2×#235—31no—
150C22×D12—31no—
151C2×C3×D8—31no—
152C2×C3×M16—31no—
153C3×C4×D4—31no—
154C3×C4×D4—31no—
155C3×#117—31no—
156C2×C3×C4⋊C4—31no—
157D4×Dic3—31no—
158D4×Dic3—31no—
159C2×#214—31no—
160C2×#213—31no—
161C4×#67—61no—
162C4×#67—61no—
163C4×#67—61no—
164C4×#67—61no—
165C2×(C2×D3)⋊C4—61no—
166#926—31no—
167C2×Dic3⋊C4—61no—
168C22×C3⋊C8—31no—
169#911—38no—
170#908—38no—
171C2×D24—31no—
172C2×D24C2×D311yescharacteristic
173C2×#204—31no—
174C2×#204—31no—
175C2×#204—31no—
176C2×#204—61no—
177C2×ΓL(1,𝔽25)C2×D311yescharacteristic
178C2×D3×C8—31no—
179#893—31no—
180#893—31no—
181#893—31no—
182#893—31no—
183#893—31no—
184#893—61no—
185#893C2×D311yescharacteristic
186#893C2×D311yescharacteristic, complemented
187#892—61no—
188#892C2×D311yescharacteristic
189D3×C4⋊C4—61no—
190D3×C4⋊C4C2×D311yescharacteristic
191#887—31no—
192#887—31no—
193#887—31no—
194#887—61no—
195#67⋊C4—61no—
196#67⋊C4—61no—
197D3×C22⋊C4—61no—
198D3×C22⋊C4—61no—
199D3×C22⋊C4—61no—
200#877—61no—
201C4×D12—31no—
202C4×D12—61no—
203C4×D12—61no—
204#872—31no—
205C4×Dic6—31no—
206C3×#107—31no—
207C3×#107—31no—
208C3×#106—21no—
209C3×#106—31no—
210C3×#106C2×D311yescharacteristic, complemented
211C3×#106C2×D311yescharacteristic, complemented
212C3×#102—31no—
213C3×#102—31no—
214C3×#97—31no—
215#832—31no—
216#832—31no—
217#821—31no—
218#818C2×D311yescharacteristic, complemented
219#816—31no—
220#815—31no—
221#815—31no—
222#815C2×D311yescharacteristic, complemented
223C8×Dic3—31no—
224C8×Dic3—31no—
225C8×Dic3—31no—
226C8×Dic3—61no—
227#810—31no—
228#810—31no—
229#810—31no—
230#810—61no—
231#809—31no—
232#809—31no—
233#809—31no—
234#809—31no—
235#809—31no—
236#809—61no—
237#809C2×D311yescharacteristic
238#809C2×D311yescharacteristic, complemented
239#808C2×D311yescharacteristic, complemented
240#807C2×D311yescharacteristic, complemented
241C4×C3⋊C8—31no—
242C22×C3⋊D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3C2×D411yescharacteristic
246C2×D32—24no—
247C2×D32—81no—
248C2×D32—81no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3C2×D411yescharacteristic
254C2×C3⋊Dic3C2×D411yescharacteristic
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)C22×C412yes—
257C4×C3⋊D3—81no—
258#634—21no—
259#634C22×C412yes—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—21no—
267C3×D12C22×C412yes—
268C3×D12C22×C412yes—
269C3×C4×D3—81no—
270C3×C4×D3—81no—
271C3×C4×D3—81no—
272C3×C4×D3C22×C412yes—
273C3×C4×D3#4112yes—
274#626—24no—
275#625—24no—
276#624—81no—
277D3×Dic3—24no—
278D3×Dic3—81no—
279D3×Dic3—81no—
280C32×C8C22×C412yes—
281C3⋊(C3⋊C8)—21no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8C22×C412yes—
284C2×AGL(1,ℤ/8)—91no—
285#520—91no—
286#518—91no—
287#442—31no—
288#442—91no—
289#440—91no—
290#440—91no—
291C4×SD16—91no—
292C4×SD16—91no—
293C4×D8—91no—
294C4×D8—91no—
295#428—31no—
296#416—91no—
297C2×#102—91no—
298#405—91no—
299C23×D3—61no—
300C23×D3—61no—
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313#237—34no—
314#237—62no—
315D3×D4—34no—
316D3×D4—62no—
317#235—34no—
318#235—62no—
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—34no—
322C2×D12—61no—
323C2×D12—62no—
324C2×D12—61no—
325C2×D12C22×D311yescharacteristic
326C2×D12C22×D311yescharacteristic
327C2×C4×D3—21no—
328C2×C4×D3—21no—
329C2×C4×D3—21no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—121no—
338C2×C4×D3C22×D311yescharacteristic
339C2×Dic6—31no—
340C2×Dic6—31no—
341C2×Dic6—61no—
342C3×D8—34no—
343C3×M16—34no—
344C2×C3×C8—21no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C42—31no—
362C3×C42—61no—
363#217—31no—
364#217—31no—
365#217—61no—
366#217—61no—
367#214—34no—
368#213—34no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—31no—
373(C2×D3)⋊C4—31no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—121no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385Dic3⋊C4—21no—
386Dic3⋊C4—31no—
387Dic3⋊C4—31no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—121no—
393C4×Dic3—21no—
394C4×Dic3—31no—
395C4×Dic3—31no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—121no—
402C4×Dic3C22×D311yescharacteristic
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—62no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409D24—34no—
410D24C4×D314yescomplemented
411#204—34no—
412#204—34no—
413#204—34no—
414#204—64no—
415ΓL(1,𝔽25)C4×D314yescomplemented
416D3×C8—62no—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—22no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3C4×D412yes—
430D32—84no—
431C32×C4—41no—
432C32×C4—41no—
433C32×C4C23×C411yescharacteristic
434C32×C4C2×#4111yescharacteristic
435C3⋊Dic3—21no—
436C3⋊Dic3—22no—
437C3⋊Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3C4×D412yes—
443C2×#41—91no—
444C22×D4—91no—
445AGL(1,ℤ/8)—98no—
446C2×SD16—91no—
447C2×SD16—91no—
448C2×D8—31no—
449C2×D8—91no—
450C2×M16—31no—
451C22×C8—91no—
452C4×Q8—91no—
453C4×Q8—91no—
454C4×D4—31no—
455C4×D4—31no—
456C4×D4—91no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—91no—
460C4×D4—181no—
461C4×D4—181no—
462C4×D4—181no—
463C4×D4—181no—
464#117—31no—
465#117—91no—
466#117—181no—
467C2×C4⋊C4—31no—
468C2×C4⋊C4—181no—
469C2×C22⋊C4—181no—
470C2×C22⋊C4—181no—
471#107—31no—
472#107—31no—
473#106—31no—
474#106D3211yescharacteristic, complemented
475#103—91no—
476#103—91no—
477#102—31no—
478#102—31no—
479#102—91no—
480#102—91no—
481#102—91no—
482#102—91no—
483#97—31no—
484#97—91no—
485C4×C8—91no—
486C4×C8—91no—
487C23×C3—31no—
488C23×C3—61no—
489C23×C3—61no—
490C22×D3—21no—
491C22×D3—21no—
492C22×D3—64no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—64no—
496C22×D3—121no—
497C22×D3—241no—
498C22×D3—241no—
499C22×D3—241no—
500C22×D3—241no—
501C22×D3D3×D411yescharacteristic
502C3×D4—32no—
503C3×D4—32no—
504C3×D4—61no—
505C3×D4—61no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—31no—
512C2×C3×C4—32no—
513C2×C3×C4—32no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—241no—
521C2×C3×C4—241no—
522C2×C3×C4—241no—
523C2×C3×C4C23×D311yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525#67—64no—
526#67—64no—
527#67—64no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—64no—
539C2×Dic3—121no—
540C2×Dic3—241no—
541C2×Dic3—241no—
542C2×Dic3D3×D411yescharacteristic
543C2×Dic3D3×D411yescharacteristic
544C2×Dic3D3×D411yescharacteristic
545D12—21no—
546D12—21no—
547D12—32no—
548D12—32no—
549D12—62no—
550D12—64no—
551D12—61no—
552D12—61no—
553D12—121no—
554D12C2×C4×D312yes—
555D12C2×C4×D312yes—
556C4×D3—64no—
557C4×D3—81no—
558C4×D3—81no—
559C4×D3—81no—
560C4×D3—241no—
561C4×D3—241no—
562C4×D3—241no—
563C4×D3—241no—
564C4×D3—242no—
565C4×D3—241no—
566C4×D3—241no—
567C4×D3C2×C4×D312yes—
568C4×D3#23912yes—
569Dic6—32no—
570Dic6—32no—
571Dic6—62no—
572Dic6—61no—
573Dic6—61no—
574Dic6—121no—
575C3×C8—22no—
576C3×C8—32no—
577C3×C8—61no—
578C3×C8C2×C4×D312yes—
579C3×C8C2×C4×D312yes—
580C3⋊C8—21no—
581C3⋊C8—61no—
582C3⋊C8—61no—
583C3⋊C8—121no—
584C3⋊C8C2×C4×D312yes—
585C2×C32C2×C4×D411yescharacteristic
586C2×C32#57611yescharacteristic
587C2×C32#57711yescharacteristic
588C3⋊D3—42no—
589C3×D3—22no—
590C3×D3—42no—
591C3×D3—42no—
592C24—181no—
593#41—94no—
594#41—182no—
595C2×Q8—91no—
596C2×D4—31no—
597C2×D4—31no—
598C2×D4—94no—
599C2×D4—91no—
600C2×D4—182no—
601C2×D4—181no—
602C2×D4—181no—
603C22×C4—31no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4—181no—
610C22×C4—181no—
611C22×C4—181no—
612SD16—94no—
613SD16—94no—
614D8—34no—
615D8—94no—
616M16—34no—
617C2×C8—31no—
618C2×C8—31no—
619C2×C8—91no—
620C2×C8—182no—
621C2×C8C2×D3211yescharacteristic
622C4⋊C4—31no—
623C4⋊C4—31no—
624C4⋊C4—61no—
625C4⋊C4—91no—
626C4⋊C4—91no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4C2×D3211yescharacteristic
630C4⋊C4C2×D3211yescharacteristic
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—91no—
635C22⋊C4—91no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C42—31no—
641C42—61no—
642C42—91no—
643C42—181no—
644C42—181no—
645C22×C3—21no—
646C22×C3—32no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—62no—
650C22×C3—62no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3C2×D3×D411yescharacteristic
656C22×C3C2×D3×D411yescharacteristic
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—22no—
660C2×D3—22no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—62no—
666C2×D3—62no—
667C2×D3—122no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—241no—
673C2×D3—241no—
674C2×D3—244no—
675C2×D3—244no—
676C2×D3#89312yes—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—32no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—41no—
684C3×C4—61no—
685C3×C4—61no—
686C3×C4—81no—
687C3×C4—81no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4C22×C4×D311yescharacteristic
691C3×C4C22×C4×D311yescharacteristic
692C3×C4C2×#23911yescharacteristic
693C3×C4D3×#4111yescharacteristic
694Dic3—21no—
695Dic3—21no—
696Dic3—41no—
697Dic3—41no—
698Dic3—62no—
699Dic3—62no—
700Dic3—61no—
701Dic3—61no—
702Dic3—61no—
703Dic3—61no—
704Dic3—62no—
705Dic3—122no—
706Dic3—121no—
707Dic3#89312yes—
708C32#294611yescharacteristic, complemented, Sylow
709C23—31no—
710C23—61no—
711C23—61no—
712C23—184no—
713C23—181no—
714C23—721no—
715C23—721no—
716Q8—92no—
717Q8—181no—
718D4—32no—
719D4—32no—
720D4—61no—
721D4—61no—
722D4—92no—
723D4—184no—
724D4—184no—
725D4—181no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—31no—
729C2×C4—32no—
730C2×C4—32no—
731C2×C4—31no—
732C2×C4—31no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—91no—
736C2×C4—91no—
737C2×C4—184no—
738C2×C4—181no—
739C2×C4—241no—
740C2×C4—241no—
741C2×C4—241no—
742C2×C4—721no—
743C2×C4—721no—
744C2×C4—721no—
745C2×C4—721no—
746C2×C4C22×D3211yescharacteristic
747C8—32no—
748C8—61no—
749C8—181no—
750C8C4×D3212yes—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—62no—
755C2×C3—122no—
756C2×C3—122no—
757C2×C3C2×#89311yescharacteristic
758C2×C3C4×D3×D411yescharacteristic
759C2×C3#577411yescharacteristic
760C2×C3#577411yescharacteristic
761C2×C3#577511yescharacteristic
762C2×C3#577811yescharacteristic
763D3—22no—
764D3—42no—
765D3—42no—
766D3—122no—
767D3—122no—
768D3—242no—
769C22—32no—
770C22—61no—
771C22—61no—
772C22—62no—
773C22—62no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—121no—
778C22—182no—
779C22—361no—
780C22—361no—
781C22—724no—
782C22D32×D411yescharacteristic
783C4—32no—
784C4—41no—
785C4—41no—
786C4—61no—
787C4—61no—
788C4—121no—
789C4—121no—
790C4—182no—
791C4—181no—
792C4—181no—
793C4C2×C4×D3211yescharacteristic
794C4D3×#23911yescharacteristic
795C3—21no—
796C3#7920111yescharacteristic, complemented
797C3#7986611yescharacteristic, complemented
798C2—62no—
799C2—122no—
800C2—122no—
801C2—362no—
802C2D3×#89311yescharacteristic
803C2#1059475011yescharacteristic
804C2#1059475411yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×#63795C2
cosocleC2×C32×C4C24
hypercenter#106D32
hypocenterC32#2946
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #10594604C2semidirect
3. #10594359C2semidirect
4. #10592551C2semidirect
5. C3×#4869C2semidirect
6. C3×#4861C2semidirect
7. #10590909C2semidirect
8. #10590777C2semidirect
9. #10590773C2semidirect
10. #10590608C2semidirect
11. D3×#809C2semidirect
12. #10590479C2semidirect
13. #10590462C2semidirect
14. #10590461C2semidirect
15. #10590456C2semidirect
22. #64096C22semidirect
26. C3×#893C22semidirect
34. #63898C22semidirect
41. #63844C22semidirect
45. #63795C4semidirect
46. C32×#106C22semidirect
47. C8×C3⋊Dic3C22semidirect
48. #63637C22semidirect
50. C3×#818C22semidirect
51. C3×#815C22semidirect
53. C3×#809C22semidirect
54. C3×#808C22semidirect
55. C3×#807C22semidirect
56. #63567C22semidirect
59. #63562C22semidirect
60. #63555C22semidirect
61. Dic3×C3⋊C8C22semidirect
81. #4869D3semidirect
82. #4861D3semidirect
110. D3×D12C2×C4semidirect
112. #3795C2×C4semidirect
121. #3744C2×C4semidirect
132. C3×D24C2×C4semidirect
133. C3×ΓL(1,𝔽25)C2×C4semidirect
143. #3716C2×C4semidirect
144. #3714C2×C4semidirect
186. #893C2×D3semidirect
210. C3×#106C2×D3semidirect
211. C3×#106C2×D3semidirect
218. #818C2×D3semidirect
222. #815C2×D3semidirect
238. #809C2×D3semidirect
239. #808C2×D3semidirect
240. #807C2×D3semidirect
410. D24C4×D3semidirect
415. ΓL(1,𝔽25)C4×D3semidirect
474. #106D32semidirect
708. C32#2946semidirect
796. C3#79201semidirect
797. C3#79866semidirect

Maximal subgroups

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

subgroupindex
C2×#637952
#105946042
#105943592
#105925512
C3×#48692
C3×#48612
#105909092
#105907772
#105907732
#105906082
D3×#8092
#105904792
#105904622
#105904612
#105904562
#798663
#792013