Finite Group Databasebeta

← #11860681

Subgroups — #11860681

Order 1152.

1151 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595223C211yesmaximal, characteristic, complemented
2C2×#63926C211yesmaximal, characteristic
3#10594606C211yesmaximal, characteristic, complemented
4#10592469C211yesmaximal, characteristic, complemented
5C3×#4785C211yesmaximal, characteristic, complemented
6C3×#4756C211yesmaximal, characteristic, complemented
7#10591430C211yesmaximal, characteristic, complemented
8Dic3×#213C211yesmaximal, characteristic, complemented
9#10590941C211yesmaximal, characteristic, complemented
10#10590910C211yesmaximal, characteristic, complemented
11#10590746C211yesmaximal, characteristic, complemented
12#10590745C211yesmaximal, characteristic, complemented
13#10590589C211yesmaximal, characteristic, complemented
14#10590574C211yesmaximal, characteristic, complemented
15#10590456C211yesmaximal, characteristic, complemented
16#79867—31nomaximal
17#79588—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3802C2211yescharacteristic
20C2×#3743C2211yescharacteristic
21#64101C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic, complemented
23C3×D4×Dic3C2211yescharacteristic, complemented
24C2×C3×#213C2211yescharacteristic
25C2×C3×#213C2211yescharacteristic
26C3×#893C2211yescharacteristic, complemented
27C3×#893C2211yescharacteristic, complemented
28#63974—21no—
29C2×#3722—21no—
30#63952—21no—
31#63952—21no—
32#63926C418yescomplemented
33D3×(C2×D3)⋊C4—21no—
34D3×(C2×D3)⋊C4—21no—
35#63902—21no—
36C4×#625—21no—
37#63894C2211yescharacteristic, complemented
38#63894C2211yescharacteristic, complemented
39Dic3×D12C2211yescharacteristic, complemented
40Dic3×D12C2211yescharacteristic, complemented
41#63874C2211yescharacteristic
42#63849C2211yescharacteristic
43C2×#3714C2211yescharacteristic
44C2×#3714C2211yescharacteristic
45C2×#3710C2211yescharacteristic
46C32×#102C2211yescharacteristic, complemented
47#63659C2211yescharacteristic, complemented
48#63648C2211yescharacteristic, complemented
49#63636C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic, complemented
51C3×#821C2211yescharacteristic, complemented
52C3×#815C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54C3×#808C2211yescharacteristic, complemented
55C3×#807C2211yescharacteristic, complemented
56#63575C2211yescharacteristic, complemented
57#63573C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59#63562C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61Dic3×C3⋊C8C2211yescharacteristic, complemented
62C2×D3×D8—31no—
63C2×D3×D8—31no—
64#5545—31no—
65#5545—31no—
66#5545—31no—
67#5545—31no—
68C3×#442—31no—
69C3×C4×D8—31no—
70#5152—31no—
71Dic3×D8—31no—
72#5014—31no—
73#5014—31no—
74C4×#213—31no—
75C4×#213—31no—
76#4880—31no—
77#4872—31no—
78#4869—31no—
79#4860—31no—
80#4785—31no—
81#4785D311yescharacteristic, complemented
82#4770—31no—
83#4770—31no—
84#4770—31no—
85#4770—31no—
86#4770—61no—
87#4756—31no—
88#4756D311yescharacteristic, complemented
89#4711—31no—
90#4708—31no—
91C4×D24—31no—
92#4689—31no—
93C23×C3⋊D3—21no—
94C22×D32—21no—
95C2×C32×D4C2311yescharacteristic
96C2×#638—21no—
97D4×C3⋊D3—22no—
98D4×C3⋊D3C2×C414yescomplemented
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×#625—21no—
108C2×#624—21no—
109C2×#624—21no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112#3802—22no—
113#3802C2×C414yescomplemented
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116#3752—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4×C3⋊Dic3—21no—
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120#3743—22no—
121C3×#217—21no—
122C3×#217—21no—
123C3×#213C2×C414yescomplemented
124C3×#213C2×C414yescomplemented
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4×Dic3C2311yescharacteristic
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133#3724D411yescharacteristic
134#3724D411yescharacteristic
135#3722—21no—
136#3722—21no—
137#3722—21no—
138#3722D411yescharacteristic
139#3722D411yescharacteristic
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143#3714C2×C414yescomplemented
144#3714C2×C414yescomplemented
145#3710C2×C414yescomplemented
146#2948—91noSylow
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—31no—
151C2×D3×D4—61no—
152C2×C3×D8—31no—
153C2×C3×D8—31no—
154C3×C4×D4—31no—
155C3×C4×D4—31no—
156C3×C4×D4—31no—
157C3×C4×D4—31no—
158D4×Dic3—31no—
159D4×Dic3—31no—
160D4×Dic3C2×D311yescharacteristic, complemented
161D4×Dic3C2×D311yescharacteristic, complemented
162C2×#213—31no—
163C2×#213—31no—
164C2×#213C2×D311yescharacteristic
165C2×#213C2×D311yescharacteristic
166C4×#67—61no—
167C4×#67—61no—
168C4×#67—61no—
169C4×#67—61no—
170C2×(C2×D3)⋊C4—61no—
171C2×(C2×D3)⋊C4—61no—
172C2×(C2×D3)⋊C4—61no—
173C2×(C2×D3)⋊C4—61no—
174D3×D8—38no—
175D3×D8—38no—
176C2×D24—31no—
177C2×D24—31no—
178C2×ΓL(1,𝔽25)—31no—
179C2×ΓL(1,𝔽25)—31no—
180C2×ΓL(1,𝔽25)—61no—
181C2×D3×C8—31no—
182C2×D3×C8—31no—
183#893—31no—
184#893—31no—
185#893C2×D311yescharacteristic, complemented
186#893C2×D311yescharacteristic, complemented
187#892—31no—
188#892—31no—
189#892—31no—
190#892—31no—
191#892—61no—
192#67⋊C4—61no—
193#67⋊C4—61no—
194#67⋊C4—61no—
195#67⋊C4—61no—
196D3×C22⋊C4—61no—
197D3×C22⋊C4—61no—
198D3×C22⋊C4—61no—
199D3×C22⋊C4—61no—
200C4×D12—31no—
201C4×D12—31no—
202C4×D12—31no—
203C4×D12—31no—
204#872—31no—
205#872—31no—
206C3×#107—31no—
207C3×#106—31no—
208C3×#102—21no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102C2×D311yescharacteristic, complemented
212C3×#102C2×D311yescharacteristic, complemented
213C3×#97—31no—
214C3×C4×C8—31no—
215#832—31no—
216#832—31no—
217#832—31no—
218#832—31no—
219#832—61no—
220#821—31no—
221#821—31no—
222#821—61no—
223#821C2×D311yescharacteristic, complemented
224#821C2×D311yescharacteristic, complemented
225#818—31no—
226#817—31no—
227#815—31no—
228#815C2×D311yescharacteristic, complemented
229C8×Dic3—31no—
230C8×Dic3C2×D311yescharacteristic, complemented
231#809—31no—
232#809—31no—
233#809—31no—
234#809—31no—
235#809—61no—
236#808—31no—
237#808C2×D311yescharacteristic, complemented
238#807—31no—
239#807C2×D311yescharacteristic, complemented
240#803—31no—
241C4×C3⋊C8—31no—
242C23×C32—21no—
243C22×C3⋊D3—21no—
244C22×C3⋊D3—24no—
245C22×C3⋊D3—81no—
246C22×C3⋊D3—81no—
247C22×C3⋊D3C2×D411yescharacteristic
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C2×D32—24no—
251C2×D32—81no—
252C2×D32—81no—
253C32×D4—21no—
254C32×D4C22×C412yes—
255C2×C32×C4—21no—
256C2×C32×C4C2411yescharacteristic
257#638—24no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3C2×D411yescharacteristic
260C4⋊(C3⋊D3)—21no—
261C4⋊(C3⋊D3)C22×C412yes—
262C4×C3⋊D3C22×C412yes—
263C4×C3⋊D3#4112yes—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—81no—
267C2×C3×Dic3—81no—
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
272C3×D12—21no—
273C3×D12—21no—
274C3×D12C22×C412yes—
275C3×D12C22×C412yes—
276C3×C4×D3—81no—
277C3×C4×D3—81no—
278#625—24no—
279#624—81no—
280#624—81no—
281D3×Dic3—81no—
282D3×Dic3—81no—
283C32×C8—21no—
284C3⋊(C3⋊C8)—21no—
285C3×C3⋊C8C22×C412yes—
286C3×C3⋊C8C22×C412yes—
287C22×D8—91no—
288#518—91no—
289#518—91no—
290#442—31no—
291#442—91no—
292#442—91no—
293#442—91no—
294C4×D8—31no—
295C4×D8—91no—
296C4×D8—91no—
297C4×D8—91no—
298#427—91no—
299#418—91no—
300#418—91no—
301#405—91no—
302C23×D3—61no—
303C23×D3—61no—
304C23×D3—61no—
305C23×D3—61no—
306C23×D3—121no—
307C2×C3×D4—21no—
308C2×C3×D4—31no—
309C2×C3×D4—31no—
310C2×C3×D4C22×D311yescharacteristic
311C2×C3×D4C22×D311yescharacteristic
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—121no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—61no—
324C22×Dic3—61no—
325D3×D4—34no—
326D3×D4—34no—
327D3×D4—34no—
328D3×D4—34no—
329D3×D4—64no—
330D3×D4—62no—
331D3×D4—62no—
332D3×D4—62no—
333D3×D4—62no—
334D3×D4—122no—
335C2×D12—31no—
336C2×D12—31no—
337C2×D12—61no—
338C2×D12C22×D311yescharacteristic
339C2×D12C22×D311yescharacteristic
340C2×C4×D3—21no—
341C2×C4×D3—21no—
342C2×C4×D3—31no—
343C2×C4×D3—31no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—61no—
350C2×C4×D3—61no—
351C3×D8—34no—
352C3×D8—34no—
353C2×C3×C8—21no—
354C2×C3×C8—31no—
355C2×C3×C8—31no—
356C2×C3×C8C22×D311yescharacteristic
357C2×C3×C8C22×D311yescharacteristic
358C3×C4⋊C4—21no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C42—31no—
368C3×C42—31no—
369#217—21no—
370#217—21no—
371#217—61no—
372#217—61no—
373#213—34no—
374#213—34no—
375#213C4×D314yescomplemented
376#213C4×D314yescomplemented
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—31no—
380(C2×D3)⋊C4—31no—
381(C2×D3)⋊C4—31no—
382(C2×D3)⋊C4—31no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—121no—
394C4⋊Dic3—31no—
395C4⋊Dic3—31no—
396C4⋊Dic3—61no—
397C4⋊Dic3C22×D311yescharacteristic
398C4⋊Dic3C22×D311yescharacteristic
399Dic3⋊C4—31no—
400Dic3⋊C4—31no—
401Dic3⋊C4—31no—
402Dic3⋊C4—31no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—121no—
408C4×Dic3C22×D311yescharacteristic
409C4×Dic3C22×D311yescharacteristic
410C2×C3⋊C8—31no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—61no—
413C2×C3⋊C8C22×D311yescharacteristic
414C2×C3⋊C8C22×D311yescharacteristic
415D24—34no—
416D24—34no—
417ΓL(1,𝔽25)—62no—
418ΓL(1,𝔽25)—62no—
419ΓL(1,𝔽25)—122no—
420D3×C8—34no—
421D3×C8—34no—
422C22×C32—22no—
423C22×C32—41no—
424C22×C32—41no—
425C22×C32C22×D411yescharacteristic
426C2×C3⋊D3—21no—
427C2×C3⋊D3—21no—
428C2×C3⋊D3—22no—
429C2×C3⋊D3—41no—
430C2×C3⋊D3—41no—
431C2×C3⋊D3—84no—
432C2×C3⋊D3C4×D412yes—
433C2×C3×D3—22no—
434C2×C3×D3—22no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439D32—84no—
440C32×C4—41no—
441C32×C4C23×C411yescharacteristic
442C32×C4C2×#4111yescharacteristic
443C3⋊Dic3—41no—
444C3⋊Dic3C4×D412yes—
445C3×Dic3—21no—
446C3×Dic3—21no—
447C3×Dic3—21no—
448C3×Dic3—21no—
449C3×Dic3—41no—
450C3×Dic3—41no—
451C22×D4—91no—
452C22×D4—91no—
453C2×D8—31no—
454C2×D8—31no—
455C2×D8—91no—
456C2×D8—91no—
457C2×D8—98no—
458C2×M16—91no—
459C22×C8—91no—
460C4×D4—31no—
461C4×D4—31no—
462C4×D4—31no—
463C4×D4—31no—
464C4×D4—91no—
465C4×D4—91no—
466C4×D4—91no—
467C4×D4—91no—
468C4×D4—181no—
469C4×D4—181no—
470C4×D4—181no—
471C4×D4—181no—
472#117—91no—
473#117—91no—
474#117—91no—
475C2×C22⋊C4—181no—
476C2×C22⋊C4—181no—
477C2×C22⋊C4—181no—
478C2×C22⋊C4—181no—
479#107—31no—
480#107—91no—
481#106—31no—
482#106—91no—
483#102—31no—
484#102—31no—
485#102—91no—
486#102—91no—
487#102—91no—
488#102—91no—
489#102—91no—
490#102D3211yescharacteristic, complemented
491#97—31no—
492#97—91no—
493C4×C8—31no—
494C4×C8—91no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—41no—
498C23×C3—61no—
499C23×C3—61no—
500C22×D3—21no—
501C22×D3—21no—
502C22×D3—31no—
503C22×D3—31no—
504C22×D3—61no—
505C22×D3—64no—
506C22×D3—64no—
507C22×D3—64no—
508C22×D3—64no—
509C22×D3—61no—
510C22×D3—61no—
511C22×D3—124no—
512C22×D3—121no—
513C22×D3—241no—
514C22×D3—241no—
515C22×D3—241no—
516C22×D3—241no—
517C22×D3—241no—
518C22×D3—241no—
519C22×D3—241no—
520C22×D3—241no—
521C22×D3—242no—
522C22×D3—242no—
523C3×D4—21no—
524C3×D4—21no—
525C3×D4—22no—
526C3×D4—32no—
527C3×D4—32no—
528C3×D4—41no—
529C3×D4—61no—
530C3×D4—61no—
531C3×D4C2×C4×D312yes—
532C3×D4C2×C4×D312yes—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—31no—
537C2×C3×C4—31no—
538C2×C3×C4—31no—
539C2×C3×C4—31no—
540C2×C3×C4—41no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—241no—
544C2×C3×C4—241no—
545C2×C3×C4—241no—
546C2×C3×C4—241no—
547C2×C3×C4C23×D311yescharacteristic
548C2×C3×C4C23×D311yescharacteristic
549#67—64no—
550#67—64no—
551#67—64no—
552#67—64no—
553#67—124no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—31no—
557C2×Dic3—31no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—81no—
562C2×Dic3—81no—
563C2×Dic3—121no—
564C2×Dic3—241no—
565C2×Dic3—241no—
566C2×Dic3D3×D411yescharacteristic
567C2×Dic3D3×D411yescharacteristic
568C2×Dic3D3×D411yescharacteristic
569C2×Dic3D3×D411yescharacteristic
570D12—21no—
571D12—21no—
572D12—32no—
573D12—32no—
574D12—62no—
575D12—61no—
576D12—61no—
577D12—121no—
578D12C2×C4×D312yes—
579D12C2×C4×D312yes—
580C4×D3—32no—
581C4×D3—32no—
582C4×D3—32no—
583C4×D3—32no—
584C4×D3—62no—
585C4×D3—62no—
586C4×D3—81no—
587C4×D3—81no—
588C4×D3—241no—
589C4×D3—241no—
590C4×D3—241no—
591C4×D3—241no—
592C4×D3—241no—
593C4×D3—241no—
594C3×C8—21no—
595C3×C8—21no—
596C3×C8—32no—
597C3×C8—32no—
598C3×C8—41no—
599C3⋊C8—61no—
600C3⋊C8—61no—
601C3⋊C8—121no—
602C3⋊C8C2×C4×D312yes—
603C3⋊C8C2×C4×D312yes—
604C2×C32—42no—
605C2×C32C2×C4×D411yescharacteristic
606C2×C32#57611yescharacteristic
607C2×C32#57611yescharacteristic
608C3⋊D3—22no—
609C3⋊D3—42no—
610C3×D3—42no—
611C3×D3—42no—
612C24—181no—
613C24—181no—
614C2×D4—31no—
615C2×D4—31no—
616C2×D4—94no—
617C2×D4—94no—
618C2×D4—91no—
619C2×D4—182no—
620C2×D4—182no—
621C2×D4—181no—
622C2×D4—181no—
623C2×D4C2×D3211yescharacteristic
624C22×C4—61no—
625C22×C4—61no—
626C22×C4—61no—
627C22×C4—61no—
628C22×C4—91no—
629C22×C4—181no—
630C22×C4—181no—
631C22×C4—181no—
632C22×C4—181no—
633D8—34no—
634D8—34no—
635D8—94no—
636D8—94no—
637M16—182no—
638C2×C8—31no—
639C2×C8—31no—
640C2×C8—94no—
641C2×C8—91no—
642C2×C8C2×D3211yescharacteristic
643C4⋊C4—31no—
644C4⋊C4—31no—
645C4⋊C4—91no—
646C4⋊C4—91no—
647C4⋊C4—91no—
648C4⋊C4C2×D3211yescharacteristic
649C22⋊C4—61no—
650C22⋊C4—61no—
651C22⋊C4—61no—
652C22⋊C4—61no—
653C22⋊C4—91no—
654C22⋊C4—91no—
655C22⋊C4—181no—
656C22⋊C4—181no—
657C22⋊C4—181no—
658C22⋊C4—181no—
659C22⋊C4—181no—
660C22⋊C4—181no—
661C42—31no—
662C42—31no—
663C42—181no—
664C42—181no—
665C22×C3—22no—
666C22×C3—22no—
667C22×C3—21no—
668C22×C3—42no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—62no—
674C22×C3—62no—
675C22×C3—81no—
676C22×C3—81no—
677C22×C3—121no—
678C22×C3—121no—
679C22×C3—121no—
680C22×C3—121no—
681C22×C3C2×D3×D411yescharacteristic
682C22×C3C2×D3×D411yescharacteristic
683C2×D3—22no—
684C2×D3—22no—
685C2×D3—32no—
686C2×D3—32no—
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—62no—
692C2×D3—61no—
693C2×D3—61no—
694C2×D3—61no—
695C2×D3—61no—
696C2×D3—62no—
697C2×D3—62no—
698C2×D3—121no—
699C2×D3—121no—
700C2×D3—122no—
701C2×D3—121no—
702C2×D3—121no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—241no—
706C2×D3—241no—
707C2×D3—244no—
708C2×D3—244no—
709C2×D3—244no—
710C2×D3—244no—
711C2×D3—248no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4—61no—
717C3×C4—61no—
718C3×C4—61no—
719C3×C4—61no—
720C3×C4—81no—
721C3×C4—121no—
722C3×C4—121no—
723C3×C4C22×C4×D311yescharacteristic
724C3×C4C22×C4×D311yescharacteristic
725C3×C4D3×#4111yescharacteristic
726C3×C4D3×#4111yescharacteristic
727Dic3—21no—
728Dic3—21no—
729Dic3—21no—
730Dic3—21no—
731Dic3—32no—
732Dic3—32no—
733Dic3—41no—
734Dic3—41no—
735Dic3—62no—
736Dic3—121no—
737Dic3—121no—
738Dic3—241no—
739C32#294811yescharacteristic, complemented, Sylow
740C23—21no—
741C23—61no—
742C23—61no—
743C23—91no—
744C23—184no—
745C23—184no—
746C23—181no—
747C23—721no—
748C23—721no—
749C23—721no—
750C23—721no—
751D4—21no—
752D4—32no—
753D4—32no—
754D4—61no—
755D4—61no—
756D4—92no—
757D4—184no—
758D4—184no—
759D4—181no—
760D4C4×D3212yes—
761C2×C4—21no—
762C2×C4—31no—
763C2×C4—31no—
764C2×C4—31no—
765C2×C4—31no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—91no—
769C2×C4—92no—
770C2×C4—92no—
771C2×C4—181no—
772C2×C4—241no—
773C2×C4—241no—
774C2×C4—241no—
775C2×C4—241no—
776C2×C4—721no—
777C2×C4—721no—
778C2×C4—721no—
779C2×C4—721no—
780C2×C4C22×D3211yescharacteristic
781C8—21no—
782C8—32no—
783C8—32no—
784C8—181no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—42no—
789C2×C3—42no—
790C2×C3—82no—
791C2×C3—122no—
792C2×C3—122no—
793C2×C3C4×D3×D411yescharacteristic
794C2×C3C4×D3×D411yescharacteristic
795C2×C3#575711yescharacteristic
796C2×C3#576911yescharacteristic
797C2×C3#577411yescharacteristic
798C2×C3#577411yescharacteristic
799D3—42no—
800D3—42no—
801D3—62no—
802D3—62no—
803D3—122no—
804D3—122no—
805D3—122no—
806D3—242no—
807C22—22no—
808C22—41no—
809C22—41no—
810C22—62no—
811C22—62no—
812C22—92no—
813C22—121no—
814C22—121no—
815C22—121no—
816C22—121no—
817C22—181no—
818C22—181no—
819C22—182no—
820C22—361no—
821C22—361no—
822C22—724no—
823C22—724no—
824C22D32×D411yescharacteristic
825C4—41no—
826C4—61no—
827C4—61no—
828C4—61no—
829C4—61no—
830C4—92no—
831C4—121no—
832C4—121no—
833C4—361no—
834C4C2×C4×D3211yescharacteristic
835C4#6431211yescharacteristic
836C3—21no—
837C3#7958811yescharacteristic, complemented
838C3#7986711yescharacteristic, complemented
839C2—42no—
840C2—122no—
841C2—122no—
842C2—182no—
843C2—362no—
844C2#1059425511yescharacteristic
845C2#1059473211yescharacteristic
846C2#1059475511yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×#63926C2
cosocleC2×C32×C4C24
hypercenter#102D32
hypocenterC32#2948
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595223C2semidirect
3. #10594606C2semidirect
4. #10592469C2semidirect
5. C3×#4785C2semidirect
6. C3×#4756C2semidirect
7. #10591430C2semidirect
8. Dic3×#213C2semidirect
9. #10590941C2semidirect
10. #10590910C2semidirect
11. #10590746C2semidirect
12. #10590745C2semidirect
13. #10590589C2semidirect
14. #10590574C2semidirect
15. #10590456C2semidirect
22. C3×D4×Dic3C22semidirect
23. C3×D4×Dic3C22semidirect
26. C3×#893C22semidirect
27. C3×#893C22semidirect
32. #63926C4semidirect
37. #63894C22semidirect
38. #63894C22semidirect
39. Dic3×D12C22semidirect
40. Dic3×D12C22semidirect
46. C32×#102C22semidirect
47. #63659C22semidirect
48. #63648C22semidirect
49. #63636C22semidirect
50. C3×#821C22semidirect
51. C3×#821C22semidirect
52. C3×#815C22semidirect
53. C3×C8×Dic3C22semidirect
54. C3×#808C22semidirect
55. C3×#807C22semidirect
56. #63575C22semidirect
57. #63573C22semidirect
58. #63562C22semidirect
59. #63562C22semidirect
60. #63554C22semidirect
61. Dic3×C3⋊C8C22semidirect
81. #4785D3semidirect
88. #4756D3semidirect
98. D4×C3⋊D3C2×C4semidirect
113. #3802C2×C4semidirect
123. C3×#213C2×C4semidirect
124. C3×#213C2×C4semidirect
143. #3714C2×C4semidirect
144. #3714C2×C4semidirect
145. #3710C2×C4semidirect
160. D4×Dic3C2×D3semidirect
161. D4×Dic3C2×D3semidirect
185. #893C2×D3semidirect
186. #893C2×D3semidirect
211. C3×#102C2×D3semidirect
212. C3×#102C2×D3semidirect
223. #821C2×D3semidirect
224. #821C2×D3semidirect
228. #815C2×D3semidirect
230. C8×Dic3C2×D3semidirect
237. #808C2×D3semidirect
239. #807C2×D3semidirect
375. #213C4×D3semidirect
376. #213C4×D3semidirect
490. #102D32semidirect
739. C32#2948semidirect
837. C3#79588semidirect
838. C3#79867semidirect

Maximal subgroups

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

subgroupindex
#105952232
C2×#639262
#105946062
#105924692
C3×#47852
C3×#47562
#105914302
Dic3×#2132
#105909412
#105909102
#105907462
#105907452
#105905892
#105905742
#105904562
#798673
#795883