Finite Group Databasebeta

← #11887410

Subgroups — #11887410

Order 1152.

907 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5565C211yesmaximal, characteristic, complemented
2C3×#5550C211yesmaximal, characteristic, complemented
3D4×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4#10591179C211yesmaximal, characteristic, complemented
5#10591166C211yesmaximal, characteristic, complemented
6#10591161C211yesmaximal, characteristic, complemented
7#10591160C211yesmaximal, characteristic, complemented
8#10591132C211yesmaximal, characteristic, complemented
9#10591090C211yesmaximal, characteristic, complemented
10#10591083C211yesmaximal, characteristic, complemented
11C2×#63562C211yesmaximal, characteristic, complemented
12#10590348C211yesmaximal, characteristic, complemented
13C4×#3713C211yesmaximal, characteristic, complemented
14#10590278C211yesmaximal, characteristic, complemented
15#10590270C211yesmaximal, characteristic, complemented
16#83614—31nomaximal
17#83495—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
23C3×#939—21no—
24C3×#937—21no—
25C3×#930C2211yescharacteristic
26C3×#930C2211yescharacteristic
27C3×#930C2211yescharacteristic, complemented
28C3×#926C2211yescharacteristic, complemented
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C3×#924C2211yescharacteristic
31C3×#898—21no—
32C3×#894—21no—
33C3×#884—21no—
34C3×#883—21no—
35C3×#67⋊C4—21no—
36C3×D3×C22⋊C4—21no—
37C3×#875C2211yescharacteristic
38C3×C4×D12C2211yescharacteristic
39C3×C4×D12C2211yescharacteristic, complemented
40C3×#870C2211yescharacteristic, complemented
41C2×#3715C2211yescharacteristic, complemented
42C2×#3713C2211yescharacteristic
43C2×#3713C2211yescharacteristic
44#63657C2211yescharacteristic
45#63657C2211yescharacteristic, complemented
46C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
47C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
48#63576C2211yescharacteristic, complemented
49#63576C2211yescharacteristic, complemented
50#63574C2211yescharacteristic, complemented
51#63565C2211yescharacteristic, complemented
52#63565C2211yescharacteristic, complemented
53#63565C2211yescharacteristic, complemented
54#63562C2211yescharacteristic
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic, complemented
61C3×#553—31no—
62C3×#546—31no—
63#5565D311yescharacteristic, complemented
64#5550D311yescharacteristic, complemented
65#5238—31no—
66#5233—31no—
67#5217—31no—
68C2×#832—31no—
69#5068—31no—
70#5066—31no—
71#5057—31no—
72#5056—31no—
73#5048—31no—
74#5044—31no—
75#5041—31no—
76#5038—31no—
77#5038—31no—
78#5037—31no—
79#5036—31no—
80#5035—31no—
81#5016—31no—
82C4×#213—31no—
83C4×#213—31no—
84D4×C3⋊C8—31no—
85D4×C3⋊C8—31no—
86D4×C3⋊C8—61no—
87#5009—31no—
88#5003—31no—
89#5002—31no—
90#4970—31no—
91C2×#809—31no—
92C23×C3×D3—21no—
93C2×C32×D4D411yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C3×#235—22no—
102C3×#235—41no—
103C2×C3×D12—22no—
104C2×C3×D12—21no—
105C2×C3×D12—41no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—21no—
112C2×C3×Dic6C2311yescharacteristic
113C32×C4⋊C4D411yescharacteristic
114C32×C22⋊C4D411yescharacteristic
115C32×C22⋊C4D411yescharacteristic
116C32×C42C2311yescharacteristic
117C2×C3⋊(C3⋊C8)—41no—
118C2×C3⋊(C3⋊C8)—41no—
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C3×#217—21no—
124C3×#217—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×C4⋊Dic3C2311yescharacteristic
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×C4×Dic3—21no—
141#3715—41no—
142#3713—22no—
143#3713—41no—
144#3297—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#235C2×D311yescharacteristic
148C22×D12C2×D311yescharacteristic
149C3×#126—61no—
150C3×#125—31no—
151C3×#124—31no—
152C3×#123—61no—
153C3×#123—61no—
154C3×C22⋊Q8—31no—
155C3×#121—31no—
156C3×#121—31no—
157C3×#121—31no—
158C3×#121—61no—
159C3×#121—61no—
160C3×#120—61no—
161C3×C4×D4—21no—
162C3×C4×D4—31no—
163C3×C4×D4—31no—
164C3×C4×D4—61no—
165C3×C4×D4C2×D311yescharacteristic
166C3×C4×D4C2×D311yescharacteristic
167C3×#117—31no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C22⋊C4—61no—
170C2×#215—31no—
171#939—21no—
172#937—21no—
173C2×#214—31no—
174C2×#213—31no—
175C2×#213—31no—
176C2×#213—31no—
177C2×#213—31no—
178#930C2×D311yescharacteristic
179#930C2×D311yescharacteristic
180#930C2×D311yescharacteristic, complemented
181#926C2×D311yescharacteristic, complemented
182C2×C4⋊Dic3C2×D311yescharacteristic
183#924C2×D311yescharacteristic
184C22×C3⋊C8—31no—
185C22×C3⋊C8—31no—
186C22×C3⋊C8—31no—
187C22×C3⋊C8—31no—
188C22×C3⋊C8—61no—
189C22×C3⋊C8—61no—
190#898—21no—
191#894—21no—
192#884—21no—
193#883—21no—
194#67⋊C4—21no—
195D3×C22⋊C4—21no—
196#875C2×D311yescharacteristic
197C4×D12C2×D311yescharacteristic
198C4×D12C2×D311yescharacteristic, complemented
199#870C2×D311yescharacteristic, complemented
200#835—31no—
201#835—31no—
202#835—31no—
203#832—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832—31no—
210#830—31no—
211#830—31no—
212#830—31no—
213#830—31no—
214#830—61no—
215#830—61no—
216#810—31no—
217#810—31no—
218#810—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#808—31no—
227#808—31no—
228#807—31no—
229#807—31no—
230#807—31no—
231#807—31no—
232C4⋊(C3⋊C8)—31no—
233C4⋊(C3⋊C8)—31no—
234C4⋊(C3⋊C8)—61no—
235C4×C3⋊C8—31no—
236C4×C3⋊C8—31no—
237C4×C3⋊C8—61no—
238C23×C32C2×D411yescharacteristic
239C23×C32C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—42no—
244C22×C3×D3—42no—
245C22×C3×D3—81no—
246C32×D4—22no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256C3×#67—42no—
257C3×#67—42no—
258C3×#67—81no—
259C3×#67—81no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—81no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—42no—
272C3×D12#4112yes—
273C3×C4×D3—42no—
274C3×C4×D3—81no—
275C3×C4×D3—81no—
276C3×Dic6—21no—
277C3×Dic6—21no—
278C3⋊(C3⋊C8)—21no—
279C3⋊(C3⋊C8)—21no—
280C3⋊(C3⋊C8)—21no—
281C3⋊(C3⋊C8)—21no—
282#553—31no—
283#546—31no—
284#488—91no—
285#484—91no—
286#482—91no—
287#478—91no—
288#466—91no—
289#465—91no—
290#463—91no—
291#449—91no—
292#447—91no—
293C4×D8—91no—
294C8×D4—91no—
295#416—91no—
296C2×#102—91no—
297C24×C3—61no—
298C23×D3—21no—
299C3×#41—62no—
300C3×#41—121no—
301C2×C3×Q8—31no—
302C2×C3×D4—21no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C2×C3×D4—62no—
307C2×C3×D4—61no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C2×C3×D4—61no—
311C2×C3×D4—61no—
312C2×C3×D4—121no—
313C2×C3×D4#6711yescharacteristic
314C2×C3×D4#6711yescharacteristic
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—61no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C22×C3×C4—61no—
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C2×#67—21no—
326C2×#67—21no—
327C2×#67—21no—
328C2×#67—21no—
329C22×Dic3—21no—
330#235—22no—
331#235—41no—
332C2×D12—22no—
333C2×D12—21no—
334C2×D12—41no—
335C2×D12C22×D311yescharacteristic
336C2×D12C22×D311yescharacteristic
337C2×D12C22×D311yescharacteristic
338C2×C4×D3—21no—
339C2×C4×D3—21no—
340C2×C4×D3—21no—
341C2×Dic6C22×D311yescharacteristic
342C3×C4⋊C4—21no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4#6711yescharacteristic
352C3×C4⋊C4#6711yescharacteristic
353C3×C22⋊C4—21no—
354C3×C22⋊C4—21no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4#6711yescharacteristic
365C3×C22⋊C4#6711yescharacteristic
366C3×C22⋊C4#6711yescharacteristic
367C3×C22⋊C4#6711yescharacteristic
368C3×C42—21no—
369C3×C42—61no—
370C3×C42C22×D311yescharacteristic
371C3×C42C22×D311yescharacteristic
372#217—21no—
373#217—21no—
374#215—121no—
375#214—121no—
376#213—62no—
377#213—62no—
378#213—121no—
379#213—121no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—21no—
387C4⋊Dic3—21no—
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391C4⋊Dic3C22×D311yescharacteristic
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394Dic3⋊C4—21no—
395C4×Dic3—21no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—121no—
409C2×C3⋊C8—121no—
410C2×C3⋊C8—121no—
411C2×C3⋊C8—121no—
412C2×C3⋊C8—122no—
413C2×C3⋊C8—122no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32#13512yes—
420C22×C32C22×D411yescharacteristic
421C2×C3×D3—22no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—84no—
431C32×C4—21no—
432C32×C4—21no—
433C32×C4—21no—
434C32×C4—21no—
435C32×C4C2×#4111yescharacteristic
436C32×C4H(5,𝔽2)11yescharacteristic
437C3×Dic3—41no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C2×#41—31no—
443C22×D4—31no—
444C2×SD16—91no—
445C2×D8—91no—
446C2×D8—91no—
447C22×C8—91no—
448C22×C8—91no—
449#126—61no—
450#125—31no—
451#124—31no—
452#123—61no—
453#123—61no—
454C22⋊Q8—31no—
455#121—31no—
456#121—31no—
457#121—31no—
458#121—61no—
459#121—61no—
460#120—61no—
461C4×D4—31no—
462C4×D4—31no—
463C4×D4—61no—
464C4×D4D3211yescharacteristic
465#117—31no—
466C2×C4⋊C4—31no—
467C2×C22⋊C4—61no—
468#107—91no—
469#107—91no—
470#106—91no—
471C4⋊C8—91no—
472#103—91no—
473#103—91no—
474#103—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481#102—91no—
482C22⋊C8—91no—
483C22⋊C8—91no—
484C4×C8—91no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—61no—
488C23×C3—61no—
489C23×C3—61no—
490C23×C3—122no—
491C23×C3—122no—
492C23×C3—241no—
493C23×C3C2×#6711yescharacteristic
494C23×C3C2×#6711yescharacteristic
495C23×C3C2×#6711yescharacteristic
496C23×C3C2×#6711yescharacteristic
497C22×D3—21no—
498C22×D3—21no—
499C22×D3—21no—
500C22×D3—42no—
501C22×D3—42no—
502C22×D3—81no—
503C3×Q8—61no—
504C3×Q8—61no—
505C3×D4—24no—
506C3×D4—22no—
507C3×D4—22no—
508C3×D4—32no—
509C3×D4—61no—
510C3×D4—61no—
511C3×D4—61no—
512C3×D4—61no—
513C3×D4—61no—
514C3×D4—122no—
515C3×D4—122no—
516C3×D4—122no—
517C3×D4—241no—
518C3×D4—241no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—122no—
542C2×C3×C4—241no—
543C2×C3×C4—241no—
544C2×C3×C4—241no—
545C2×C3×C4C2×#6711yescharacteristic
546C2×C3×C4C2×#6711yescharacteristic
547C2×C3×C4C2×#6711yescharacteristic
548C2×C3×C4C2×#6711yescharacteristic
549C2×C3×C4C2×#6711yescharacteristic
550C2×C3×C4C2×#6711yescharacteristic
551C2×C3×C4C2×#6711yescharacteristic
552C2×C3×C4C2×#6711yescharacteristic
553C2×C3×C4C23×D311yescharacteristic
554C2×C3×C4C23×D311yescharacteristic
555#67—42no—
556#67—42no—
557#67—81no—
558#67—81no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—81no—
565D12—21no—
566D12—21no—
567D12—21no—
568D12—21no—
569D12—21no—
570D12—42no—
571D12#23712yes—
572C4×D3—42no—
573C4×D3—81no—
574C4×D3—81no—
575Dic6—21no—
576Dic6—21no—
577C3⋊C8—62no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—61no—
582C3⋊C8—61no—
583C3⋊C8—61no—
584C3⋊C8—61no—
585C3⋊C8—61no—
586C3⋊C8—121no—
587C3⋊C8—121no—
588C3⋊C8—121no—
589C2×C32—22no—
590C2×C32—41no—
591C2×C32#54611yescharacteristic
592C2×C32C2×#13511yescharacteristic
593C2×C32#57611yescharacteristic
594C3×D3—42no—
595C3×D3—81no—
596C3×D3—81no—
597C24—61no—
598#41—62no—
599#41—121no—
600C2×Q8—31no—
601C2×D4—31no—
602C2×D4—31no—
603C2×D4—31no—
604C2×D4—62no—
605C2×D4—61no—
606C2×D4—61no—
607C2×D4—61no—
608C2×D4—61no—
609C2×D4—61no—
610C2×D4—121no—
611C2×D4#62511yescharacteristic
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4C2×D3211yescharacteristic
617C22×C4C2×D3211yescharacteristic
618SD16—361no—
619D8—182no—
620D8—361no—
621C2×C8—91no—
622C2×C8—91no—
623C2×C8—91no—
624C2×C8—91no—
625C2×C8—361no—
626C2×C8—361no—
627C4⋊C4—31no—
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4—31no—
631C4⋊C4—61no—
632C4⋊C4—61no—
633C4⋊C4—61no—
634C4⋊C4—61no—
635C4⋊C4#62511yescharacteristic
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—61no—
643C22⋊C4—61no—
644C22⋊C4—61no—
645C22⋊C4#62511yescharacteristic
646C22⋊C4#62511yescharacteristic
647C42—61no—
648C42C2×D3211yescharacteristic
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—22no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—22no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—62no—
667C22×C3—121no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3—244no—
676C22×C3#95012yes—
677C22×C3#95012yes—
678C22×C3C22×#6711yescharacteristic
679C22×C3C22×#6711yescharacteristic
680C2×D3—22no—
681C2×D3—41no—
682C2×D3—41no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—84no—
690C3×C4—22no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—21no—
698C3×C4—21no—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—41no—
704C3×C4—121no—
705C3×C4—121no—
706C3×C4—121no—
707C3×C4—121no—
708C3×C4—121no—
709C3×C4C2×#23711yescharacteristic
710C3×C4#100411yescharacteristic
711C3×C4D3×#4111yescharacteristic
712C3×C4#100911yescharacteristic
713Dic3—41no—
714Dic3—41no—
715Dic3—41no—
716Dic3—41no—
717Dic3—41no—
718C32#329711yescharacteristic, complemented, Sylow
719C23—61no—
720C23—61no—
721C23—61no—
722C23—122no—
723C23—122no—
724C23—241no—
725C23C2×#62511yescharacteristic
726C23C2×#62511yescharacteristic
727Q8—61no—
728Q8—61no—
729D4—22no—
730D4—32no—
731D4—61no—
732D4—61no—
733D4—61no—
734D4—61no—
735D4—61no—
736D4—122no—
737D4—122no—
738D4—122no—
739D4—241no—
740D4—241no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—122no—
751C2×C4—241no—
752C2×C4—241no—
753C2×C4—241no—
754C2×C4C2×#62511yescharacteristic
755C2×C4C2×#62511yescharacteristic
756C2×C4C2×#62511yescharacteristic
757C2×C4C2×#62511yescharacteristic
758C2×C4C22×D3211yescharacteristic
759C8—181no—
760C8—181no—
761C8—181no—
762C8—181no—
763C2×C3—22no—
764C2×C3—22no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—42no—
769C2×C3—42no—
770C2×C3—41no—
771C2×C3—41no—
772C2×C3—122no—
773C2×C3—241no—
774C2×C3—241no—
775C2×C3#580611yescharacteristic
776C2×C3C2×#95011yescharacteristic
777C2×C3C2×#95011yescharacteristic
778C2×C3#582911yescharacteristic
779C2×C3#583511yescharacteristic
780C2×C3#583511yescharacteristic
781D3—42no—
782D3—81no—
783D3—81no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—62no—
790C22—121no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22—121no—
795C22—121no—
796C22—121no—
797C22—121no—
798C22—244no—
799C22#6382212yes—
800C22C22×#62511yescharacteristic
801C4—21no—
802C4—21no—
803C4—21no—
804C4—21no—
805C4—121no—
806C4—121no—
807C4—121no—
808C4—121no—
809C4—121no—
810C4D3×#23711yescharacteristic
811C4#6431411yescharacteristic
812C3—21no—
813C3#8349511yescharacteristic, complemented
814C3#8361411yescharacteristic, complemented
815C2—22no—
816C2—41no—
817C2—122no—
818C2—241no—
819C2—241no—
820C2C2×#6382211yescharacteristic
821C2#1059524411yescharacteristic
822C2#1059544411yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5565C2semidirect
2. C3×#5550C2semidirect
3. D4×C3⋊(C3⋊C8)C2semidirect
4. #10591179C2semidirect
5. #10591166C2semidirect
6. #10591161C2semidirect
7. #10591160C2semidirect
8. #10591132C2semidirect
9. #10591090C2semidirect
10. #10591083C2semidirect
11. C2×#63562C2semidirect
12. #10590348C2semidirect
13. C4×#3713C2semidirect
14. #10590278C2semidirect
15. #10590270C2semidirect
22. C22×C3⋊(C3⋊C8)C22semidirect
27. C3×#930C22semidirect
28. C3×#926C22semidirect
39. C3×C4×D12C22semidirect
40. C3×#870C22semidirect
41. C2×#3715C22semidirect
45. #63657C22semidirect
46. C4⋊(C3⋊(C3⋊C8))C22semidirect
47. C4×C3⋊(C3⋊C8)C22semidirect
48. #63576C22semidirect
49. #63576C22semidirect
50. #63574C22semidirect
51. #63565C22semidirect
52. #63565C22semidirect
53. #63565C22semidirect
60. #63562C22semidirect
63. #5565D3semidirect
64. #5550D3semidirect
180. #930C2×D3semidirect
181. #926C2×D3semidirect
198. C4×D12C2×D3semidirect
199. #870C2×D3semidirect
718. C32#3297semidirect
813. C3#83495semidirect
814. C3#83614semidirect

Maximal subgroups

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

subgroupindex
C3×#55652
C3×#55502
D4×C3⋊(C3⋊C8)2
#105911792
#105911662
#105911612
#105911602
#105911322
#105910902
#105910832
C2×#635622
#105903482
C4×#37132
#105902782
#105902702
#836143
#834953