Finite Group Databasebeta

← #11884334

Subgroups — #11884334

Order 1152.

1055 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#919C211yesmaximal, characteristic, complemented
2#10595428C211yesmaximal, characteristic, complemented
3#10595358C211yesmaximal, characteristic, complemented
4C2×#63798C211yesmaximal, characteristic, complemented
5#10592888C211yesmaximal, characteristic, complemented
6C3×#5190C211yesmaximal, characteristic, complemented
7#10591656C211yesmaximal, characteristic, complemented
8#10591652C211yesmaximal, characteristic, complemented
9#10591597C211yesmaximal, characteristic, complemented
10#10591586C211yesmaximal, characteristic, complemented
11#10591567C211yesmaximal, characteristic, complemented
12#10591564C211yesmaximal, characteristic, complemented
13#10590829C211yesmaximal, characteristic, complemented
14#10590771C211yesmaximal, characteristic, complemented
15#10590726C211yesmaximal, characteristic, complemented
16#83921—31nomaximal
17#81882—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic, complemented
20C2×#3802C2211yescharacteristic
21C2×#3796C2211yescharacteristic
22C2×C32×Q16C2211yescharacteristic, complemented
23#64155C2211yescharacteristic
24#64155C2211yescharacteristic
25C2×#3743C2211yescharacteristic
26C3×#947C2211yescharacteristic
27C3×#944C2211yescharacteristic, complemented
28C2×C3×#216C2211yescharacteristic, complemented
29C2×C3×#215C2211yescharacteristic
30C2×C3×#215C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic, complemented
32C3×#919—24no—
33C2×C3×D24C2211yescharacteristic
34C2×C3×#204C2211yescharacteristic
35C2×C3×D3×C8C2211yescharacteristic, complemented
36#63922—21no—
37D3×(C2×D3)⋊C4—21no—
38#63908C2211yescharacteristic
39#63905—21no—
40C4×#626C2211yescharacteristic
41Dic3×D12C2211yescharacteristic
42Dic3×D12C2211yescharacteristic, complemented
43#63886—21no—
44#63885—21no—
45#63884—21no—
46D3×Dic3⋊C4—21no—
47#63856C2211yescharacteristic, complemented
48#63850—21no—
49C2×#3715C2211yescharacteristic
50C2×#3713C2211yescharacteristic
51#63798—24no—
52#63662C2211yescharacteristic, complemented
53#63662C2211yescharacteristic, complemented
54#63644C2211yescharacteristic, complemented
55C3×#815C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic, complemented
61#63557C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×C3×#135—31no—
64#5829—31no—
65#5824—31no—
66C2×#919D311yescharacteristic, complemented
67C2×#914—31no—
68C2×#911—31no—
69#5726—31no—
70#5676—31no—
71C3×#497—31no—
72#5239—31no—
73#5238—31no—
74#5190D311yescharacteristic, complemented
75#5189—31no—
76#5189—31no—
77#5189—61no—
78#5187—31no—
79#5187—31no—
80#5173—31no—
81#5172—31no—
82#5171—31no—
83#5169—31no—
84#5169—31no—
85#5165—31no—
86#5162—31no—
87#5152—31no—
88#5114—31no—
89#5111—31no—
90#5083—31no—
91#5057—31no—
92#4711—31no—
93#4706—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C2×C4×C3⋊D3C2311yescharacteristic
98C3×#239—22no—
99C3×#239—22no—
100C3×#239—41no—
101C3×#239—41no—
102C2×C3×D12—21no—
103C2×C3×D12—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×#626—21no—
112C2×#626D411yescharacteristic
113C2×#625—21no—
114C2×#625—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117C2×D3×Dic3—21no—
118#3802—22no—
119#3802—41no—
120#3796—22no—
121#3796—41no—
122C32×Q16—22no—
123C2×C32×C8C2311yescharacteristic
124#3752—21no—
125#3752—21no—
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128#3750—21no—
129#3750—21no—
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131#3743—22no—
132C3×#216—41no—
133C3×#215—22no—
134C3×#215—22no—
135C3×#215—41no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×D24D414yescomplemented
144C3×#204—22no—
145C3×D3×C8—22no—
146#3724—21no—
147Dic3⋊Dic3D411yescharacteristic
148#3722D411yescharacteristic
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3—21no—
153(C2×D3)⋊Dic3D411yescharacteristic
154#3715—22no—
155#3713—22no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×#239—31no—
160C2×#239C2×D311yescharacteristic
161C2×#239C2×D311yescharacteristic, complemented
162C2×#237—31no—
163C2×D3×D4—31no—
164C2×D3×D4—31no—
165C3×#135—64no—
166C2×C3×Q16—21no—
167C2×C3×Q16—31no—
168C2×C3×Q16C2×D311yescharacteristic, complemented
169C2×C3×Q16C2×D311yescharacteristic, complemented
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×SD16—31no—
174C2×C3×D8—31no—
175C22×C3×C8—31no—
176C3×C4⋊Q8—31no—
177C3×#124—31no—
178#947C2×D311yescharacteristic
179#946—31no—
180#946—31no—
181#946—31no—
182#946—31no—
183#946—31no—
184#946—61no—
185#946—61no—
186#944C2×D311yescharacteristic, complemented
187C2×#216C2×D311yescharacteristic, complemented
188C2×#215—31no—
189C2×#215C2×D311yescharacteristic
190C2×#215C2×D311yescharacteristic
191C2×#215C2×D311yescharacteristic, complemented
192#939—61no—
193#939—61no—
194#938—31no—
195#937—61no—
196#935—61no—
197D4×Dic3—31no—
198D4×Dic3—31no—
199C2×#214—31no—
200C2×#213—31no—
201C2×#213—31no—
202#930—31no—
203#929—61no—
204#929—61no—
205C4×#67—31no—
206C2×(C2×D3)⋊C4—61no—
207#924—31no—
208C2×Dic3⋊C4—61no—
209#919—24no—
210#914—64no—
211#911—64no—
212C2×D24C2×D311yescharacteristic
213C2×#204C2×D311yescharacteristic
214C2×ΓL(1,𝔽25)—31no—
215C2×ΓL(1,𝔽25)—31no—
216C2×ΓL(1,𝔽25)—61no—
217C2×D3×C8C2×D311yescharacteristic, complemented
218#895—61no—
219#894—61no—
220#894—61no—
221D3×C4⋊C4—61no—
222#884—61no—
223#883—61no—
224#882—61no—
225D3×C22⋊C4—61no—
226C4×D12—31no—
227C4×D12—31no—
228C4×D12—31no—
229C3×#97—31no—
230#835—31no—
231#835—31no—
232#835—31no—
233#835—31no—
234#835—31no—
235#835—61no—
236#835—61no—
237#832—31no—
238#832—31no—
239#832—31no—
240#830—31no—
241#821—31no—
242#821—31no—
243#821—31no—
244(C2×D3)⋊C8—31no—
245(C2×D3)⋊C8—31no—
246(C2×D3)⋊C8—31no—
247#817—31no—
248#817—31no—
249#817—61no—
250#816—31no—
251#815C2×D311yescharacteristic, complemented
252Dic3⋊C8—31no—
253C4⋊(C3⋊C8)—31no—
254C22×C3⋊D3C2×D411yescharacteristic
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3C2×D411yescharacteristic
259C2×D32—42no—
260C2×D32—42no—
261C2×D32—81no—
262C32×Q8—21no—
263C32×Q8—21no—
264C32×Q8—21no—
265C32×Q8—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4C2411yescharacteristic
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3C2×D411yescharacteristic
272C4×C3⋊D3—21no—
273C4×C3⋊D3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—42no—
283C3×D12—42no—
284C3×D12C2×D412yes—
285C3×D12C2×D412yes—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×C4×D3—42no—
289C3×C4×D3—42no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292#626—41no—
293#626—42no—
294#625—42no—
295#625—81no—
296D3×Dic3—42no—
297D3×Dic3—42no—
298D3×Dic3—81no—
299C32×C8C2×D412yes—
300C3⋊(C3⋊C8)—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—31no—
305#547—91no—
306#546—91no—
307#497—31no—
308#470—91no—
309#465—91no—
310#463—91no—
311#461—91no—
312#452—91no—
313#452—91no—
314#450—91no—
315#449—91no—
316#442—91no—
317#435—91no—
318C23×D3—61no—
319C23×D3—61no—
320C3×#41—62no—
321C3×#41—62no—
322C3×#41—121no—
323C3×#41—121no—
324C2×C3×Q8—21no—
325C2×C3×Q8—21no—
326C2×C3×Q8—31no—
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C22×C3×C4—31no—
337C22×C3×C4—61no—
338C22×C3×C4—61no—
339C2×#67—31no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C22×Dic3—61no—
346C22×Dic3—61no—
347C22×Dic3—61no—
348#239—22no—
349#239—22no—
350#239—41no—
351#239—41no—
352#239—62no—
353#239—121no—
354#237—62no—
355#237—121no—
356D3×D4—62no—
357D3×D4—62no—
358D3×D4—121no—
359D3×D4—121no—
360C2×D12—21no—
361C2×D12—21no—
362C2×D12—31no—
363C2×D12—61no—
364C2×D12C22×D311yescharacteristic
365C2×D12C22×D311yescharacteristic
366C2×D12C22×D311yescharacteristic
367C2×C4×D3—21no—
368C2×C4×D3—21no—
369C2×C4×D3—31no—
370C2×C4×D3—31no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—61no—
374C2×C4×D3—61no—
375C2×C4×D3C22×D311yescharacteristic
376C2×Dic6C22×D311yescharacteristic
377C3×Q16—22no—
378C3×Q16—22no—
379C3×Q16—42no—
380C3×Q16—121no—
381C3×SD16—62no—
382C3×SD16—62no—
383C3×SD16—62no—
384C3×SD16—121no—
385C3×D8—34no—
386C2×C3×C8—21no—
387C2×C3×C8—31no—
388C2×C3×C8—31no—
389C2×C3×C8—62no—
390C2×C3×C8C22×D311yescharacteristic
391C2×C3×C8C22×D311yescharacteristic
392C3×C4⋊C4—61no—
393C3×C4⋊C4—61no—
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C42—31no—
397#217—31no—
398#217—61no—
399#217—61no—
400#217—61no—
401#217—61no—
402#216—41no—
403#215—22no—
404#215—22no—
405#215—41no—
406#215—62no—
407#214—62no—
408#213—62no—
409#213—62no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—21no—
412(C2×D3)⋊C4—31no—
413(C2×D3)⋊C4—31no—
414(C2×D3)⋊C4—31no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—121no—
424(C2×D3)⋊C4—121no—
425C4⋊Dic3—31no—
426C4⋊Dic3—31no—
427C4⋊Dic3—31no—
428C4⋊Dic3—31no—
429C4⋊Dic3—31no—
430C4⋊Dic3—61no—
431C4⋊Dic3—61no—
432Dic3⋊C4—21no—
433Dic3⋊C4—21no—
434Dic3⋊C4—31no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438Dic3⋊C4—61no—
439Dic3⋊C4—61no—
440Dic3⋊C4—61no—
441Dic3⋊C4—121no—
442Dic3⋊C4—121no—
443C4×Dic3C22×D311yescharacteristic
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—61no—
447C2×C3⋊C8C22×D311yescharacteristic
448C2×C3⋊C8C22×D311yescharacteristic
449D24#6714yescomplemented
450#204—22no—
451ΓL(1,𝔽25)—62no—
452ΓL(1,𝔽25)—62no—
453ΓL(1,𝔽25)—122no—
454D3×C8—22no—
455C22×C32C22×D411yescharacteristic
456C2×C3⋊D3—21no—
457C2×C3⋊D3—21no—
458C2×C3⋊D3—21no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471D32—84no—
472C32×C4—41no—
473C32×C4—41no—
474C32×C4C22×D411yescharacteristic
475C32×C4H(5,𝔽2)11yescharacteristic
476C3⋊Dic3—21no—
477C3⋊Dic3—41no—
478C3⋊Dic3—41no—
479C3×Dic3—21no—
480C3×Dic3—21no—
481C3×Dic3—21no—
482C3×Dic3—41no—
483C2×#41—31no—
484C2×#41—31no—
485C2×#41—91no—
486C22×D4—91no—
487AGL(1,ℤ/8)—184no—
488#135—64no—
489C2×Q16—31no—
490C2×Q16D3211yescharacteristic, complemented
491C2×SD16—31no—
492C2×SD16—31no—
493C2×SD16—31no—
494C2×SD16—31no—
495C2×SD16—91no—
496C2×D8—31no—
497C2×D8—91no—
498C2×M16—91no—
499C22×C8—31no—
500C4⋊Q8—31no—
501#124—31no—
502#123—181no—
503#123—181no—
504#123—181no—
505C22⋊Q8—91no—
506C22⋊Q8—91no—
507C22⋊Q8—91no—
508#121—91no—
509#121—181no—
510#121—181no—
511#120—181no—
512C4×D4—91no—
513C4×D4—91no—
514C4×D4—91no—
515C2×C4⋊C4—181no—
516C2×C22⋊C4—181no—
517#106—91no—
518C4⋊C8—91no—
519#103—91no—
520#103—91no—
521#103—91no—
522#102—91no—
523#102—91no—
524#102—91no—
525C22⋊C8—91no—
526C22⋊C8—91no—
527#97—31no—
528C23×C3—31no—
529C23×C3—61no—
530C23×C3—61no—
531C23×C3—61no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—31no—
536C22×D3—31no—
537C22×D3—61no—
538C22×D3—122no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3—122no—
542C22×D3—241no—
543C22×D3—241no—
544C22×D3D3×D411yescharacteristic
545C3×Q8—21no—
546C3×Q8—21no—
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—21no—
550C3×Q8—21no—
551C3×Q8—21no—
552C3×Q8—21no—
553C3×Q8—41no—
554C3×Q8—41no—
555C3×Q8—41no—
556C3×Q8—41no—
557C3×Q8—61no—
558C3×Q8—61no—
559C3×D4—32no—
560C3×D4—32no—
561C3×D4—61no—
562C3×D4—61no—
563C3×D4—61no—
564C3×D4—61no—
565C3×D4—122no—
566C3×D4—122no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—31no—
573C2×C3×C4—31no—
574C2×C3×C4—31no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—122no—
581C2×C3×C4—122no—
582C2×C3×C4C23×D311yescharacteristic
583C2×C3×C4C23×D311yescharacteristic
584#67—121no—
585#67—122no—
586#67—122no—
587#67—122no—
588#67—241no—
589#67—241no—
590C2×Dic3—21no—
591C2×Dic3—31no—
592C2×Dic3—31no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—121no—
599C2×Dic3—121no—
600C2×Dic3—122no—
601C2×Dic3—122no—
602C2×Dic3—241no—
603C2×Dic3D3×D411yescharacteristic
604C2×Dic3D3×D411yescharacteristic
605C2×Dic3D3×D411yescharacteristic
606D12—21no—
607D12—21no—
608D12—21no—
609D12—21no—
610D12—42no—
611D12—42no—
612D12—121no—
613D12—122no—
614D12C2×#6712yes—
615D12C2×#6712yes—
616C4×D3—21no—
617C4×D3—21no—
618C4×D3—42no—
619C4×D3—42no—
620C4×D3—61no—
621C4×D3—61no—
622C4×D3—61no—
623C4×D3—61no—
624C4×D3—121no—
625C4×D3—121no—
626C4×D3—122no—
627C4×D3—122no—
628C4×D3—241no—
629Dic6—21no—
630Dic6—21no—
631C3×C8—22no—
632C3×C8—61no—
633C3×C8—61no—
634C3×C8D3×D412yes—
635C3×C8C2×#6712yes—
636C3⋊C8—21no—
637C3⋊C8—21no—
638C3⋊C8—61no—
639C3⋊C8—61no—
640C3⋊C8—121no—
641C2×C32D4211yescharacteristic
642C2×C32#57511yescharacteristic
643C2×C32#57711yescharacteristic
644C3⋊D3—41no—
645C3×D3—42no—
646C3×D3—41no—
647C3×D3—42no—
648C3×D3—81no—
649C24—181no—
650#41—62no—
651#41—62no—
652#41—121no—
653#41—121no—
654#41—182no—
655#41—361no—
656C2×Q8—31no—
657C2×Q8C2×D3211yescharacteristic
658C2×Q8C2×D3211yescharacteristic
659C2×D4—31no—
660C2×D4—31no—
661C2×D4—31no—
662C2×D4—61no—
663C2×D4—61no—
664C2×D4—91no—
665C2×D4—181no—
666C2×D4—181no—
667C2×D4—182no—
668C2×D4—181no—
669C2×D4—361no—
670C22×C4—31no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—91no—
674C22×C4—181no—
675C22×C4—181no—
676C22×C4—181no—
677Q16—22no—
678Q16—121no—
679SD16—62no—
680SD16—62no—
681SD16—62no—
682SD16—121no—
683SD16—182no—
684D8—34no—
685D8—182no—
686M16—182no—
687C2×C8—31no—
688C2×C8—31no—
689C2×C8—62no—
690C2×C8—91no—
691C2×C8C2×D3211yescharacteristic
692C4⋊C4—61no—
693C4⋊C4—61no—
694C4⋊C4—91no—
695C4⋊C4—91no—
696C4⋊C4—91no—
697C4⋊C4—181no—
698C4⋊C4—181no—
699C4⋊C4—181no—
700C22⋊C4—61no—
701C22⋊C4—61no—
702C22⋊C4—91no—
703C22⋊C4—91no—
704C22⋊C4—181no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C42—31no—
711C22×C3—21no—
712C22×C3—62no—
713C22×C3—62no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—61no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3—121no—
723C22×C3—121no—
724C22×C3C2×D3×D411yescharacteristic
725C22×C3C2×D3×D411yescharacteristic
726C2×D3—21no—
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—22no—
730C2×D3—22no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—41no—
737C2×D3—41no—
738C2×D3—61no—
739C2×D3—61no—
740C2×D3—61no—
741C2×D3—61no—
742C2×D3—61no—
743C2×D3—61no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—121no—
747C2×D3—244no—
748C2×D3—244no—
749C3×C4—21no—
750C3×C4—21no—
751C3×C4—41no—
752C3×C4—41no—
753C3×C4—41no—
754C3×C4—41no—
755C3×C4—61no—
756C3×C4—61no—
757C3×C4—61no—
758C3×C4—81no—
759C3×C4—81no—
760C3×C4—121no—
761C3×C4C2×D3×D411yescharacteristic
762C3×C4#100411yescharacteristic
763C3×C4#100411yescharacteristic
764C3×C4C22×#6711yescharacteristic
765Dic3—21no—
766Dic3—21no—
767Dic3—21no—
768Dic3—41no—
769Dic3—61no—
770Dic3—61no—
771Dic3—121no—
772Dic3—121no—
773Dic3—121no—
774Dic3—121no—
775Dic3—121no—
776Dic3—241no—
777Dic3—241no—
778C32#326711yescharacteristic, complemented, Sylow
779C23—31no—
780C23—61no—
781C23—61no—
782C23—61no—
783C23—91no—
784C23—362no—
785C23—362no—
786C23—721no—
787Q8—21no—
788Q8—21no—
789Q8—21no—
790Q8—21no—
791Q8—61no—
792Q8—61no—
793D4—32no—
794D4—32no—
795D4—61no—
796D4—61no—
797D4—61no—
798D4—61no—
799D4—122no—
800D4—122no—
801D4—361no—
802D4—362no—
803D4—362no—
804D4—721no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—31no—
808C2×C4—31no—
809C2×C4—31no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—91no—
814C2×C4—122no—
815C2×C4—122no—
816C2×C4—181no—
817C2×C4—181no—
818C2×C4—181no—
819C2×C4—181no—
820C2×C4—362no—
821C2×C4—362no—
822C2×C4—721no—
823C2×C4C22×D3211yescharacteristic
824C8—61no—
825C8—61no—
826C8—181no—
827C8D3×#6712yes—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—122no—
832C2×C3—121no—
833C2×C3—122no—
834C2×C3—241no—
835C2×C3#571711yescharacteristic
836C2×C3#576811yescharacteristic
837C2×C3#577011yescharacteristic
838C2×C3#577711yescharacteristic
839C2×C3#577811yescharacteristic
840C2×C3D4×#6711yescharacteristic
841D3—41no—
842D3—42no—
843D3—42no—
844D3—81no—
845D3—121no—
846D3—121no—
847D3—241no—
848C22—61no—
849C22—61no—
850C22—61no—
851C22—62no—
852C22—62no—
853C22—121no—
854C22—121no—
855C22—121no—
856C22—121no—
857C22—121no—
858C22—121no—
859C22—121no—
860C22—181no—
861C22—181no—
862C22—181no—
863C22—724no—
864C22D32×D411yescharacteristic
865C4—41no—
866C4—41no—
867C4—61no—
868C4—61no—
869C4—61no—
870C4—121no—
871C4—181no—
872C4—361no—
873C4—361no—
874C4#6431311yescharacteristic
875C4C2×D3×#6711yescharacteristic
876C3—21no—
877C3#8188211yescharacteristic, complemented
878C3#8392111yescharacteristic, complemented
879C2—121no—
880C2—122no—
881C2—122no—
882C2—241no—
883C2—361no—
884C2#1059476311yescharacteristic
885C2#1059477011yescharacteristic
886C2#1059529311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
hypercenterC2×Q16D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#919C2semidirect
2. #10595428C2semidirect
3. #10595358C2semidirect
4. C2×#63798C2semidirect
5. #10592888C2semidirect
6. C3×#5190C2semidirect
7. #10591656C2semidirect
8. #10591652C2semidirect
9. #10591597C2semidirect
10. #10591586C2semidirect
11. #10591567C2semidirect
12. #10591564C2semidirect
13. #10590829C2semidirect
14. #10590771C2semidirect
15. #10590726C2semidirect
19. C2×C3×#239C22semidirect
22. C2×C32×Q16C22semidirect
27. C3×#944C22semidirect
28. C2×C3×#216C22semidirect
31. C2×C3×#215C22semidirect
35. C2×C3×D3×C8C22semidirect
42. Dic3×D12C22semidirect
47. #63856C22semidirect
52. #63662C22semidirect
53. #63662C22semidirect
54. #63644C22semidirect
55. C3×#815C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63566C22semidirect
60. #63563C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
66. C2×#919D3semidirect
74. #5190D3semidirect
143. C3×D24D4semidirect
161. C2×#239C2×D3semidirect
168. C2×C3×Q16C2×D3semidirect
169. C2×C3×Q16C2×D3semidirect
186. #944C2×D3semidirect
187. C2×#216C2×D3semidirect
191. C2×#215C2×D3semidirect
217. C2×D3×C8C2×D3semidirect
251. #815C2×D3semidirect
449. D24#67semidirect
490. C2×Q16D32semidirect
778. C32#3267semidirect
877. C3#81882semidirect
878. C3#83921semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9192
#105954282
#105953582
C2×#637982
#105928882
C3×#51902
#105916562
#105916522
#105915972
#105915862
#105915672
#105915642
#105908292
#105907712
#105907262
#839213
#818823