Finite Group Databasebeta

← #11884323

Subgroups — #11884323

Order 1152.

1062 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#916C211yesmaximal, characteristic, complemented
2#10595427C211yesmaximal, characteristic, complemented
3#10595252C211yesmaximal, characteristic, complemented
4C2×#63925C211yesmaximal, characteristic, complemented
5#10592864C211yesmaximal, characteristic, complemented
6C3×#5173C211yesmaximal, characteristic, complemented
7#10591638C211yesmaximal, characteristic, complemented
8#10591629C211yesmaximal, characteristic, complemented
9#10591597C211yesmaximal, characteristic, complemented
10#10591452C211yesmaximal, characteristic, complemented
11#10591436C211yesmaximal, characteristic, complemented
12#10590942C211yesmaximal, characteristic, complemented
13#10590847C211yesmaximal, characteristic, complemented
14#10590748C211yesmaximal, characteristic, complemented
15#10590723C211yesmaximal, characteristic, complemented
16#83921—31nomaximal
17#80265—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×#237C2211yescharacteristic, complemented
21C2×D3×D12C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic, complemented
23#64156C2211yescharacteristic
24D4×C3⋊Dic3C2211yescharacteristic, complemented
25C2×#3753C2211yescharacteristic
26C3×#946C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic, complemented
28C2×C3×#216C2211yescharacteristic, complemented
29C2×C3×#213C2211yescharacteristic
30C3×#916—24no—
31C2×C3×#204C2211yescharacteristic
32C2×C3×D3×C8C2211yescharacteristic, complemented
33#63980—21no—
34C2×#3724—21no—
35#63961—21no—
36#63961—21no—
37#63925—24no—
38#63922—21no—
39D3×(C2×D3)⋊C4—21no—
40#63909C2211yescharacteristic
41C4×#625C2211yescharacteristic
42#63898C2211yescharacteristic
43#63886—21no—
44#63873C2211yescharacteristic, complemented
45#63856C2211yescharacteristic
46#63856C2211yescharacteristic, complemented
47#63850—21no—
48C2×#3717C2211yescharacteristic
49C2×#3717C2211yescharacteristic
50C2×#3715C2211yescharacteristic
51C2×#3711C2211yescharacteristic
52#63662C2211yescharacteristic, complemented
53#63648C2211yescharacteristic
54#63641C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×#816C2211yescharacteristic, complemented
58#63573C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63563C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63555C2211yescharacteristic, complemented
63C2×C3×#135—31no—
64#5829—31no—
65#5824—31no—
66#5824—31no—
67C2×#949—31no—
68C2×#916D311yescharacteristic, complemented
69C2×#911—31no—
70#5630—31no—
71C3×#452—31no—
72#5239—31no—
73#5238—31no—
74#5190—31no—
75#5190—31no—
76#5189—31no—
77#5187—31no—
78#5173D311yescharacteristic, complemented
79#5169—31no—
80#5165—31no—
81#5165—31no—
82#5165—61no—
83#5162—31no—
84#5152—31no—
85#5114—31no—
86#5111—31no—
87#5052—31no—
88#4818—31no—
89#4807—31no—
90#4785—31no—
91#4781—31no—
92#4731—31no—
93#4728—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C22×C3⋊Dic3—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C3×#239—22no—
104C3×#239—41no—
105C3×#237—22no—
106C3×#237—22no—
107C3×#237—41no—
108C3×#237—41no—
109C2×C3×D12—21no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×Dic6C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×#626—21no—
117C2×#626—21no—
118C2×#625D411yescharacteristic
119C2×D3×Dic3—21no—
120D3×D12—22no—
121D3×D12—41no—
122C32×SD16—22no—
123C2×C32×C8C2311yescharacteristic
124#3757—21no—
125#3753—22no—
126#3752—21no—
127#3752—21no—
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129C4×C3⋊Dic3C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C3×#216—22no—
132C3×#216—41no—
133C3×#213D414yescomplemented
134C3×(C2×D3)⋊C4—21no—
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×#204—22no—
140C3×D3×C8—22no—
141#3724—21no—
142#3724—21no—
143#3724—21no—
144#3724—21no—
145#3724D411yescharacteristic
146#3722—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3D411yescharacteristic
151(C2×D3)⋊Dic3D411yescharacteristic
152#3717—22no—
153#3717—41no—
154#3715—22no—
155#3711—22no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×C3×#41—31no—
160C2×#239C2×D311yescharacteristic
161C2×#237C2×D311yescharacteristic
162C2×#237C2×D311yescharacteristic, complemented
163C2×D3×D4—31no—
164C22×D12—31no—
165C3×#135—64no—
166C2×C3×Q16—31no—
167C2×C3×Q16—31no—
168C2×C3×SD16—21no—
169C2×C3×SD16—31no—
170C2×C3×SD16C2×D311yescharacteristic, complemented
171C2×C3×SD16C2×D311yescharacteristic, complemented
172C2×C3×D8—31no—
173C22×C3×C8—31no—
174C3×C22⋊Q8—31no—
175#949—64no—
176#947—31no—
177#947—31no—
178#947—61no—
179#946—31no—
180#946—31no—
181#946C2×D311yescharacteristic
182#944—31no—
183#944—31no—
184C2×#216C2×D311yescharacteristic, complemented
185C2×#216C2×D311yescharacteristic, complemented
186C2×#215—31no—
187C2×#215—31no—
188C2×#215—31no—
189#939—61no—
190#939—61no—
191#939—61no—
192#937—61no—
193#935—61no—
194#935—61no—
195D4×Dic3—31no—
196D4×Dic3—31no—
197D4×Dic3—31no—
198D4×Dic3—61no—
199C2×#214—31no—
200C2×#213—31no—
201C2×#213—31no—
202C2×#213—61no—
203C2×#213C2×D311yescharacteristic
204#930—31no—
205#929—61no—
206#929—61no—
207#929—61no—
208C4×#67—31no—
209C4×#67—31no—
210C2×(C2×D3)⋊C4—61no—
211#924—31no—
212#924—31no—
213C2×Dic3⋊C4—61no—
214C2×Dic3⋊C4—61no—
215C2×#208—31no—
216#916—24no—
217#911—64no—
218C2×#204—31no—
219C2×#204—31no—
220C2×#204C2×D311yescharacteristic
221C2×ΓL(1,𝔽25)—31no—
222C2×D3×C8C2×D311yescharacteristic, complemented
223#895—31no—
224#895—61no—
225#894—61no—
226#893—31no—
227#882—61no—
228D3×C22⋊C4—61no—
229C3×#103—31no—
230C3×#102—31no—
231C3×C22⋊C8—31no—
232#835—31no—
233#835—31no—
234#835—31no—
235#835—61no—
236#832—31no—
237#832C2×D311yescharacteristic, complemented
238#830—31no—
239#821—31no—
240#821—31no—
241#821—31no—
242#821—61no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8C2×D311yescharacteristic
245#817—31no—
246#816C2×D311yescharacteristic, complemented
247#815—31no—
248#815—31no—
249Dic3⋊C8—31no—
250Dic3⋊C8—31no—
251Dic3⋊C8—61no—
252#810—31no—
253#808—31no—
254C23×C32—21no—
255C22×C3⋊D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3C2×D411yescharacteristic
258C22×C3×D3C2×D411yescharacteristic
259C2×D32—42no—
260C2×D32—42no—
261C2×D32—81no—
262C32×Q8—21no—
263C32×Q8—21no—
264C32×D4—21no—
265C32×D4C2×D412yes—
266C2×C32×C4—21no—
267C2×C32×C4C2411yescharacteristic
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—42no—
270C2×C3⋊Dic3C2×D411yescharacteristic
271C2×C3⋊Dic3C2×D411yescharacteristic
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—21no—
274C3×#67—42no—
275C3×#67—42no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—42no—
280C2×C3×Dic3—42no—
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C3×D12—21no—
284C3×D12—42no—
285C3×D12C2×D412yes—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—42no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295#626—42no—
296#626—81no—
297#625—41no—
298D3×Dic3—81no—
299C32×C8—21no—
300C3⋊(C3⋊C8)—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yes—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—31no—
305#547—91no—
306#546—91no—
307#497—91no—
308#470—91no—
309#465—91no—
310#463—91no—
311#461—91no—
312#452—31no—
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—62no—
323C3×#41—121no—
324C3×#41—121no—
325C3×#41—121no—
326C2×C3×Q8—21no—
327C2×C3×Q8—31no—
328C2×C3×Q8—31no—
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×D4—21no—
332C2×C3×D4—31no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4C22×D311yescharacteristic
337C2×C3×D4C22×D311yescharacteristic
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—61no—
341C22×C3×C4—61no—
342C22×C3×C4—61no—
343C2×#67—21no—
344C2×#67—21no—
345C2×#67—31no—
346C2×#67—31no—
347C2×#67—61no—
348C2×#67—61no—
349C22×Dic3—21no—
350C22×Dic3—21no—
351C22×Dic3—61no—
352C22×Dic3—61no—
353C22×Dic3—61no—
354C22×Dic3—121no—
355#239—22no—
356#239—41no—
357#237—22no—
358#237—22no—
359#237—41no—
360#237—41no—
361D3×D4—62no—
362D3×D4—121no—
363C2×D12—21no—
364C2×D12—31no—
365C2×D12—31no—
366C2×D12—61no—
367C2×D12—62no—
368C2×D12—61no—
369C2×D12—61no—
370C2×D12—121no—
371C2×D12C22×D311yescharacteristic
372C2×C4×D3—21no—
373C2×C4×D3—61no—
374C2×C4×D3C22×D311yescharacteristic
375C2×C4×D3C22×D311yescharacteristic
376C2×Dic6C22×D311yescharacteristic
377C2×Dic6C22×D311yescharacteristic
378C3×Q16—62no—
379C3×Q16—121no—
380C3×SD16—22no—
381C3×SD16—22no—
382C3×SD16—42no—
383C3×SD16—62no—
384C3×D8—34no—
385C2×C3×C8—21no—
386C2×C3×C8—31no—
387C2×C3×C8—31no—
388C2×C3×C8—62no—
389C2×C3×C8C22×D311yescharacteristic
390C2×C3×C8C22×D311yescharacteristic
391C3×C4⋊C4—31no—
392C3×C4⋊C4—61no—
393C3×C22⋊C4—61no—
394#217—31no—
395#217—31no—
396#217—61no—
397#217—61no—
398#217—61no—
399#217—61no—
400#217—61no—
401#217—121no—
402#216—22no—
403#216—41no—
404#215—62no—
405#215—62no—
406#215—121no—
407#214—62no—
408#213—62no—
409#213—62no—
410#213—122no—
411#213#6714yescomplemented
412(C2×D3)⋊C4—21no—
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—61no—
424(C2×D3)⋊C4—121no—
425(C2×D3)⋊C4—121no—
426C4⋊Dic3—31no—
427C4⋊Dic3—31no—
428C4⋊Dic3—61no—
429C4⋊Dic3C22×D311yescharacteristic
430Dic3⋊C4—21no—
431Dic3⋊C4—31no—
432Dic3⋊C4—31no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438Dic3⋊C4—61no—
439Dic3⋊C4—61no—
440Dic3⋊C4—61no—
441C4×Dic3—31no—
442C4×Dic3—31no—
443C4×Dic3—61no—
444#208—62no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—61no—
448C2×C3⋊C8C22×D311yescharacteristic
449C2×C3⋊C8C22×D311yescharacteristic
450#204—22no—
451#204—62no—
452#204—121no—
453ΓL(1,𝔽25)—62no—
454D3×C8—22no—
455C22×C32—22no—
456C22×C32—41no—
457C22×C32—41no—
458C22×C32C22×D411yescharacteristic
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3⋊D3—41no—
462C2×C3×D3—22no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471D32—84no—
472C32×C4—41no—
473C32×C4C22×D411yescharacteristic
474C32×C4H(5,𝔽2)11yescharacteristic
475C3⋊Dic3—21no—
476C3⋊Dic3—21no—
477C3⋊Dic3—41no—
478C3×Dic3—21no—
479C3×Dic3—21no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C2×#41—31no—
484C2×#41—31no—
485C2×#41—31no—
486C22×D4—91no—
487AGL(1,ℤ/8)—184no—
488#135—64no—
489C2×Q16—31no—
490C2×Q16—31no—
491C2×SD16—31no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16D3211yescharacteristic, complemented
496C2×D8—31no—
497C2×D8—91no—
498C2×M16—91no—
499C22×C8—31no—
500C4⋊Q8—91no—
501#124—91no—
502#123—181no—
503#123—181no—
504#123—181no—
505C22⋊Q8—31no—
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—31no—
520#103—91no—
521#103—91no—
522#102—31no—
523#102—91no—
524#102—91no—
525C22⋊C8—31no—
526C22⋊C8—91no—
527#97—91no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—31no—
531C23×C3—31no—
532C23×C3—41no—
533C23×C3—61no—
534C22×D3—21no—
535C22×D3—61no—
536C22×D3—61no—
537C22×D3—121no—
538C22×D3—122no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3—122no—
542C22×D3—241no—
543C22×D3—241no—
544C22×D3D3×D411yescharacteristic
545C22×D3D3×D411yescharacteristic
546C3×Q8—21no—
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—21no—
550C3×Q8—41no—
551C3×Q8—41no—
552C3×Q8—61no—
553C3×Q8—61no—
554C3×Q8—61no—
555C3×Q8—61no—
556C3×D4—21no—
557C3×D4—21no—
558C3×D4—22no—
559C3×D4—32no—
560C3×D4—41no—
561C3×D4—61no—
562C3×D4—122no—
563C3×D4—122no—
564C3×D4—122no—
565C3×D4D3×D412yes—
566C3×D4C2×#6712yes—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—31no—
571C2×C3×C4—31no—
572C2×C3×C4—41no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—122no—
581C2×C3×C4—122no—
582C2×C3×C4—122no—
583C2×C3×C4C23×D311yescharacteristic
584C2×C3×C4C23×D311yescharacteristic
585#67—42no—
586#67—42no—
587#67—122no—
588#67—121no—
589#67—121no—
590#67—241no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—31no—
595C2×Dic3—31no—
596C2×Dic3—31no—
597C2×Dic3—31no—
598C2×Dic3—42no—
599C2×Dic3—42no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—121no—
605C2×Dic3—122no—
606C2×Dic3—122no—
607C2×Dic3—242no—
608C2×Dic3—241no—
609C2×Dic3D3×D411yescharacteristic
610C2×Dic3D3×D411yescharacteristic
611D12—21no—
612D12—42no—
613D12—61no—
614D12—61no—
615D12—61no—
616D12—61no—
617D12—121no—
618D12—121no—
619D12—122no—
620D12—241no—
621D12C2×#6712yes—
622C4×D3—21no—
623C4×D3—21no—
624C4×D3—21no—
625C4×D3—21no—
626C4×D3—42no—
627C4×D3—241no—
628Dic6—21no—
629Dic6—21no—
630Dic6—21no—
631Dic6—21no—
632C3×C8—21no—
633C3×C8—21no—
634C3×C8—32no—
635C3×C8—41no—
636C3×C8—61no—
637C3⋊C8—21no—
638C3⋊C8—61no—
639C3⋊C8—61no—
640C3⋊C8—121no—
641C3⋊C8C2×#6712yes—
642C2×C32—42no—
643C2×C32D4211yescharacteristic
644C2×C32#57511yescharacteristic
645C2×C32#57711yescharacteristic
646C3⋊D3—81no—
647C3×D3—41no—
648C3×D3—42no—
649C3×D3—41no—
650C24—181no—
651#41—62no—
652#41—62no—
653#41—62no—
654#41—121no—
655#41—121no—
656#41—121no—
657C2×Q8—31no—
658C2×Q8—31no—
659C2×Q8C2×D3211yescharacteristic
660C2×D4—31no—
661C2×D4—61no—
662C2×D4—61no—
663C2×D4—61no—
664C2×D4—91no—
665C2×D4—91no—
666C2×D4—181no—
667C2×D4—182no—
668C2×D4—181no—
669C2×D4—361no—
670C2×D4C2×D3211yescharacteristic
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4—181no—
677C22×C4—181no—
678Q16—62no—
679Q16—121no—
680SD16—22no—
681SD16—62no—
682SD16—182no—
683SD16—182no—
684SD16—361no—
685D8—34no—
686D8—182no—
687M16—182no—
688C2×C8—31no—
689C2×C8—31no—
690C2×C8—62no—
691C2×C8—91no—
692C2×C8C2×D3211yescharacteristic
693C4⋊C4—31no—
694C4⋊C4—61no—
695C4⋊C4—91no—
696C4⋊C4—91no—
697C4⋊C4—181no—
698C4⋊C4—181no—
699C4⋊C4—181no—
700C4⋊C4—181no—
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—
710C22⋊C4—181no—
711C42—91no—
712C22×C3—22no—
713C22×C3—22no—
714C22×C3—21no—
715C22×C3—42no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—61no—
721C22×C3—61no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—61no—
725C22×C3—62no—
726C22×C3—61no—
727C22×C3—81no—
728C22×C3—81no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3C2×D3×D411yescharacteristic
732C22×C3C2×D3×D411yescharacteristic
733C2×D3—21no—
734C2×D3—21no—
735C2×D3—21no—
736C2×D3—21no—
737C2×D3—21no—
738C2×D3—22no—
739C2×D3—21no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—121no—
747C2×D3—121no—
748C2×D3—241no—
749C2×D3—241no—
750C2×D3—241no—
751C2×D3—244no—
752C2×D3—244no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—41no—
756C3×C4—41no—
757C3×C4—61no—
758C3×C4—61no—
759C3×C4—81no—
760C3×C4—121no—
761C3×C4—121no—
762C3×C4—121no—
763C3×C4C2×D3×D411yescharacteristic
764C3×C4#100411yescharacteristic
765C3×C4#100411yescharacteristic
766C3×C4C22×#6711yescharacteristic
767Dic3—21no—
768Dic3—21no—
769Dic3—41no—
770Dic3—41no—
771Dic3—41no—
772Dic3—61no—
773Dic3—61no—
774Dic3—61no—
775Dic3—61no—
776Dic3—121no—
777Dic3—121no—
778Dic3—121no—
779Dic3—121no—
780Dic3—241no—
781C32#326711yescharacteristic, complemented, Sylow
782C23—21no—
783C23—31no—
784C23—31no—
785C23—61no—
786C23—181no—
787C23—362no—
788C23—362no—
789C23—721no—
790Q8—21no—
791Q8—21no—
792Q8—61no—
793Q8—61no—
794Q8—61no—
795Q8—61no—
796D4—21no—
797D4—32no—
798D4—61no—
799D4—122no—
800D4—122no—
801D4—122no—
802D4—181no—
803D4—181no—
804D4—362no—
805D4—361no—
806D4—721no—
807D4D3×#6712yes—
808C2×C4—21no—
809C2×C4—31no—
810C2×C4—31no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—91no—
819C2×C4—91no—
820C2×C4—122no—
821C2×C4—122no—
822C2×C4—122no—
823C2×C4—181no—
824C2×C4—362no—
825C2×C4—721no—
826C2×C4C22×D3211yescharacteristic
827C8—21no—
828C8—32no—
829C8—61no—
830C8—181no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—42no—
835C2×C3—42no—
836C2×C3—82no—
837C2×C3—122no—
838C2×C3—121no—
839C2×C3—121no—
840C2×C3#559011yescharacteristic
841C2×C3#576811yescharacteristic
842C2×C3#577011yescharacteristic
843C2×C3#577011yescharacteristic
844C2×C3#577711yescharacteristic
845C2×C3D4×#6711yescharacteristic
846D3—41no—
847D3—41no—
848D3—42no—
849D3—241no—
850D3—241no—
851D3—481no—
852C22—22no—
853C22—41no—
854C22—41no—
855C22—61no—
856C22—61no—
857C22—61no—
858C22—61no—
859C22—61no—
860C22—61no—
861C22—62no—
862C22—121no—
863C22—121no—
864C22—361no—
865C22—361no—
866C22—361no—
867C22—724no—
868C22D32×D411yescharacteristic
869C4—41no—
870C4—61no—
871C4—61no—
872C4—121no—
873C4—121no—
874C4—121no—
875C4—181no—
876C4—181no—
877C4—361no—
878C4#6431311yescharacteristic
879C4C2×D3×#6711yescharacteristic
880C3—21no—
881C3#8026511yescharacteristic, complemented
882C3#8392111yescharacteristic, complemented
883C2—42no—
884C2—121no—
885C2—121no—
886C2—122no—
887C2—721no—
888C2#1059474611yescharacteristic
889C2#1059475711yescharacteristic
890C2#1059528711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#916C2semidirect
2. #10595427C2semidirect
3. #10595252C2semidirect
4. C2×#63925C2semidirect
5. #10592864C2semidirect
6. C3×#5173C2semidirect
7. #10591638C2semidirect
8. #10591629C2semidirect
9. #10591597C2semidirect
10. #10591452C2semidirect
11. #10591436C2semidirect
12. #10590942C2semidirect
13. #10590847C2semidirect
14. #10590748C2semidirect
15. #10590723C2semidirect
20. C2×C3×#237C22semidirect
22. C2×C32×SD16C22semidirect
24. D4×C3⋊Dic3C22semidirect
27. C2×C3×#216C22semidirect
28. C2×C3×#216C22semidirect
32. C2×C3×D3×C8C22semidirect
44. #63873C22semidirect
46. #63856C22semidirect
52. #63662C22semidirect
54. #63641C22semidirect
55. C3×#832C22semidirect
57. C3×#816C22semidirect
58. #63573C22semidirect
59. #63565C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63555C22semidirect
68. C2×#916D3semidirect
78. #5173D3semidirect
133. C3×#213D4semidirect
162. C2×#237C2×D3semidirect
170. C2×C3×SD16C2×D3semidirect
171. C2×C3×SD16C2×D3semidirect
184. C2×#216C2×D3semidirect
185. C2×#216C2×D3semidirect
222. C2×D3×C8C2×D3semidirect
237. #832C2×D3semidirect
246. #816C2×D3semidirect
411. #213#67semidirect
495. C2×SD16D32semidirect
781. C32#3267semidirect
881. C3#80265semidirect
882. C3#83921semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9162
#105954272
#105952522
C2×#639252
#105928642
C3×#51732
#105916382
#105916292
#105915972
#105914522
#105914362
#105909422
#105908472
#105907482
#105907232
#839213
#802653