Finite Group Databasebeta

← #11909907

Subgroups — #11909907

Order 1152.

2124 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#634C211yesmaximal, characteristic, complemented
2C3×#5557C211yesmaximal, characteristic
3C3×#5542C211yesmaximal, characteristic, complemented
4#10595173C212yesmaximal
5#10595119C212yesmaximal, complemented
6#10594939C212yesmaximal, complemented
7#10594915C212yesmaximal, complemented
8#10594828C212yesmaximal, complemented
9#10594824C212yesmaximal, complemented
10#10594385C212yesmaximal, complemented
11#10594322C212yesmaximal, complemented
12#10594116C214yesmaximal, complemented
13#10594031C214yesmaximal, complemented
14C4×D3×Dic6C211yesmaximal, characteristic, complemented
15#10593864C211yesmaximal, characteristic, complemented
16#10593860C211yesmaximal, characteristic, complemented
17#10593859C211yesmaximal, characteristic, complemented
18#86993—31nomaximal
19#86129—31nomaximal
20C22×#634C2212yes—
21C2×D3×Dic6C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic
23D4×C3⋊Dic3C2212yes—
24#64133C2212yes—
25#64097C2212yes—
26#64087C2214yes—
27#64078C2211yescharacteristic
28C4×#634C2211yescharacteristic
29C3×#938C2211yescharacteristic
30C3×#936C2211yescharacteristic
31C3×#936C2212yes—
32C3×C4×#67C2212yes—
33C3×#926C2212yes—
34C3×#926C2212yes—
35C3×#924C2212yes—
36C3×#897C2211yescharacteristic
37C3×#890C2211yescharacteristic
38C3×#887C2212yes—
39C3×#883C2212yes—
40C3×#879C2214yes—
41C3×#879C2212yes—
42C3×C42×D3C2211yescharacteristic
43C3×#869C2211yescharacteristic
44C3×C4×Dic6C2211yescharacteristic
45C3×C4×Dic6C2211yescharacteristic
46#63982C2214yes—
47#67⋊Dic3C2214yes—
48#63969C2214yes—
49#63957C2214yes—
50#63957C2214yes—
51#63956C2214yes—
52#63956C2214yes—
53#63956C2214yes—
54C4×#627C2212yes—
55#63896C2214yes—
56D3×C4⋊Dic3C2211yescharacteristic
57#63877C2214yes—
58D3×Dic3⋊C4C2212yes—
59C4×D3×Dic3C2212yes—
60#63873C2212yes—
61#63869C2212yes—
62#63869C2212yes—
63#63869C2212yes—
64#63867C2214yes—
65#63866C2212yes—
66#63857C2212yes—
67#63856C2212yes—
68#63847C2214yes—
69#63847C2214yes—
70#63846C2214yes—
71#63845C2214yes—
72#63844C2212yes—
73#63844C2211yescharacteristic
74#63844C2214yes—
75#63844C2212yes—
76#63844C2212yes—
77#63844C2214yes—
78#63843C2212yes—
79Dic3×Dic6C2211yescharacteristic
80Dic3×Dic6C2212yes—
81Dic3×Dic6C2212yes—
82#63841C2212yes—
83#63840C2214yes—
84#63837C2212yes—
85C3×#556—31no—
86C3×#529—31no—
87#5728—31no—
88#5721—31no—
89#5708—34no—
90#5701—34no—
91#5701—34no—
92#5685—32no—
93#5680—32no—
94#5671—32no—
95#5671—32no—
96#5650—34no—
97#5632—32no—
98#5625—32no—
99#5622—32no—
100#5600—32no—
101#5578—32no—
102C4×D3×Q8—31no—
103#5570—31no—
104#5569—32no—
105#5567—31no—
106#5567—31no—
107#5557D311yescharacteristic
108#5542D311yescharacteristic, complemented
109#5541—32no—
110D4×Dic6—31no—
111D4×Dic6—31no—
112D4×Dic6—32no—
113D4×Dic6—61no—
114#5529—32no—
115#5518—32no—
116#5516—32no—
117#5516—32no—
118#5470—31no—
119C2×C4×Dic6—31no—
120C2×C32×D4C2311yescharacteristic
121C22×C32×C4C2312yes—
122C22×C3⋊Dic3C2314yes—
123C2×#634—28no—
124C2×#634C2312yes—
125C2×#634C2314yes—
126C2×#634C2311yescharacteristic
127C2×C3×#67C2312yes—
128C2×C3×C4×D3C2311yescharacteristic
129C2×C3×C4×D3C2311yescharacteristic
130C2×C3×C4×D3C2311yescharacteristic
131C2×C3×Dic6C2312yes—
132C2×C3×Dic6C2311yescharacteristic
133C2×C3×Dic6C2311yescharacteristic
134C2×#627C2312yes—
135C2×D3×Dic3C2312yes—
136C2×D3×Dic3C2312yes—
137D3×Dic6—24no—
138C32×C4⋊C4C2311yescharacteristic
139C32×C22⋊C4C2312yes—
140C32×C42C2311yescharacteristic
141#3757C2314yes—
142C4⋊(C3⋊Dic3)C2311yescharacteristic
143C4⋊(C3⋊Dic3)C2312yes—
144C4⋊(C3⋊Dic3)C2312yes—
145#3750C2312yes—
146#3750C2314yes—
147C4×C3⋊Dic3C2312yes—
148C3×#217C2314yes—
149C3×#217C2314yes—
150C3×#217C2312yes—
151C3×#217C2312yes—
152C3×#217C2312yes—
153C3×(C2×D3)⋊C4C2312yes—
154C3×C4⋊Dic3C2312yes—
155C3×C4⋊Dic3C2312yes—
156C3×C4⋊Dic3C2312yes—
157C3×C4⋊Dic3C2311yescharacteristic
158C3×C4⋊Dic3C2312yes—
159C3×C4⋊Dic3C2311yescharacteristic
160C3×Dic3⋊C4C2312yes—
161C3×Dic3⋊C4C2312yes—
162C3×Dic3⋊C4C2314yes—
163C3×Dic3⋊C4C2312yes—
164C3×C4×Dic3C2311yescharacteristic
165C3×C4×Dic3C2314yes—
166C3×C4×Dic3C2312yes—
167C3×C4×Dic3C2311yescharacteristic
168C3×C4×Dic3C2311yescharacteristic
169C3×C4×Dic3C2312yes—
170#3724C2312yes—
171#3724C2314yes—
172#3724C2314yes—
173#3724C2314yes—
174#3724C2314yes—
175Dic3⋊Dic3C2312yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2312yes—
180Dic3⋊Dic3C2314yes—
181(C2×D3)⋊Dic3C2314yes—
182Dic32C2312yes—
183Dic32C2312yes—
184Dic32C2314yes—
185Dic32C2314yes—
186Dic32C2314yes—
187#3523—91noSylow
188C2×D3×Q8—31no—
189C22×Dic6—32no—
190C22×Dic6—32no—
191C22×Dic6—31no—
192C22×Dic6—62no—
193C3×C4⋊Q8—31no—
194C3×#126—32no—
195C3×#126—34no—
196C3×#125—31no—
197C3×#124—31no—
198C3×#124—32no—
199C3×#123—32no—
200C3×C22⋊Q8—32no—
201C3×C22⋊Q8—31no—
202C3×#121—31no—
203C3×C4×Q8—32no—
204C3×C4×Q8—31no—
205C3×C4×Q8—31no—
206C3×C4×D4—21no—
207C3×C4×D4—32no—
208C3×C4×D4C2×D311yescharacteristic
209C3×C4×D4C2×D311yescharacteristic
210C3×#117—32no—
211C3×#117—32no—
212C2×C3×C42—31no—
213#946—32no—
214Q8×Dic3—32no—
215Q8×Dic3—32no—
216Q8×Dic3—32no—
217Q8×Dic3—31no—
218#944—32no—
219#944—32no—
220#944—32no—
221#938C2×D311yescharacteristic
222#936C2×D311yescharacteristic
223#936C2×D312yes—
224#935—34no—
225D4×Dic3—32no—
226D4×Dic3—32no—
227D4×Dic3—34no—
228D4×Dic3—62no—
229C4×#67C2×D312yes—
230#926—32no—
231#926C2×D312yes—
232#926C2×D312yes—
233C2×C4⋊Dic3—31no—
234#924—32no—
235#924—32no—
236#924—32no—
237#924—32no—
238#924—62no—
239#924C2×D312yes—
240C2×Dic3⋊C4—32no—
241C2×C4×Dic3—32no—
242#897—32no—
243#897C2×D311yescharacteristic
244#896—34no—
245#892—32no—
246D3×C4⋊C4—32no—
247D3×C4⋊C4—31no—
248#890—34no—
249#890—34no—
250#890—32no—
251#890—32no—
252#890—32no—
253#890C2×D311yescharacteristic
254#889—34no—
255#889—34no—
256#889—34no—
257#889—34no—
258#889—34no—
259#889—34no—
260#889—34no—
261#888—32no—
262#888—32no—
263#888—34no—
264#888—34no—
265#888—62no—
266#887—32no—
267#887—32no—
268#887—34no—
269#887—32no—
270#887—34no—
271#887—32no—
272#887—31no—
273#887—32no—
274#887C2×D312yes—
275#883—34no—
276#883C2×D312yes—
277#67⋊C4—34no—
278#879—34no—
279#879—34no—
280#879—34no—
281#879—34no—
282#879—34no—
283#879—34no—
284#879C2×D314yes—
285#879C2×D312yes—
286#878—34no—
287#878—34no—
288#878—34no—
289#878—34no—
290#878—34no—
291#878—64no—
292#877—34no—
293#877—34no—
294#877—34no—
295#877—34no—
296#877—34no—
297#872—34no—
298C42×D3—32no—
299C42×D3C2×D311yescharacteristic
300#870—32no—
301#870—32no—
302#870—32no—
303#870—34no—
304#869—32no—
305#869—31no—
306#869—31no—
307#869—61no—
308#869C2×D311yescharacteristic
309C4×Dic6—32no—
310C4×Dic6—32no—
311C4×Dic6—31no—
312C4×Dic6—31no—
313C4×Dic6—31no—
314C4×Dic6—34no—
315C4×Dic6—34no—
316C4×Dic6—31no—
317C4×Dic6—32no—
318C4×Dic6—32no—
319C4×Dic6—32no—
320C4×Dic6—32no—
321C4×Dic6—32no—
322C4×Dic6—32no—
323C4×Dic6—61no—
324C4×Dic6C2×D311yescharacteristic
325C4×Dic6C2×D311yescharacteristic
326C23×C32C2412yes—
327C22×C3×D3C2411yescharacteristic
328C32×D4—22no—
329C2×C32×C4—24no—
330C2×C32×C4C2412yes—
331C2×C32×C4C2411yescharacteristic
332C2×C32×C4C2411yescharacteristic
333C2×C32×C4C2411yescharacteristic
334C2×C3⋊Dic3—28no—
335C2×C3⋊Dic3C2414yes—
336C2×C3⋊Dic3C2412yes—
337C2×C3⋊Dic3C2412yes—
338#634—24no—
339#634—28no—
340#634#4114yes—
341C3×#67—24no—
342C2×C3×Dic3C2411yescharacteristic
343C2×C3×Dic3C2411yescharacteristic
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2414yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2411yescharacteristic
350C3×C4×D3—22no—
351C3×C4×D3—22no—
352C3×C4×D3—22no—
353C3×Dic6—22no—
354C3×Dic6—24no—
355C3×Dic6—22no—
356#627—24no—
357D3×Dic3—24no—
358D3×Dic3—24no—
359#557—91no—
360#557—92no—
361#557—91no—
362#556—31no—
363#556—92no—
364#552—92no—
365#552—94no—
366D4×Q8—92no—
367D4×Q8—91no—
368#541—92no—
369#541—94no—
370#533—91no—
371#533—92no—
372#529—31no—
373#529—92no—
374#519—92no—
375C2×C4×Q8—91no—
376C2×C3×Q8—31no—
377C2×C3×Q8—31no—
378C2×C3×Q8—32no—
379C2×C3×D4—21no—
380C2×C3×D4—32no—
381C2×C3×D4C22×D311yescharacteristic
382C2×C3×D4C22×D311yescharacteristic
383C22×C3×C4—22no—
384C22×C3×C4—31no—
385C22×C3×C4—31no—
386C22×C3×C4—31no—
387C22×C3×C4C22×D312yes—
388C22×C3×C4C22×D312yes—
389C2×#67C22×D312yes—
390C22×Dic3—34no—
391C22×Dic3—34no—
392C22×Dic3—32no—
393C22×Dic3—32no—
394C22×Dic3—64no—
395D3×Q8—64no—
396C2×C4×D3—32no—
397C2×C4×D3—32no—
398C2×C4×D3C22×D311yescharacteristic
399C2×C4×D3C22×D311yescharacteristic
400C2×C4×D3C22×D311yescharacteristic
401C2×Dic6—31no—
402C2×Dic6—31no—
403C2×Dic6—32no—
404C2×Dic6—34no—
405C2×Dic6—32no—
406C2×Dic6—34no—
407C2×Dic6—32no—
408C2×Dic6—32no—
409C2×Dic6—61no—
410C2×Dic6—62no—
411C2×Dic6—64no—
412C2×Dic6—64no—
413C2×Dic6—68no—
414C2×Dic6—68no—
415C2×Dic6—128no—
416C2×Dic6C22×D311yescharacteristic
417C2×Dic6C22×D311yescharacteristic
418C2×Dic6C22×D312yes—
419C3×C4⋊C4—21no—
420C3×C4⋊C4—31no—
421C3×C4⋊C4—32no—
422C3×C4⋊C4—32no—
423C3×C4⋊C4—31no—
424C3×C4⋊C4—32no—
425C3×C4⋊C4—32no—
426C3×C4⋊C4—32no—
427C3×C4⋊C4—34no—
428C3×C4⋊C4—32no—
429C3×C4⋊C4—32no—
430C3×C4⋊C4C22×D311yescharacteristic
431C3×C4⋊C4C22×D311yescharacteristic
432C3×C22⋊C4—22no—
433C3×C22⋊C4—32no—
434C3×C22⋊C4—32no—
435C3×C22⋊C4—34no—
436C3×C22⋊C4—32no—
437C3×C22⋊C4—34no—
438C3×C22⋊C4—32no—
439C3×C22⋊C4C22×D312yes—
440C3×C22⋊C4C22×D312yes—
441C3×C42—21no—
442C3×C42—31no—
443C3×C42—31no—
444C3×C42—32no—
445C3×C42—31no—
446C3×C42—32no—
447C3×C42—34no—
448C3×C42C22×D311yescharacteristic
449C3×C42C22×D311yescharacteristic
450#217—34no—
451#217—34no—
452#217—34no—
453#217—64no—
454#217C22×D312yes—
455#217C22×D312yes—
456#217C22×D314yes—
457#217C22×D312yes—
458#217C22×D314yes—
459(C2×D3)⋊C4—34no—
460(C2×D3)⋊C4C22×D312yes—
461C4⋊Dic3—31no—
462C4⋊Dic3—32no—
463C4⋊Dic3—32no—
464C4⋊Dic3—31no—
465C4⋊Dic3—32no—
466C4⋊Dic3—32no—
467C4⋊Dic3—32no—
468C4⋊Dic3—32no—
469C4⋊Dic3—34no—
470C4⋊Dic3—34no—
471C4⋊Dic3—34no—
472C4⋊Dic3—34no—
473C4⋊Dic3—61no—
474C4⋊Dic3—62no—
475C4⋊Dic3—62no—
476C4⋊Dic3C22×D311yescharacteristic
477C4⋊Dic3C22×D312yes—
478C4⋊Dic3C22×D312yes—
479C4⋊Dic3C22×D312yes—
480C4⋊Dic3C22×D311yescharacteristic
481C4⋊Dic3C22×D312yes—
482Dic3⋊C4—32no—
483Dic3⋊C4—32no—
484Dic3⋊C4—34no—
485Dic3⋊C4—34no—
486Dic3⋊C4—32no—
487Dic3⋊C4—32no—
488Dic3⋊C4—32no—
489Dic3⋊C4—34no—
490Dic3⋊C4—32no—
491Dic3⋊C4—34no—
492Dic3⋊C4—34no—
493Dic3⋊C4—34no—
494Dic3⋊C4—34no—
495Dic3⋊C4—34no—
496Dic3⋊C4—34no—
497Dic3⋊C4—34no—
498Dic3⋊C4—34no—
499Dic3⋊C4—34no—
500Dic3⋊C4—34no—
501Dic3⋊C4—34no—
502Dic3⋊C4—62no—
503Dic3⋊C4—64no—
504Dic3⋊C4C22×D312yes—
505Dic3⋊C4C22×D312yes—
506Dic3⋊C4C22×D312yes—
507Dic3⋊C4C22×D314yes—
508C4×Dic3—32no—
509C4×Dic3—32no—
510C4×Dic3—32no—
511C4×Dic3—34no—
512C4×Dic3—32no—
513C4×Dic3—34no—
514C4×Dic3—32no—
515C4×Dic3—34no—
516C4×Dic3—34no—
517C4×Dic3—34no—
518C4×Dic3—34no—
519C4×Dic3—32no—
520C4×Dic3—62no—
521C4×Dic3C22×D311yescharacteristic
522C4×Dic3C22×D312yes—
523C4×Dic3C22×D312yes—
524C4×Dic3C22×D311yescharacteristic
525C4×Dic3C22×D311yescharacteristic
526C4×Dic3C22×D314yes—
527C22×C32—22no—
528C22×C32—22no—
529C22×C32—22no—
530C22×C32C2511yescharacteristic
531C2×C3×D3—21no—
532C2×C3×D3—21no—
533C2×C3×D32−1+412yes—
534C32×C4—22no—
535C32×C4—21no—
536C32×C4C2×#4112yes—
537C32×C42−1+412yes—
538C3⋊Dic3—24no—
539C3⋊Dic3—22no—
540C3⋊Dic3C2×#4114yes—
541C3×Dic3—22no—
542C3×Dic3—21no—
543C3×Dic3—22no—
544C3×Dic3—24no—
545C3×Dic3—22no—
546C3×Dic3—21no—
547C3×Dic3—21no—
548C3×Dic3—22no—
549C22×Q8—91no—
550C22×Q8—92no—
551C4⋊Q8—31no—
552C4⋊Q8—92no—
553C4⋊Q8—94no—
554C4⋊Q8—92no—
555C4⋊Q8—92no—
556C4⋊Q8—91no—
557#126—32no—
558#126—34no—
559#126—94no—
560#126—94no—
561#126—94no—
562#125—31no—
563#125—92no—
564#125—92no—
565#125—94no—
566#125—92no—
567#125—94no—
568#125—94no—
569#125—94no—
570#125—94no—
571#124—31no—
572#124—32no—
573#123—32no—
574#123—94no—
575C22⋊Q8—32no—
576C22⋊Q8—31no—
577C22⋊Q8—94no—
578C22⋊Q8—94no—
579C22⋊Q8—92no—
580C22⋊Q8—92no—
581C22⋊Q8—92no—
582C22⋊Q8—94no—
583#121—31no—
584C4×Q8—32no—
585C4×Q8—31no—
586C4×Q8—31no—
587C4×Q8—92no—
588C4×Q8—91no—
589C4×Q8—92no—
590C4×Q8—92no—
591C4×Q8—94no—
592C4×Q8—92no—
593C4×Q8—94no—
594C4×Q8—92no—
595C4×Q8—91no—
596C4×Q8—92no—
597C4×Q8—92no—
598C4×Q8—92no—
599C4×Q8—91no—
600C4×D4—32no—
601C4×D4—94no—
602C4×D4—92no—
603C4×D4D3211yescharacteristic
604#117—32no—
605#117—32no—
606#117—94no—
607#117—94no—
608#117—94no—
609#117—92no—
610C2×C4⋊C4—92no—
611C2×C4⋊C4—91no—
612C2×C42—31no—
613C2×C42—92no—
614C23×C3—22no—
615C23×C3—31no—
616C23×C3C23×D312yes—
617C23×C3C23×D312yes—
618C22×D3C23×D311yescharacteristic
619C3×Q8—62no—
620C3×Q8—62no—
621C3×Q8—64no—
622C3×D4—24no—
623C3×D4—22no—
624C3×D4—22no—
625C3×D4—64no—
626C2×C3×C4—24no—
627C2×C3×C4—24no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—22no—
632C2×C3×C4—31no—
633C2×C3×C4—31no—
634C2×C3×C4—32no—
635C2×C3×C4—32no—
636C2×C3×C4—32no—
637C2×C3×C4—34no—
638C2×C3×C4—32no—
639C2×C3×C4—31no—
640C2×C3×C4—44no—
641C2×C3×C4—62no—
642C2×C3×C4—62no—
643C2×C3×C4—62no—
644C2×C3×C4C23×D312yes—
645C2×C3×C4C23×D311yescharacteristic
646C2×C3×C4C23×D311yescharacteristic
647C2×C3×C4C23×D312yes—
648C2×C3×C4C23×D311yescharacteristic
649C2×C3×C4C23×D311yescharacteristic
650C2×C3×C4C23×D311yescharacteristic
651C2×C3×C4C23×D311yescharacteristic
652#67—24no—
653C2×Dic3—32no—
654C2×Dic3—32no—
655C2×Dic3—32no—
656C2×Dic3—32no—
657C2×Dic3—34no—
658C2×Dic3—34no—
659C2×Dic3—62no—
660C2×Dic3—62no—
661C2×Dic3—64no—
662C2×Dic3—64no—
663C2×Dic3—64no—
664C2×Dic3—68no—
665C2×Dic3—68no—
666C2×Dic3—128no—
667C2×Dic3C23×D311yescharacteristic
668C2×Dic3C23×D311yescharacteristic
669C2×Dic3C23×D312yes—
670C2×Dic3C23×D312yes—
671C2×Dic3C23×D314yes—
672C2×Dic3C23×D312yes—
673C2×Dic3C23×D312yes—
674C2×Dic3C23×D311yescharacteristic
675C4×D3—22no—
676C4×D3—22no—
677C4×D3—22no—
678C4×D3—64no—
679C4×D3—64no—
680Dic6—22no—
681Dic6—24no—
682Dic6—22no—
683Dic6—34no—
684Dic6—34no—
685Dic6—64no—
686Dic6—64no—
687Dic6—64no—
688Dic6—68no—
689Dic6—68no—
690Dic6—64no—
691Dic6—64no—
692Dic6—128no—
693Dic6—124no—
694C2×C32—42no—
695C2×C32C22×#4111yescharacteristic
696C2×C32C2×2−1+411yescharacteristic
697C2×C32C2×2−1+411yescharacteristic
698C3×D3—22no—
699C2×Q8—31no—
700C2×Q8—32no—
701C2×Q8—31no—
702C2×Q8—92no—
703C2×Q8—91no—
704C2×Q8—94no—
705C2×Q8—92no—
706C2×Q8—188no—
707C2×Q8—184no—
708C2×D4—32no—
709C2×D4C2×D3211yescharacteristic
710C22×C4—31no—
711C22×C4—31no—
712C22×C4—31no—
713C22×C4—92no—
714C22×C4—92no—
715C22×C4—94no—
716C22×C4C2×D3212yes—
717C4⋊C4—31no—
718C4⋊C4—32no—
719C4⋊C4—32no—
720C4⋊C4—32no—
721C4⋊C4—32no—
722C4⋊C4—32no—
723C4⋊C4—32no—
724C4⋊C4—31no—
725C4⋊C4—34no—
726C4⋊C4—32no—
727C4⋊C4—92no—
728C4⋊C4—92no—
729C4⋊C4—92no—
730C4⋊C4—94no—
731C4⋊C4—94no—
732C4⋊C4—94no—
733C4⋊C4—94no—
734C4⋊C4—94no—
735C4⋊C4—94no—
736C4⋊C4—94no—
737C4⋊C4—94no—
738C4⋊C4—92no—
739C4⋊C4—91no—
740C4⋊C4—94no—
741C4⋊C4—92no—
742C4⋊C4—92no—
743C4⋊C4C2×D3211yescharacteristic
744C22⋊C4—32no—
745C22⋊C4—32no—
746C22⋊C4—34no—
747C22⋊C4—32no—
748C22⋊C4—34no—
749C22⋊C4—32no—
750C22⋊C4—94no—
751C22⋊C4—94no—
752C22⋊C4C2×D3212yes—
753C42—31no—
754C42—31no—
755C42—31no—
756C42—32no—
757C42—34no—
758C42—32no—
759C42—92no—
760C42—92no—
761C42—94no—
762C42—94no—
763C42—94no—
764C42—92no—
765C42C2×D3211yescharacteristic
766C22×C3—24no—
767C22×C3—22no—
768C22×C3—22no—
769C22×C3—22no—
770C22×C3—22no—
771C22×C3—22no—
772C22×C3—22no—
773C22×C3—21no—
774C22×C3—32no—
775C22×C3—42no—
776C22×C3—42no—
777C22×C3—61no—
778C22×C3—61no—
779C22×C3C24×D311yescharacteristic
780C22×C3C24×D311yescharacteristic
781C2×D3—21no—
782C2×D3—21no—
783C2×D3#101012yes—
784C3×C4—22no—
785C3×C4—22no—
786C3×C4—21no—
787C3×C4—21no—
788C3×C4—22no—
789C3×C4—22no—
790C3×C4—42no—
791C3×C4—41no—
792C3×C4—61no—
793C3×C4—62no—
794C3×C4—62no—
795C3×C4—61no—
796C3×C4—64no—
797C3×C4—62no—
798C3×C4—61no—
799C3×C4—62no—
800C3×C4D3×#4112yes—
801C3×C4D3×#4112yes—
802C3×C4#101012yes—
803C3×C4#101012yes—
804Dic3—22no—
805Dic3—21no—
806Dic3—22no—
807Dic3—24no—
808Dic3—21no—
809Dic3—21no—
810Dic3—22no—
811Dic3—22no—
812Dic3—34no—
813Dic3—34no—
814Dic3—64no—
815Dic3—64no—
816Dic3—64no—
817Dic3—62no—
818Dic3—62no—
819Dic3—124no—
820Dic3—122no—
821C32#352311yescharacteristic, complemented, Sylow
822C23—31no—
823C23C22×D3212yes—
824Q8—62no—
825Q8—64no—
826Q8—62no—
827Q8—94no—
828Q8—188no—
829Q8—184no—
830Q8—184no—
831D4—22no—
832D4—64no—
833C2×C4—24no—
834C2×C4—32no—
835C2×C4—31no—
836C2×C4—31no—
837C2×C4—31no—
838C2×C4—32no—
839C2×C4—34no—
840C2×C4—32no—
841C2×C4—32no—
842C2×C4—62no—
843C2×C4—62no—
844C2×C4—62no—
845C2×C4—92no—
846C2×C4—92no—
847C2×C4—94no—
848C2×C4—184no—
849C2×C4—184no—
850C2×C4—188no—
851C2×C4C22×D3212yes—
852C2×C4C22×D3211yescharacteristic
853C2×C4C22×D3211yescharacteristic
854C2×C4C22×D3211yescharacteristic
855C2×C3—21no—
856C2×C3—21no—
857C2×C3—21no—
858C2×C3—44no—
859C2×C3—42no—
860C2×C3—42no—
861C2×C3—62no—
862C2×C3C2×D3×#4111yescharacteristic
863C2×C3C2×D3×#4111yescharacteristic
864C2×C3C2×#101011yescharacteristic
865C2×C3C2×#101011yescharacteristic
866C2×C3C2×#101011yescharacteristic
867C2×C3D3×2−1+411yescharacteristic
868D3—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—32no—
873C22—61no—
874C22—61no—
875C22C23×D3211yescharacteristic
876C4—22no—
877C4—21no—
878C4—61no—
879C4—62no—
880C4—64no—
881C4—61no—
882C4—62no—
883C4—61no—
884C4—62no—
885C4—62no—
886C4—94no—
887C4—184no—
888C4—182no—
889C4#6429812yes—
890C4#6431212yes—
891C3—21no—
892C3#8612911yescharacteristic, complemented
893C3#8699311yescharacteristic, complemented
894C2—42no—
895C2—62no—
896C2C2×#6429811yescharacteristic
897C2C2×#6431211yescharacteristic
898C2D3×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
prime radicalC3×#938C22
hypercenterC4×D4D32
hypocenterC32#3523
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. D4×#634C2semidirect
3. C3×#5542C2semidirect
5. #10595119C2semidirect
6. #10594939C2semidirect
7. #10594915C2semidirect
8. #10594828C2semidirect
9. #10594824C2semidirect
10. #10594385C2semidirect
11. #10594322C2semidirect
12. #10594116C2semidirect
13. #10594031C2semidirect
14. C4×D3×Dic6C2semidirect
15. #10593864C2semidirect
16. #10593860C2semidirect
17. #10593859C2semidirect
108. #5542D3semidirect
821. C32#3523semidirect
892. C3#86129semidirect
893. C3#86993semidirect

Maximal subgroups

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

subgroupindex
D4×#6342
C3×#55572
C3×#55422
#105951732
#105951192
#105949392
#105949152
#105948282
#105948242
#105943852
#105943222
#105941162
#105940312
C4×D3×Dic62
#105938642
#105938602
#105938592
#869933
#861293