Finite Group Databasebeta

← #11909908

Subgroups — #11909908

Order 1152.

2101 conjugacy classes of subgroups.

The subgroup lattice has 919 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596028C211yesmaximal, characteristic
2C3×#5542C211yesmaximal, characteristic, complemented
3C3×D4×Dic6C211yesmaximal, characteristic, complemented
4#10595273C212yesmaximal, complemented
5#10595191C212yesmaximal
6#10594970C212yesmaximal, complemented
7#10594826C212yesmaximal, complemented
8#10594818C212yesmaximal, complemented
9#10594803C212yesmaximal, complemented
10#10594397C212yesmaximal, complemented
11#10594317C212yesmaximal, complemented
12#10594028C214yesmaximal, complemented
13#10594026C214yesmaximal, complemented
14C4×#3797C211yesmaximal, characteristic, complemented
15#10593866C211yesmaximal, characteristic, complemented
16#10593864C211yesmaximal, characteristic, complemented
17#10593861C211yesmaximal, characteristic, complemented
18#86993—31nomaximal
19#86753—31nomaximal
20C22×C3×Dic6C2212yes—
21C2×#3797C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic
23#64147C2211yescharacteristic
24#64145C2211yescharacteristic
25C4×#638C2212yes—
26#64135C2212yes—
27#64106C2211yescharacteristic
28#64099C2211yescharacteristic
29#64092C2212yes—
30#64088C2212yes—
31C42×C3⋊D3C2211yescharacteristic
32C4×#634C2211yescharacteristic
33C3×#936C2212yes—
34C3×D4×Dic3C2212yes—
35C3×#926C2212yes—
36C3×#924C2212yes—
37C3×#924C2212yes—
38C3×#888C2212yes—
39C3×#887C2212yes—
40C3×#879C2214yes—
41C3×#878C2214yes—
42C3×#869C2211yescharacteristic
43C3×#869C2211yescharacteristic
44C3×C4×Dic6C2211yescharacteristic
45C3×C4×Dic6C2211yescharacteristic
46#63975C2214yes—
47#63964C2214yes—
48#63956C2214yes—
49#63956C2214yes—
50#63956C2214yes—
51#63955C2214yes—
52#63955C2214yes—
53#63952C2214yes—
54C4×#627C2212yes—
55#63900C2211yescharacteristic
56#63888C2214yes—
57#63883C2212yes—
58C4×#624C2212yes—
59#63873C2212yes—
60#63872C2212yes—
61#63872C2212yes—
62#63871C2212yes—
63#63871C2212yes—
64#63869C2212yes—
65#63867C2214yes—
66#63866C2212yes—
67#63849C2212yes—
68#63847C2214yes—
69#63846C2214yes—
70#63845C2214yes—
71#63845C2214yes—
72#63844C2212yes—
73#63843C2211yescharacteristic
74#63843C2212yes—
75#63843C2212yes—
76#63843C2212yes—
77#63843C2211yescharacteristic
78#63843C2212yes—
79Dic3×Dic6C2214yes—
80Dic3×Dic6C2214yes—
81Dic3×Dic6C2212yes—
82#63839C2214yes—
83#63838C2212yes—
84#63836C2214yes—
85C3×#556—31no—
86C3×D4×Q8—31no—
87Q8×#67—32no—
88#5812—32no—
89#5728—32no—
90#5728—31no—
91#5728—31no—
92#5721—32no—
93#5721—31no—
94#5721—31no—
95#5708—34no—
96#5701—34no—
97#5680—32no—
98#5671—32no—
99#5639—32no—
100#5639—34no—
101#5632—32no—
102#5625—32no—
103#5625—32no—
104#5625—34no—
105#5578—32no—
106C4×D3×Q8—31no—
107C4×D3×Q8—31no—
108#5570—31no—
109#5569—32no—
110#5567—31no—
111#5557—31no—
112#5557—31no—
113#5557—32no—
114#5557—61no—
115#5542—32no—
116#5542D311yescharacteristic, complemented
117D4×Dic6D311yescharacteristic, complemented
118#5529—32no—
119#5516—32no—
120C2×C32×D4C2311yescharacteristic
121C22×C32×C4C2312yes—
122C2×#638C2312yes—
123C2×C4×C3⋊D3C2311yescharacteristic
124C2×C4×C3⋊D3C2311yescharacteristic
125C2×C4×C3⋊D3C2311yescharacteristic
126C2×#634C2311yescharacteristic
127C22×C3×Dic3C2314yes—
128C2×C3×Dic6—28no—
129C2×C3×Dic6C2314yes—
130C2×C3×Dic6C2312yes—
131C2×C3×Dic6C2311yescharacteristic
132C2×C3×Dic6C2312yes—
133C2×C3×Dic6C2311yescharacteristic
134C2×#627C2312yes—
135C2×#624C2312yes—
136C2×#624C2312yes—
137#3797—24no—
138C32×C4⋊C4C2311yescharacteristic
139C32×C22⋊C4C2312yes—
140C32×C42C2311yescharacteristic
141#3757C2312yes—
142#3757C2312yes—
143#3757C2312yes—
144#3752C2312yes—
145C4⋊(C3⋊Dic3)C2311yescharacteristic
146C4⋊(C3⋊Dic3)C2312yes—
147C4⋊(C3⋊Dic3)C2312yes—
148#3750C2312yes—
149#3750C2312yes—
150C4×C3⋊Dic3C2312yes—
151C4×C3⋊Dic3C2311yescharacteristic
152C4×C3⋊Dic3C2311yescharacteristic
153C4×C3⋊Dic3C2311yescharacteristic
154C3×#217C2314yes—
155C3×#217C2314yes—
156C3×#217C2314yes—
157C3×C4⋊Dic3C2312yes—
158C3×C4⋊Dic3C2312yes—
159C3×C4⋊Dic3C2312yes—
160C3×C4⋊Dic3C2311yescharacteristic
161C3×C4⋊Dic3C2312yes—
162C3×C4⋊Dic3C2311yescharacteristic
163C3×Dic3⋊C4C2312yes—
164C3×Dic3⋊C4C2314yes—
165C3×Dic3⋊C4C2312yes—
166C3×Dic3⋊C4C2314yes—
167C3×C4×Dic3C2314yes—
168C3×C4×Dic3C2312yes—
169C3×C4×Dic3C2312yes—
170#3724C2312yes—
171#3724C2314yes—
172#3724C2314yes—
173Dic3⋊Dic3C2314yes—
174Dic3⋊Dic3C2314yes—
175Dic3⋊Dic3C2312yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2312yes—
181#3722C2314yes—
182Dic32C2314yes—
183Dic32C2312yes—
184Dic32C2312yes—
185Dic32C2314yes—
186Dic32C2314yes—
187#3523—91noSylow
188C22×C3×Q8—32no—
189C2×D3×Q8—31no—
190C2×D3×Q8—31no—
191C22×Dic6C2×D312yes—
192C3×C4⋊Q8—32no—
193C3×C4⋊Q8—31no—
194C3×C4⋊Q8—31no—
195C3×#126—34no—
196C3×#124—32no—
197C3×C22⋊Q8—32no—
198C3×C22⋊Q8—32no—
199C3×C22⋊Q8—34no—
200C3×C4×Q8—32no—
201C3×C4×Q8—31no—
202C3×C4×Q8—31no—
203C3×C4×D4—21no—
204C3×C4×D4—32no—
205C3×C4×D4C2×D311yescharacteristic
206C3×C4×D4C2×D311yescharacteristic
207C3×#117—32no—
208#946—32no—
209#946—32no—
210#946—34no—
211Q8×Dic3—32no—
212Q8×Dic3—32no—
213Q8×Dic3—32no—
214Q8×Dic3—31no—
215Q8×Dic3—32no—
216Q8×Dic3—31no—
217Q8×Dic3—34no—
218Q8×Dic3—32no—
219Q8×Dic3—34no—
220#944—32no—
221#944—32no—
222#944—34no—
223#944—32no—
224#938—31no—
225#938—31no—
226#938—61no—
227#936—31no—
228#936—31no—
229#936—61no—
230#936C2×D312yes—
231D4×Dic3C2×D312yes—
232C4×#67—32no—
233C4×#67—32no—
234C4×#67—34no—
235C4×#67—62no—
236#926—32no—
237#926—32no—
238#926—34no—
239#926—34no—
240#926—62no—
241#926C2×D312yes—
242#924—34no—
243#924C2×D312yes—
244#924C2×D312yes—
245#897—32no—
246#897—32no—
247#897—31no—
248#897—31no—
249#897—61no—
250#896—34no—
251#892—32no—
252#892—32no—
253#892—34no—
254D3×C4⋊C4—31no—
255D3×C4⋊C4—31no—
256D3×C4⋊C4—32no—
257D3×C4⋊C4—32no—
258#890—31no—
259#890—31no—
260#890—34no—
261#890—32no—
262#890—32no—
263#890—32no—
264#890—32no—
265#890—34no—
266#890—34no—
267#890—32no—
268#890—61no—
269#889—34no—
270#889—34no—
271#889—34no—
272#889—34no—
273#889—34no—
274#889—34no—
275#888—34no—
276#888C2×D312yes—
277#887—32no—
278#887—32no—
279#887—32no—
280#887—31no—
281#887—32no—
282#887—31no—
283#887—32no—
284#887—32no—
285#887—32no—
286#887C2×D312yes—
287#883—32no—
288#883—32no—
289#883—34no—
290#883—34no—
291#883—62no—
292#67⋊C4—34no—
293#879—32no—
294#879—32no—
295#879—34no—
296#879—34no—
297#879—34no—
298#879—34no—
299#879—34no—
300#879—34no—
301#879—62no—
302#879C2×D314yes—
303#878—34no—
304#878C2×D314yes—
305#877—34no—
306#877—34no—
307#872—34no—
308C42×D3—31no—
309C42×D3—31no—
310C42×D3—32no—
311C42×D3—32no—
312C42×D3—61no—
313#870—32no—
314#870—34no—
315#869—32no—
316#869C2×D311yescharacteristic
317#869C2×D311yescharacteristic
318C4×Dic6—34no—
319C4×Dic6—34no—
320C4×Dic6—32no—
321C4×Dic6—31no—
322C4×Dic6—31no—
323C4×Dic6—32no—
324C4×Dic6—32no—
325C4×Dic6—32no—
326C4×Dic6—61no—
327C4×Dic6C2×D311yescharacteristic
328C4×Dic6C2×D311yescharacteristic
329C23×C32C2412yes—
330C22×C3⋊D3C2411yescharacteristic
331C32×D4—22no—
332C2×C32×C4—24no—
333C2×C32×C4C2412yes—
334C2×C32×C4C2411yescharacteristic
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2411yescharacteristic
337#638—24no—
338C2×C3⋊Dic3C2411yescharacteristic
339C2×C3⋊Dic3C2411yescharacteristic
340C2×C3⋊Dic3C2412yes—
341C2×C3⋊Dic3C2412yes—
342C2×C3⋊Dic3C2411yescharacteristic
343C4×C3⋊D3—22no—
344C4×C3⋊D3—22no—
345C4×C3⋊D3—22no—
346#634—22no—
347C2×C3×Dic3—28no—
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2414yes—
350C2×C3×Dic3C2414yes—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2412yes—
354C3×Dic6—22no—
355C3×Dic6—24no—
356C3×Dic6—24no—
357C3×Dic6—28no—
358C3×Dic6#4114yes—
359#627—24no—
360#624—24no—
361#624—24no—
362#557—91no—
363#557—92no—
364#557—91no—
365#556—31no—
366#556—92no—
367#552—92no—
368#552—94no—
369D4×Q8—31no—
370D4×Q8—92no—
371#541—92no—
372#541—94no—
373#533—92no—
374#533—91no—
375#529—92no—
376#529—91no—
377#519—92no—
378C2×C4×Q8—91no—
379C2×C3×Q8—31no—
380C2×C3×Q8—31no—
381C2×C3×Q8—32no—
382C2×C3×Q8—34no—
383C2×C3×Q8—32no—
384C2×C3×Q8—68no—
385C2×C3×D4—21no—
386C2×C3×D4C22×D311yescharacteristic
387C2×C3×D4C22×D311yescharacteristic
388C22×C3×C4—22no—
389C22×C3×C4—34no—
390C22×C3×C4C22×D312yes—
391C22×C3×C4C22×D312yes—
392C2×#67—32no—
393C2×#67—32no—
394C2×#67—62no—
395C22×Dic3C22×D314yes—
396D3×Q8—64no—
397D3×Q8—64no—
398C2×C4×D3—31no—
399C2×C4×D3—31no—
400C2×C4×D3—31no—
401C2×C4×D3—31no—
402C2×C4×D3—31no—
403C2×C4×D3—31no—
404C2×C4×D3—32no—
405C2×C4×D3—32no—
406C2×C4×D3—32no—
407C2×C4×D3—32no—
408C2×C4×D3—61no—
409C2×C4×D3—61no—
410C2×C4×D3—61no—
411C2×Dic6—28no—
412C2×Dic6—31no—
413C2×Dic6—31no—
414C2×Dic6—32no—
415C2×Dic6—32no—
416C2×Dic6—61no—
417C2×Dic6C22×D314yes—
418C2×Dic6C22×D312yes—
419C2×Dic6C22×D311yescharacteristic
420C2×Dic6C22×D312yes—
421C2×Dic6C22×D311yescharacteristic
422C3×C4⋊C4—21no—
423C3×C4⋊C4—31no—
424C3×C4⋊C4—32no—
425C3×C4⋊C4—32no—
426C3×C4⋊C4—32no—
427C3×C4⋊C4—32no—
428C3×C4⋊C4—31no—
429C3×C4⋊C4—34no—
430C3×C4⋊C4—34no—
431C3×C4⋊C4—32no—
432C3×C4⋊C4—32no—
433C3×C4⋊C4C22×D311yescharacteristic
434C3×C4⋊C4C22×D311yescharacteristic
435C3×C22⋊C4—22no—
436C3×C22⋊C4—34no—
437C3×C22⋊C4—34no—
438C3×C22⋊C4—34no—
439C3×C22⋊C4C22×D312yes—
440C3×C22⋊C4C22×D312yes—
441C3×C42—21no—
442C3×C42—32no—
443C3×C42—32no—
444C3×C42—34no—
445C3×C42C22×D311yescharacteristic
446C3×C42C22×D311yescharacteristic
447#217—32no—
448#217—32no—
449#217—32no—
450#217—32no—
451#217—32no—
452#217—32no—
453#217—62no—
454#217—62no—
455#217—62no—
456#217C22×D314yes—
457#217C22×D314yes—
458#217C22×D314yes—
459(C2×D3)⋊C4—32no—
460(C2×D3)⋊C4—32no—
461(C2×D3)⋊C4—34no—
462(C2×D3)⋊C4—34no—
463(C2×D3)⋊C4—62no—
464C4⋊Dic3—31no—
465C4⋊Dic3—32no—
466C4⋊Dic3—32no—
467C4⋊Dic3—31no—
468C4⋊Dic3—32no—
469C4⋊Dic3—32no—
470C4⋊Dic3—32no—
471C4⋊Dic3—32no—
472C4⋊Dic3—34no—
473C4⋊Dic3—34no—
474C4⋊Dic3—34no—
475C4⋊Dic3—34no—
476C4⋊Dic3—34no—
477C4⋊Dic3—34no—
478C4⋊Dic3—61no—
479C4⋊Dic3—62no—
480C4⋊Dic3—62no—
481C4⋊Dic3C22×D312yes—
482C4⋊Dic3C22×D311yescharacteristic
483C4⋊Dic3C22×D311yescharacteristic
484C4⋊Dic3C22×D312yes—
485C4⋊Dic3C22×D312yes—
486C4⋊Dic3C22×D312yes—
487Dic3⋊C4—32no—
488Dic3⋊C4—32no—
489Dic3⋊C4—32no—
490Dic3⋊C4—32no—
491Dic3⋊C4—32no—
492Dic3⋊C4—34no—
493Dic3⋊C4—32no—
494Dic3⋊C4—34no—
495Dic3⋊C4—34no—
496Dic3⋊C4—34no—
497Dic3⋊C4—32no—
498Dic3⋊C4—32no—
499Dic3⋊C4—34no—
500Dic3⋊C4—34no—
501Dic3⋊C4—34no—
502Dic3⋊C4—34no—
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—62no—
506Dic3⋊C4—62no—
507Dic3⋊C4C22×D312yes—
508Dic3⋊C4C22×D312yes—
509Dic3⋊C4C22×D314yes—
510Dic3⋊C4C22×D314yes—
511C4×Dic3—31no—
512C4×Dic3—31no—
513C4×Dic3—32no—
514C4×Dic3—32no—
515C4×Dic3—31no—
516C4×Dic3—31no—
517C4×Dic3—31no—
518C4×Dic3—31no—
519C4×Dic3—32no—
520C4×Dic3—34no—
521C4×Dic3—34no—
522C4×Dic3—34no—
523C4×Dic3—34no—
524C4×Dic3—32no—
525C4×Dic3—32no—
526C4×Dic3—32no—
527C4×Dic3—34no—
528C4×Dic3—34no—
529C4×Dic3—62no—
530C4×Dic3—61no—
531C4×Dic3—61no—
532C4×Dic3—61no—
533C4×Dic3C22×D312yes—
534C4×Dic3C22×D312yes—
535C4×Dic3C22×D314yes—
536C22×C32—22no—
537C22×C32—22no—
538C22×C32—22no—
539C22×C32C2511yescharacteristic
540C2×C3⋊D3—21no—
541C2×C3⋊D3—21no—
542C2×C3⋊D32−1+412yes—
543C32×C4—22no—
544C32×C4—21no—
545C32×C4C2×#4112yes—
546C32×C42−1+412yes—
547C3⋊Dic3—21no—
548C3⋊Dic3—22no—
549C3⋊Dic3—21no—
550C3⋊Dic3—21no—
551C3⋊Dic3—22no—
552C3×Dic3—22no—
553C3×Dic3—24no—
554C3×Dic3—22no—
555C3×Dic3—22no—
556C3×Dic3—24no—
557C3×Dic3C2×#4114yes—
558C22×Q8—32no—
559C22×Q8—91no—
560C4⋊Q8—32no—
561C4⋊Q8—31no—
562C4⋊Q8—31no—
563C4⋊Q8—92no—
564C4⋊Q8—94no—
565C4⋊Q8—92no—
566#126—34no—
567#126—94no—
568#126—94no—
569#126—94no—
570#126—92no—
571#125—92no—
572#125—94no—
573#125—94no—
574#125—92no—
575#125—94no—
576#125—94no—
577#125—94no—
578#125—92no—
579#125—91no—
580#124—32no—
581#124—91no—
582#123—94no—
583#123—92no—
584C22⋊Q8—32no—
585C22⋊Q8—32no—
586C22⋊Q8—34no—
587C22⋊Q8—94no—
588C22⋊Q8—92no—
589C22⋊Q8—94no—
590C22⋊Q8—92no—
591C22⋊Q8—91no—
592#121—91no—
593C4×Q8—32no—
594C4×Q8—31no—
595C4×Q8—31no—
596C4×Q8—92no—
597C4×Q8—92no—
598C4×Q8—94no—
599C4×Q8—94no—
600C4×Q8—92no—
601C4×Q8—92no—
602C4×Q8—91no—
603C4×Q8—91no—
604C4×Q8—92no—
605C4×Q8—92no—
606C4×Q8—92no—
607C4×Q8—92no—
608C4×Q8—91no—
609C4×D4—32no—
610C4×D4—94no—
611C4×D4—92no—
612C4×D4D3211yescharacteristic
613#117—32no—
614#117—94no—
615#117—94no—
616#117—94no—
617#117—92no—
618#117—92no—
619C2×C4⋊C4—91no—
620C2×C4⋊C4—92no—
621C2×C42—92no—
622C2×C42—91no—
623C23×C3—22no—
624C23×C3C23×D312yes—
625C23×C3C23×D312yes—
626C22×D3—31no—
627C22×D3—31no—
628C22×D3—61no—
629C3×Q8—34no—
630C3×Q8—68no—
631C3×Q8—62no—
632C3×Q8—64no—
633C3×Q8—64no—
634C3×D4—22no—
635C3×D4—22no—
636C3×D4—42no—
637C2×C3×C4—24no—
638C2×C3×C4—24no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—22no—
643C2×C3×C4—32no—
644C2×C3×C4—32no—
645C2×C3×C4—34no—
646C2×C3×C4—34no—
647C2×C3×C4—32no—
648C2×C3×C4—32no—
649C2×C3×C4—44no—
650C2×C3×C4—68no—
651C2×C3×C4C23×D311yescharacteristic
652C2×C3×C4C23×D311yescharacteristic
653C2×C3×C4C23×D312yes—
654C2×C3×C4C23×D312yes—
655C2×C3×C4C23×D311yescharacteristic
656C2×C3×C4C23×D311yescharacteristic
657C2×C3×C4C23×D311yescharacteristic
658C2×C3×C4C23×D311yescharacteristic
659#67—64no—
660#67—64no—
661#67—124no—
662C2×Dic3—28no—
663C2×Dic3—31no—
664C2×Dic3—31no—
665C2×Dic3—31no—
666C2×Dic3—31no—
667C2×Dic3—32no—
668C2×Dic3—32no—
669C2×Dic3—32no—
670C2×Dic3—32no—
671C2×Dic3—31no—
672C2×Dic3—31no—
673C2×Dic3—61no—
674C2×Dic3—61no—
675C2×Dic3—61no—
676C2×Dic3—62no—
677C2×Dic3—62no—
678C2×Dic3C23×D312yes—
679C2×Dic3C23×D314yes—
680C2×Dic3C23×D314yes—
681C2×Dic3C23×D312yes—
682C2×Dic3C23×D312yes—
683C2×Dic3C23×D312yes—
684C4×D3—64no—
685C4×D3—64no—
686C4×D3—64no—
687C4×D3—62no—
688C4×D3—62no—
689C4×D3—62no—
690C4×D3—62no—
691C4×D3—62no—
692C4×D3—62no—
693C4×D3—64no—
694C4×D3—122no—
695C4×D3—122no—
696C4×D3—122no—
697Dic6—24no—
698Dic6—22no—
699Dic6—24no—
700Dic6—28no—
701Dic6—64no—
702Dic6—62no—
703Dic6—62no—
704Dic6—64no—
705Dic6—122no—
706Dic6#23714yes—
707C2×C32—42no—
708C2×C32C22×#4111yescharacteristic
709C2×C32C2×2−1+411yescharacteristic
710C2×C32C2×2−1+411yescharacteristic
711C3⋊D3—22no—
712C2×Q8—31no—
713C2×Q8—32no—
714C2×Q8—31no—
715C2×Q8—34no—
716C2×Q8—32no—
717C2×Q8—68no—
718C2×Q8—92no—
719C2×Q8—91no—
720C2×Q8—184no—
721C2×D4—92no—
722C2×D4C2×D3211yescharacteristic
723C22×C4—34no—
724C22×C4—92no—
725C22×C4—92no—
726C22×C4—91no—
727C22×C4—91no—
728C22×C4—91no—
729C22×C4C2×D3212yes—
730C4⋊C4—31no—
731C4⋊C4—32no—
732C4⋊C4—31no—
733C4⋊C4—32no—
734C4⋊C4—32no—
735C4⋊C4—34no—
736C4⋊C4—32no—
737C4⋊C4—32no—
738C4⋊C4—32no—
739C4⋊C4—34no—
740C4⋊C4—92no—
741C4⋊C4—92no—
742C4⋊C4—92no—
743C4⋊C4—94no—
744C4⋊C4—94no—
745C4⋊C4—94no—
746C4⋊C4—94no—
747C4⋊C4—94no—
748C4⋊C4—94no—
749C4⋊C4—94no—
750C4⋊C4—94no—
751C4⋊C4—92no—
752C4⋊C4—92no—
753C4⋊C4—92no—
754C4⋊C4—91no—
755C4⋊C4—92no—
756C4⋊C4C2×D3211yescharacteristic
757C22⋊C4—34no—
758C22⋊C4—34no—
759C22⋊C4—34no—
760C22⋊C4—94no—
761C22⋊C4—92no—
762C22⋊C4—92no—
763C22⋊C4—92no—
764C22⋊C4—92no—
765C22⋊C4C2×D3212yes—
766C42—32no—
767C42—32no—
768C42—34no—
769C42—92no—
770C42—92no—
771C42—94no—
772C42—94no—
773C42—94no—
774C42—91no—
775C42—91no—
776C42—91no—
777C42—92no—
778C42C2×D3211yescharacteristic
779C22×C3—22no—
780C22×C3—22no—
781C22×C3—22no—
782C22×C3—22no—
783C22×C3—22no—
784C22×C3—22no—
785C22×C3—21no—
786C22×C3—42no—
787C22×C3—42no—
788C22×C3—42no—
789C22×C3C24×D311yescharacteristic
790C22×C3C24×D311yescharacteristic
791C2×D3—32no—
792C2×D3—32no—
793C2×D3—62no—
794C2×D3—61no—
795C2×D3—61no—
796C2×D3—61no—
797C2×D3—61no—
798C2×D3—121no—
799C2×D3—121no—
800C3×C4—22no—
801C3×C4—22no—
802C3×C4—21no—
803C3×C4—21no—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—34no—
807C3×C4—41no—
808C3×C4—42no—
809C3×C4—62no—
810C3×C4—64no—
811C3×C4—64no—
812C3×C4—62no—
813C3×C4—62no—
814C3×C4C2×#23712yes—
815C3×C4#100712yes—
816C3×C4D3×#4112yes—
817C3×C4#101012yes—
818Dic3—24no—
819Dic3—22no—
820Dic3—24no—
821Dic3—22no—
822Dic3—22no—
823Dic3—61no—
824Dic3—62no—
825Dic3—61no—
826Dic3—61no—
827Dic3—62no—
828Dic3—61no—
829Dic3—61no—
830Dic3—61no—
831Dic3—62no—
832Dic3—62no—
833Dic3—122no—
834Dic3—121no—
835Dic3—121no—
836Dic3—121no—
837Dic3—122no—
838Dic3C2×#23714yes—
839C32#352311yescharacteristic, complemented, Sylow
840C23—91no—
841C23C22×D3212yes—
842Q8—34no—
843Q8—68no—
844Q8—64no—
845Q8—64no—
846Q8—62no—
847Q8—184no—
848Q8—182no—
849D4—22no—
850D4—184no—
851C2×C4—24no—
852C2×C4—32no—
853C2×C4—32no—
854C2×C4—34no—
855C2×C4—32no—
856C2×C4—32no—
857C2×C4—34no—
858C2×C4—68no—
859C2×C4—91no—
860C2×C4—91no—
861C2×C4—92no—
862C2×C4—92no—
863C2×C4—91no—
864C2×C4—182no—
865C2×C4—184no—
866C2×C4—184no—
867C2×C4—182no—
868C2×C4—182no—
869C2×C4C22×D3212yes—
870C2×C4C22×D3211yescharacteristic
871C2×C4C22×D3211yescharacteristic
872C2×C4C22×D3211yescharacteristic
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—42no—
877C2×C3—42no—
878C2×C3—82no—
879C2×C3C22×#23711yescharacteristic
880C2×C3C2×#100711yescharacteristic
881C2×C3C2×D3×#4111yescharacteristic
882C2×C3C2×#101011yescharacteristic
883C2×C3D3×2−1+411yescharacteristic
884C2×C3D3×2−1+411yescharacteristic
885D3—62no—
886D3—62no—
887D3—122no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—92no—
892C22—181no—
893C22—181no—
894C22C23×D3211yescharacteristic
895C4—22no—
896C4—21no—
897C4—34no—
898C4—64no—
899C4—64no—
900C4—62no—
901C4—62no—
902C4—62no—
903C4—181no—
904C4—182no—
905C4—181no—
906C4—181no—
907C4—182no—
908C4#6429712yes—
909C4D3×#23712yes—
910C3—21no—
911C3#8675311yescharacteristic, complemented
912C3#8699311yescharacteristic, complemented
913C2—42no—
914C2—182no—
915C2C2×#6429711yescharacteristic
916C2C2×D3×#23711yescharacteristic
917C2#1059669411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
prime radical#64147C22
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
2. C3×#5542C2semidirect
3. C3×D4×Dic6C2semidirect
4. #10595273C2semidirect
6. #10594970C2semidirect
7. #10594826C2semidirect
8. #10594818C2semidirect
9. #10594803C2semidirect
10. #10594397C2semidirect
11. #10594317C2semidirect
12. #10594028C2semidirect
13. #10594026C2semidirect
14. C4×#3797C2semidirect
15. #10593866C2semidirect
16. #10593864C2semidirect
17. #10593861C2semidirect
116. #5542D3semidirect
117. D4×Dic6D3semidirect
839. C32#3523semidirect
911. C3#86753semidirect
912. C3#86993semidirect

Maximal subgroups

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

subgroupindex
#105960282
C3×#55422
C3×D4×Dic62
#105952732
#105951912
#105949702
#105948262
#105948182
#105948032
#105943972
#105943172
#105940282
#105940262
C4×#37972
#105938662
#105938642
#105938612
#869933
#867533