Finite Group Databasebeta

← #11903761

Subgroups — #11903761

Order 1152.

2247 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596199C211yesmaximal, characteristic, complemented
2C3×#5727C211yesmaximal, characteristic, complemented
3C3×#5721C211yesmaximal, characteristic, complemented
4#10595403C212yesmaximal, complemented
5#10595371C212yesmaximal, complemented
6#10595368C212yesmaximal, complemented
7D3×Q8×Dic3C212yesmaximal, complemented
8#10594452C212yesmaximal, complemented
9#10594448C212yesmaximal, complemented
10#10594396C214yesmaximal, complemented
11#10594388C214yesmaximal, complemented
12#10594360C212yesmaximal
13#10594317C212yesmaximal, complemented
14#10593960C211yesmaximal, characteristic, complemented
15C4×#3797C211yesmaximal, characteristic, complemented
16C4×#3796C211yesmaximal, characteristic
17Dic62C211yesmaximal, characteristic, complemented
18#87015—31nomaximal
19Q8×#237—31nomaximal
20C2×C3×D3×Q8C2212yes—
21C2×#3797C2211yescharacteristic
22C2×#3796C2211yescharacteristic
23C32×C4⋊Q8C2211yescharacteristic
24#64155C2212yes—
25Q8×C3⋊Dic3C2212yes—
26#64106C2212yes—
27#64101C2212yes—
28#64099C2212yes—
29#64096C2212yes—
30C42×C3⋊D3C2211yescharacteristic
31#64078C2211yescharacteristic
32C3×#946C2212yes—
33C3×Q8×Dic3C2212yes—
34C3×#944C2212yes—
35C3×#896C2214yes—
36C3×#893C2212yes—
37C3×#890C2212yes—
38C3×#889C2214yes—
39C3×#888C2212yes—
40C3×#887C2212yes—
41C3×C4×D12C2211yescharacteristic
42C3×C4×Dic6C2211yescharacteristic
43C3×C4×Dic6C2211yescharacteristic
44C3×C4×Dic6C2211yescharacteristic
45#63918C2212yes—
46#63918C2212yes—
47C4×#627C2212yes—
48#63904C2214yes—
49C4×#626C2212yes—
50#63900C2211yescharacteristic
51#63899C2214yes—
52#63898C2211yescharacteristic
53#63896C2214yes—
54#63895C2214yes—
55#63893C2214yes—
56Dic3×D12C2212yes—
57D3×C4⋊Dic3C2212yes—
58D3×C4⋊Dic3C2214yes—
59#63888C2214yes—
60#63883C2212yes—
61C4×#624C2212yes—
62#63881C2212yes—
63#63880C2214yes—
64#63878C2214yes—
65#63878C2212yes—
66C4×D3×Dic3C2212yes—
67C4×D3×Dic3C2214yes—
68#63869C2212yes—
69#63867C2214yes—
70#63856C2212yes—
71#63851C2214yes—
72#63849C2211yescharacteristic
73#63845C2214yes—
74#63843C2211yescharacteristic
75#63843C2211yescharacteristic
76#63843C2214yes—
77#63843C2211yescharacteristic
78Dic3×Dic6C2214yes—
79Dic3×Dic6C2212yes—
80Dic3×Dic6C2212yes—
81#63840C2214yes—
82#63839C2214yes—
83#63838C2214yes—
84#63838C2212yes—
85C3×#557—31no—
86C3×D4×Q8—31no—
87Q8×#67—32no—
88C2×Q8×Dic3—32no—
89#5728—31no—
90#5728—31no—
91#5728—32no—
92#5728—32no—
93#5728—61no—
94#5727—32no—
95#5727D311yescharacteristic, complemented
96#5721—32no—
97#5721D311yescharacteristic, complemented
98#5690—34no—
99#5690—32no—
100#5688—34no—
101#5688—32no—
102#5635—32no—
103#5635—34no—
104#5622—32no—
105#5622—34no—
106#5579—32no—
107#5579—31no—
108C4×#239—32no—
109C4×#239—31no—
110C4×D3×Q8—32no—
111C4×D3×Q8—31no—
112C4×D3×Q8—31no—
113#5569—32no—
114Q8×Dic6—31no—
115Q8×Dic6—31no—
116#5543—32no—
117#5543—31no—
118C4×#237—32no—
119C4×#237—31no—
120C2×C32×Q8C2312yes—
121C2×C4×C3⋊D3C2311yescharacteristic
122C2×C4×C3⋊D3C2311yescharacteristic
123C2×C4×C3⋊D3C2311yescharacteristic
124C2×#634C2312yes—
125C3×D3×Q8—28no—
126C2×C3×D12C2311yescharacteristic
127C2×C3×C4×D3C2314yes—
128C2×C3×C4×D3C2312yes—
129C2×C3×Dic6C2314yes—
130C2×C3×Dic6C2311yescharacteristic
131C2×C3×Dic6C2311yescharacteristic
132C2×C3×Dic6C2311yescharacteristic
133C2×#627C2312yes—
134C2×#627C2314yes—
135C2×#626C2312yes—
136C2×#624C2312yes—
137C2×#624C2312yes—
138C2×D3×Dic3C2314yes—
139C2×D3×Dic3C2312yes—
140C2×D3×Dic3C2312yes—
141#3797—24no—
142#3796Q818yescomplemented
143C32×C4⋊C4C2312yes—
144C32×C4⋊C4C2312yes—
145C32×C42C2311yescharacteristic
146#3752C2314yes—
147C4⋊(C3⋊Dic3)C2312yes—
148C4⋊(C3⋊Dic3)C2312yes—
149C4⋊(C3⋊Dic3)C2314yes—
150#3750C2314yes—
151C4×C3⋊Dic3C2311yescharacteristic
152C4×C3⋊Dic3C2311yescharacteristic
153C4×C3⋊Dic3C2311yescharacteristic
154C4×C3⋊Dic3C2314yes—
155C3×(C2×D3)⋊C4C2314yes—
156C3×(C2×D3)⋊C4C2312yes—
157C3×C4⋊Dic3C2311yescharacteristic
158C3×C4⋊Dic3C2314yes—
159C3×C4⋊Dic3C2311yescharacteristic
160C3×C4⋊Dic3C2311yescharacteristic
161C3×C4⋊Dic3C2311yescharacteristic
162C3×Dic3⋊C4C2314yes—
163C3×Dic3⋊C4C2314yes—
164C3×Dic3⋊C4C2312yes—
165C3×Dic3⋊C4C2312yes—
166C3×Dic3⋊C4C2314yes—
167C3×Dic3⋊C4C2312yes—
168C3×C4×Dic3C2314yes—
169C3×C4×Dic3C2312yes—
170C3×C4×Dic3C2312yes—
171C3×C4×Dic3C2312yes—
172#3724C2314yes—
173#3724C2312yes—
174Dic3⋊Dic3C2312yes—
175Dic3⋊Dic3C2314yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2312yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2312yes—
180#3722C2312yes—
181(C2×D3)⋊Dic3C2312yes—
182(C2×D3)⋊Dic3C2314yes—
183Dic32C2312yes—
184Dic32C2312yes—
185Dic32C2312yes—
186Dic32C2314yes—
187Dic32C2312yes—
188Q8×#41—91noSylow
189C22×C3×Q8—32no—
190C2×#239—31no—
191C2×D3×Q8—31no—
192C2×D3×Q8—31no—
193C2×D3×Q8C2×D312yes—
194C2×#237—31no—
195C3×C4⋊Q8—21no—
196C3×C4⋊Q8—32no—
197C3×C4⋊Q8—32no—
198C3×C4⋊Q8C2×D311yescharacteristic
199C3×C4⋊Q8C2×D311yescharacteristic
200C3×#125—34no—
201C3×#125—32no—
202C3×C22⋊Q8—32no—
203C3×C22⋊Q8—34no—
204C3×C4×Q8—32no—
205C3×C4×Q8—32no—
206C3×C4×Q8—31no—
207C3×C4×Q8—31no—
208C3×C4×Q8—31no—
209C3×C4×D4—32no—
210C3×C4×D4—31no—
211#946—32no—
212#946—32no—
213#946—32no—
214#946—34no—
215#946—62no—
216#946C2×D312yes—
217Q8×Dic3—32no—
218Q8×Dic3—32no—
219Q8×Dic3—31no—
220Q8×Dic3—34no—
221Q8×Dic3—31no—
222Q8×Dic3—31no—
223Q8×Dic3—34no—
224Q8×Dic3—32no—
225Q8×Dic3—32no—
226Q8×Dic3—62no—
227Q8×Dic3C2×D312yes—
228#944—34no—
229#944C2×D312yes—
230D4×Dic3—31no—
231D4×Dic3—32no—
232C4×#67—34no—
233C4×#67—32no—
234C2×C4⋊Dic3—32no—
235C2×C4⋊Dic3—34no—
236#924—32no—
237#924—34no—
238C2×C4×Dic3—32no—
239C2×C4×Dic3—34no—
240#897—32no—
241#897—32no—
242#897—34no—
243#897—34no—
244#897—62no—
245#896—34no—
246#896—34no—
247#896—34no—
248#896—34no—
249#896—34no—
250#896C2×D314yes—
251#893—31no—
252#893—34no—
253#893—32no—
254#893C2×D312yes—
255#892—32no—
256#892—32no—
257#892—32no—
258#892—34no—
259#892—31no—
260#892—31no—
261#892—62no—
262D3×C4⋊C4—34no—
263D3×C4⋊C4—32no—
264D3×C4⋊C4—31no—
265D3×C4⋊C4—31no—
266D3×C4⋊C4—32no—
267D3×C4⋊C4—32no—
268#890—32no—
269#890—32no—
270#890—34no—
271#890—32no—
272#890—62no—
273#890C2×D312yes—
274#889—34no—
275#889—34no—
276#889C2×D314yes—
277#888—34no—
278#888—34no—
279#888—34no—
280#888—32no—
281#888—32no—
282#888C2×D312yes—
283#887—34no—
284#887—31no—
285#887—31no—
286#887—31no—
287#887—32no—
288#887—32no—
289#887—34no—
290#887—32no—
291#887—34no—
292#887—32no—
293#887—62no—
294#887C2×D312yes—
295#67⋊C4—32no—
296#67⋊C4—34no—
297#878—34no—
298#878—34no—
299#878—34no—
300#877—32no—
301#877—34no—
302C4×D12—32no—
303C4×D12—32no—
304C4×D12—34no—
305C4×D12C2×D311yescharacteristic
306C42×D3—34no—
307C42×D3—32no—
308C42×D3—31no—
309C42×D3—31no—
310C42×D3—32no—
311C42×D3—32no—
312C42×D3—61no—
313#870—32no—
314#870—34no—
315#869—31no—
316#869—31no—
317#869—32no—
318#869—32no—
319#869—61no—
320C4×Dic6—34no—
321C4×Dic6—32no—
322C4×Dic6—32no—
323C4×Dic6—32no—
324C4×Dic6—32no—
325C4×Dic6C2×D311yescharacteristic
326C4×Dic6C2×D311yescharacteristic
327C4×Dic6C2×D311yescharacteristic
328C22×C3⋊D3C2411yescharacteristic
329C22×C3×D3C2412yes—
330C32×Q8—24no—
331C2×C32×C4C2414yes—
332C2×C32×C4C2411yescharacteristic
333C2×C32×C4C2411yescharacteristic
334C2×C32×C4C2411yescharacteristic
335C2×C3⋊Dic3C2411yescharacteristic
336C2×C3⋊Dic3C2414yes—
337C2×C3⋊Dic3C2411yescharacteristic
338C2×C3⋊Dic3C2411yescharacteristic
339C4×C3⋊D3—22no—
340C4×C3⋊D3—41no—
341C4×C3⋊D3C2×Q814yescomplemented
342#634—42no—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2412yes—
350C3×D12C2×Q814yescomplemented
351C3×C4×D3—24no—
352C3×C4×D3—28no—
353C3×Dic6—22no—
354C3×Dic6—28no—
355C3×Dic6C2×Q814yescomplemented
356C3×Dic6#4114yescomplemented
357#627—24no—
358#627—44no—
359#626C2×Q818yescomplemented
360#624—24no—
361#624—42no—
362D3×Dic3—44no—
363D3×Dic3—42no—
364D3×Dic3C2×Q818yescomplemented
365Q82—91no—
366#557—31no—
367#557—92no—
368#554—91no—
369#554—92no—
370#554—92no—
371#554—94no—
372D4×Q8—31no—
373D4×Q8—92no—
374#533—94no—
375#533—92no—
376#533—92no—
377#533—91no—
378C4×#41—92no—
379C4×#41—91no—
380C2×C4×Q8—91no—
381C2×C4×Q8—92no—
382C2×C3×Q8—22no—
383C2×C3×Q8—31no—
384C2×C3×Q8—31no—
385C2×C3×Q8—34no—
386C2×C3×Q8—31no—
387C2×C3×Q8—68no—
388C2×C3×Q8C22×D312yes—
389C2×C3×Q8C22×D312yes—
390C2×C3×D4—31no—
391C22×C3×C4—34no—
392C22×C3×C4—32no—
393C2×#67—32no—
394C22×Dic3—32no—
395C22×Dic3—32no—
396C22×Dic3—34no—
397#239—38no—
398D3×Q8—28no—
399D3×Q8—64no—
400D3×Q8—64no—
401#237—38no—
402C2×D12—32no—
403C2×D12C22×D311yescharacteristic
404C2×C4×D3—32no—
405C2×C4×D3—31no—
406C2×C4×D3—31no—
407C2×C4×D3—31no—
408C2×C4×D3—31no—
409C2×C4×D3—32no—
410C2×C4×D3—32no—
411C2×C4×D3—34no—
412C2×C4×D3—32no—
413C2×C4×D3—31no—
414C2×C4×D3—31no—
415C2×C4×D3—32no—
416C2×C4×D3—32no—
417C2×C4×D3—61no—
418C2×C4×D3—61no—
419C2×C4×D3—61no—
420C2×C4×D3C22×D312yes—
421C2×C4×D3C22×D314yes—
422C2×Dic6—32no—
423C2×Dic6—32no—
424C2×Dic6—32no—
425C2×Dic6—32no—
426C2×Dic6—34no—
427C2×Dic6—34no—
428C2×Dic6—62no—
429C2×Dic6C22×D314yes—
430C2×Dic6C22×D311yescharacteristic
431C2×Dic6C22×D311yescharacteristic
432C2×Dic6C22×D311yescharacteristic
433C3×C4⋊C4—22no—
434C3×C4⋊C4—22no—
435C3×C4⋊C4—32no—
436C3×C4⋊C4—31no—
437C3×C4⋊C4—34no—
438C3×C4⋊C4—31no—
439C3×C4⋊C4—31no—
440C3×C4⋊C4—32no—
441C3×C4⋊C4—34no—
442C3×C4⋊C4—34no—
443C3×C4⋊C4—32no—
444C3×C4⋊C4—31no—
445C3×C4⋊C4—34no—
446C3×C4⋊C4C22×D312yes—
447C3×C4⋊C4C22×D312yes—
448C3×C4⋊C4C22×D312yes—
449C3×C4⋊C4C22×D312yes—
450C3×C22⋊C4—32no—
451C3×C22⋊C4—34no—
452C3×C42—21no—
453C3×C42—32no—
454C3×C42—32no—
455C3×C42—34no—
456C3×C42—32no—
457C3×C42C22×D311yescharacteristic
458C3×C42C22×D311yescharacteristic
459#217—32no—
460#217—34no—
461(C2×D3)⋊C4—32no—
462(C2×D3)⋊C4—34no—
463(C2×D3)⋊C4—34no—
464(C2×D3)⋊C4—34no—
465(C2×D3)⋊C4—32no—
466(C2×D3)⋊C4—32no—
467(C2×D3)⋊C4—64no—
468(C2×D3)⋊C4C22×D314yes—
469(C2×D3)⋊C4C22×D312yes—
470C4⋊Dic3—32no—
471C4⋊Dic3—32no—
472C4⋊Dic3—34no—
473C4⋊Dic3—32no—
474C4⋊Dic3—32no—
475C4⋊Dic3—34no—
476C4⋊Dic3—32no—
477C4⋊Dic3—32no—
478C4⋊Dic3—34no—
479C4⋊Dic3—34no—
480C4⋊Dic3—32no—
481C4⋊Dic3—34no—
482C4⋊Dic3—62no—
483C4⋊Dic3—62no—
484C4⋊Dic3—64no—
485C4⋊Dic3C22×D311yescharacteristic
486C4⋊Dic3C22×D311yescharacteristic
487C4⋊Dic3C22×D311yescharacteristic
488C4⋊Dic3C22×D311yescharacteristic
489C4⋊Dic3C22×D314yes—
490Dic3⋊C4—34no—
491Dic3⋊C4—34no—
492Dic3⋊C4—32no—
493Dic3⋊C4—34no—
494Dic3⋊C4—32no—
495Dic3⋊C4—34no—
496Dic3⋊C4—32no—
497Dic3⋊C4—32no—
498Dic3⋊C4—34no—
499Dic3⋊C4—34no—
500Dic3⋊C4—32no—
501Dic3⋊C4—34no—
502Dic3⋊C4—64no—
503Dic3⋊C4C22×D312yes—
504Dic3⋊C4C22×D312yes—
505Dic3⋊C4C22×D312yes—
506Dic3⋊C4C22×D314yes—
507Dic3⋊C4C22×D314yes—
508Dic3⋊C4C22×D314yes—
509C4×Dic3—31no—
510C4×Dic3—31no—
511C4×Dic3—31no—
512C4×Dic3—31no—
513C4×Dic3—31no—
514C4×Dic3—34no—
515C4×Dic3—31no—
516C4×Dic3—34no—
517C4×Dic3—34no—
518C4×Dic3—32no—
519C4×Dic3—34no—
520C4×Dic3—32no—
521C4×Dic3—32no—
522C4×Dic3—32no—
523C4×Dic3—32no—
524C4×Dic3—32no—
525C4×Dic3—32no—
526C4×Dic3—32no—
527C4×Dic3—61no—
528C4×Dic3—61no—
529C4×Dic3—61no—
530C4×Dic3—64no—
531C4×Dic3C22×D312yes—
532C4×Dic3C22×D312yes—
533C4×Dic3C22×D312yes—
534C4×Dic3C22×D314yes—
535C22×C32C2511yescharacteristic
536C2×C3⋊D3—21no—
537C2×C3⋊D3—21no—
538C2×C3⋊D3C22×Q812yes—
539C2×C3×D3—22no—
540C2×C3×D3—22no—
541C2×C3×D3C22×Q814yes—
542C32×C4—21no—
543C32×C4—24no—
544C32×C4C22×Q812yes—
545C32×C4C2×#4112yes—
546C3⋊Dic3—21no—
547C3⋊Dic3—21no—
548C3⋊Dic3—24no—
549C3⋊Dic3C22×Q812yes—
550C3×Dic3—22no—
551C3×Dic3—22no—
552C3×Dic3—22no—
553C3×Dic3—22no—
554C3×Dic3—22no—
555C3×Dic3C22×Q814yes—
556C3×Dic3C2×#4114yes—
557C2×#41—91no—
558C22×Q8—32no—
559C22×Q8—91no—
560C4⋊Q8—32no—
561C4⋊Q8—32no—
562C4⋊Q8—92no—
563C4⋊Q8—92no—
564C4⋊Q8—94no—
565C4⋊Q8—94no—
566C4⋊Q8—91no—
567C4⋊Q8D3211yescharacteristic
568#125—34no—
569#125—32no—
570#125—94no—
571#125—92no—
572#125—94no—
573#125—92no—
574C22⋊Q8—32no—
575C22⋊Q8—34no—
576C22⋊Q8—94no—
577C22⋊Q8—94no—
578C22⋊Q8—94no—
579C22⋊Q8—94no—
580C22⋊Q8—94no—
581C22⋊Q8—94no—
582C22⋊Q8—92no—
583C22⋊Q8—92no—
584C22⋊Q8—92no—
585C4×Q8—32no—
586C4×Q8—32no—
587C4×Q8—31no—
588C4×Q8—31no—
589C4×Q8—31no—
590C4×Q8—92no—
591C4×Q8—92no—
592C4×Q8—94no—
593C4×Q8—92no—
594C4×Q8—92no—
595C4×Q8—94no—
596C4×Q8—91no—
597C4×Q8—94no—
598C4×Q8—91no—
599C4×Q8—91no—
600C4×Q8—92no—
601C4×Q8—92no—
602C4×D4—32no—
603C4×D4—31no—
604C4×D4—94no—
605C4×D4—92no—
606C4×D4—92no—
607C4×D4—92no—
608C4×D4—94no—
609C4×D4—91no—
610#117—92no—
611#117—94no—
612#117—91no—
613#117—92no—
614C2×C4⋊C4—91no—
615C2×C4⋊C4—92no—
616C2×C4⋊C4—92no—
617C2×C4⋊C4—94no—
618C2×C42—92no—
619C2×C42—94no—
620C2×C42—92no—
621C2×C42—91no—
622C23×C3—32no—
623C22×D3—31no—
624C22×D3—31no—
625C22×D3—61no—
626C22×D3C23×D312yes—
627C3×Q8—24no—
628C3×Q8—24no—
629C3×Q8—34no—
630C3×Q8—34no—
631C3×Q8—44no—
632C3×Q8—68no—
633C3×Q8—62no—
634C3×D4—34no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—24no—
639C2×C3×C4—32no—
640C2×C3×C4—32no—
641C2×C3×C4—32no—
642C2×C3×C4—32no—
643C2×C3×C4—32no—
644C2×C3×C4—32no—
645C2×C3×C4—32no—
646C2×C3×C4—68no—
647C2×C3×C4—64no—
648C2×C3×C4C23×D314yes—
649C2×C3×C4C23×D314yes—
650C2×C3×C4C23×D311yescharacteristic
651C2×C3×C4C23×D311yescharacteristic
652C2×C3×C4C23×D311yescharacteristic
653C2×C3×C4C23×D311yescharacteristic
654C2×C3×C4C23×D311yescharacteristic
655C2×C3×C4C23×D311yescharacteristic
656#67—38no—
657C2×Dic3—31no—
658C2×Dic3—31no—
659C2×Dic3—38no—
660C2×Dic3—31no—
661C2×Dic3—31no—
662C2×Dic3—31no—
663C2×Dic3—31no—
664C2×Dic3—34no—
665C2×Dic3—34no—
666C2×Dic3—61no—
667C2×Dic3—61no—
668C2×Dic3—61no—
669C2×Dic3—64no—
670C2×Dic3—122no—
671C2×Dic3—124no—
672C2×Dic3C23×D312yes—
673C2×Dic3C23×D312yes—
674C2×Dic3C23×D312yes—
675C2×Dic3C23×D312yes—
676C2×Dic3C23×D312yes—
677C2×Dic3C23×D312yes—
678C2×Dic3C23×D312yes—
679D12—38no—
680D12D3×Q814yescomplemented
681C4×D3—24no—
682C4×D3—28no—
683C4×D3—38no—
684C4×D3—34no—
685C4×D3—34no—
686C4×D3—64no—
687C4×D3—64no—
688C4×D3—62no—
689C4×D3—62no—
690C4×D3—64no—
691C4×D3—122no—
692C4×D3—122no—
693C4×D3—122no—
694C4×D3—121no—
695C4×D3—121no—
696C4×D3—124no—
697C4×D3—122no—
698C4×D3—122no—
699Dic6—22no—
700Dic6—28no—
701Dic6—64no—
702Dic6—64no—
703Dic6—124no—
704Dic6—124no—
705Dic6—122no—
706Dic6—122no—
707Dic6—124no—
708Dic6#23714yescomplemented
709Dic6D3×Q814yescomplemented
710C2×C32C23×Q811yescharacteristic
711C2×C32C22×#4111yescharacteristic
712C2×C32#58511yescharacteristic
713C3⋊D3—22no—
714C3×D3—24no—
715#41—98no—
716C2×Q8—31no—
717C2×Q8—31no—
718C2×Q8—31no—
719C2×Q8—34no—
720C2×Q8—68no—
721C2×Q8—92no—
722C2×Q8—94no—
723C2×Q8—92no—
724C2×Q8—184no—
725C2×Q8C2×D3212yes—
726C2×D4—31no—
727C2×D4—92no—
728C22×C4—34no—
729C22×C4—32no—
730C22×C4—92no—
731C22×C4—92no—
732C22×C4—92no—
733C22×C4—94no—
734C22×C4—92no—
735C22×C4—91no—
736C22×C4—91no—
737C22×C4—91no—
738C4⋊C4—31no—
739C4⋊C4—32no—
740C4⋊C4—31no—
741C4⋊C4—32no—
742C4⋊C4—34no—
743C4⋊C4—31no—
744C4⋊C4—32no—
745C4⋊C4—31no—
746C4⋊C4—34no—
747C4⋊C4—34no—
748C4⋊C4—34no—
749C4⋊C4—92no—
750C4⋊C4—92no—
751C4⋊C4—94no—
752C4⋊C4—92no—
753C4⋊C4—94no—
754C4⋊C4—94no—
755C4⋊C4—92no—
756C4⋊C4—94no—
757C4⋊C4—94no—
758C4⋊C4—92no—
759C4⋊C4—92no—
760C4⋊C4—94no—
761C4⋊C4C2×D3212yes—
762C4⋊C4C2×D3212yes—
763C22⋊C4—34no—
764C22⋊C4—32no—
765C22⋊C4—92no—
766C22⋊C4—92no—
767C22⋊C4—94no—
768C22⋊C4—94no—
769C42—32no—
770C42—34no—
771C42—32no—
772C42—32no—
773C42—92no—
774C42—92no—
775C42—92no—
776C42—92no—
777C42—94no—
778C42—91no—
779C42—94no—
780C42—91no—
781C42—91no—
782C42C2×D3211yescharacteristic
783C22×C3—21no—
784C22×C3—34no—
785C22×C3—62no—
786C22×C3—62no—
787C22×C3C24×D311yescharacteristic
788C22×C3C24×D311yescharacteristic
789C2×D3—22no—
790C2×D3—22no—
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—
800C2×D3C2×D3×Q814yes—
801C3×C4—22no—
802C3×C4—24no—
803C3×C4—24no—
804C3×C4—21no—
805C3×C4—21no—
806C3×C4—22no—
807C3×C4—22no—
808C3×C4—34no—
809C3×C4—34no—
810C3×C4—44no—
811C3×C4—62no—
812C3×C4—62no—
813C3×C4—62no—
814C3×C4—62no—
815C3×C4—62no—
816C3×C4C2×#23712yes—
817C3×C4C2×D3×Q812yes—
818C3×C4C2×D3×Q812yes—
819C3×C4D3×#4112yes—
820Dic3—22no—
821Dic3—22no—
822Dic3—22no—
823Dic3—22no—
824Dic3—22no—
825Dic3—32no—
826Dic3—32no—
827Dic3—62no—
828Dic3—61no—
829Dic3—61no—
830Dic3—64no—
831Dic3—64no—
832Dic3—61no—
833Dic3—61no—
834Dic3—124no—
835Dic3—121no—
836Dic3—121no—
837Dic3C2×#23714yes—
838Dic3C2×D3×Q814yes—
839C32Q8×#4111yescharacteristic, complemented, Sylow
840C23—32no—
841C23—91no—
842Q8—24no—
843Q8—34no—
844Q8—34no—
845Q8—68no—
846Q8—62no—
847Q8—184no—
848Q8—362no—
849Q8—364no—
850D4—34no—
851D4—98no—
852C2×C4—32no—
853C2×C4—32no—
854C2×C4—32no—
855C2×C4—32no—
856C2×C4—32no—
857C2×C4—32no—
858C2×C4—32no—
859C2×C4—68no—
860C2×C4—64no—
861C2×C4—98no—
862C2×C4—91no—
863C2×C4—94no—
864C2×C4—91no—
865C2×C4—91no—
866C2×C4—94no—
867C2×C4—184no—
868C2×C4—182no—
869C2×C4—361no—
870C2×C4—362no—
871C2×C4—364no—
872C2×C4—362no—
873C2×C4C22×D3214yes—
874C2×C4C22×D3211yescharacteristic
875C2×C4C22×D3211yescharacteristic
876C2×C4C22×D3211yescharacteristic
877C2×C3—21no—
878C2×C3—21no—
879C2×C3—21no—
880C2×C3—64no—
881C2×C3C22×#23711yescharacteristic
882C2×C3C22×D3×Q811yescharacteristic
883C2×C3C22×D3×Q811yescharacteristic
884C2×C3C2×D3×#4111yescharacteristic
885C2×C3#596811yescharacteristic
886C2×C3#596811yescharacteristic
887D3—24no—
888D3—62no—
889D3—62no—
890D3—122no—
891C22—34no—
892C22—62no—
893C22—62no—
894C22—92no—
895C22—181no—
896C22—181no—
897C22C23×D3211yescharacteristic
898C4—24no—
899C4—21no—
900C4—34no—
901C4—34no—
902C4—62no—
903C4—62no—
904C4—62no—
905C4—62no—
906C4—62no—
907C4—92no—
908C4—181no—
909C4—181no—
910C4—184no—
911C4D3×#23712yes—
912C4D32×Q812yes—
913C3—21no—
914C3Q8×#23711yescharacteristic, complemented
915C3#8701511yescharacteristic, complemented
916C2—64no—
917C2—182no—
918C2C2×D3×#23711yescharacteristic
919C2C2×D32×Q811yescharacteristic
920C2#1059668911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
prime radicalC2×#3796C22
hypercenterC4⋊Q8D32
hypocenterC32Q8×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596199C2semidirect
2. C3×#5727C2semidirect
3. C3×#5721C2semidirect
4. #10595403C2semidirect
5. #10595371C2semidirect
6. #10595368C2semidirect
7. D3×Q8×Dic3C2semidirect
8. #10594452C2semidirect
9. #10594448C2semidirect
10. #10594396C2semidirect
11. #10594388C2semidirect
13. #10594317C2semidirect
14. #10593960C2semidirect
15. C4×#3797C2semidirect
17. Dic62C2semidirect
95. #5727D3semidirect
97. #5721D3semidirect
142. #3796Q8semidirect
341. C4×C3⋊D3C2×Q8semidirect
350. C3×D12C2×Q8semidirect
355. C3×Dic6C2×Q8semidirect
356. C3×Dic6#41semidirect
359. #626C2×Q8semidirect
364. D3×Dic3C2×Q8semidirect
680. D12D3×Q8semidirect
708. Dic6#237semidirect
709. Dic6D3×Q8semidirect
839. C32Q8×#41semidirect
914. C3Q8×#237semidirect
915. C3#87015semidirect

Maximal subgroups

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

subgroupindex
#105961992
C3×#57272
C3×#57212
#105954032
#105953712
#105953682
D3×Q8×Dic32
#105944522
#105944482
#105943962
#105943882
#105943602
#105943172
#105939602
C4×#37972
C4×#37962
Dic622
#870153
Q8×#2373