Finite Group Databasebeta

← #11906350

Subgroups — #11906350

Order 1152.

2260 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#634C211yesmaximal, characteristic, complemented
2C3×D4×Dic6C211yesmaximal, characteristic, complemented
3C3×C4×#237C211yesmaximal, characteristic
4#10595272C212yesmaximal, complemented
5#10595222C212yesmaximal
6#10594915C212yesmaximal, complemented
7Dic6×#67C212yesmaximal, complemented
8C2×#63866C212yesmaximal, complemented
9#10594808C212yesmaximal, complemented
10#10594502C212yesmaximal, complemented
11#10594312C212yesmaximal, complemented
12#10594146C214yesmaximal, complemented
13#10594035C214yesmaximal, complemented
14D3×#869C211yesmaximal, characteristic, complemented
15#10593873C211yesmaximal, characteristic, complemented
16#10593861C211yesmaximal, characteristic, complemented
17#10593860C211yesmaximal, characteristic, complemented
18#86747—31nomaximal
19#85828—31nomaximal
20C22×#634C2212yes—
21C2×C3×#237C2211yescharacteristic
22C22×C3×Dic6C2212yes—
23C2×D3×Dic6C2212yes—
24C32×C4×D4C2211yescharacteristic
25D4×C3⋊Dic3C2212yes—
26#64133C2212yes—
27#64097C2212yes—
28#64087C2214yes—
29#64078C2211yescharacteristic
30C4×#634C2211yescharacteristic
31C3×D4×Dic3C2211yescharacteristic
32C3×D4×Dic3C2212yes—
33C3×C4×#67C2212yes—
34C3×#924C2212yes—
35C2×C3×C4×Dic3C2212yes—
36C3×#892C2211yescharacteristic
37C3×#888C2212yes—
38C3×#887C2211yescharacteristic
39C3×#67⋊C4C2212yes—
40C3×#878C2214yes—
41C3×#877C2212yes—
42C3×C42×D3C2211yescharacteristic
43C3×#869C2211yescharacteristic
44C3×C4×Dic6C2211yescharacteristic
45C3×C4×Dic6C2211yescharacteristic
46#63982C2214yes—
47#67⋊Dic3C2214yes—
48Dic3×#67C2214yes—
49C2×Dic3⋊Dic3C2214yes—
50C2×Dic3⋊Dic3C2214yes—
51#63964C2214yes—
52#63964C2214yes—
53#63955C2214yes—
54#63918C2212yes—
55#63918C2211yescharacteristic
56#63918C2212yes—
57C4×#627C2212yes—
58#63896C2214yes—
59D3×C4⋊Dic3C2212yes—
60D3×C4⋊Dic3C2212yes—
61#63887C2214yes—
62#63872C2212yes—
63#63869C2212yes—
64#63867C2212yes—
65#63867C2214yes—
66#63866C2214yes—
67#63866C2211yescharacteristic
68#63866C2212yes—
69#63866C2212yes—
70#63866C2212yes—
71#63866C2214yes—
72#63857C2211yescharacteristic
73#63856C2211yescharacteristic
74#63855C2212yes—
75#63851C2212yes—
76#63846C2214yes—
77#63845C2214yes—
78#63844C2212yes—
79#63843C2212yes—
80Dic3×Dic6C2212yes—
81Dic3×Dic6C2212yes—
82#63840C2214yes—
83#63839C2214yes—
84#63837C2214yes—
85C3×D4×Q8—31no—
86C3×C4×#41—31no—
87#5827—32no—
88Q8×#67—32no—
89C2×#944—32no—
90#5729—32no—
91D3×C4⋊Q8—31no—
92#5722—32no—
93#5721—31no—
94#5636—34no—
95#5632—32no—
96#5623—34no—
97#5622—32no—
98#5578—31no—
99#5570—31no—
100#5570—31no—
101#5567—31no—
102Q8×Dic6—32no—
103#5546—32no—
104#5543—32no—
105#5543—34no—
106#5539—32no—
107D4×Dic6—32no—
108D4×Dic6—31no—
109D4×Dic6—31no—
110D4×Dic6—32no—
111D4×Dic6—61no—
112D4×Dic6D311yescharacteristic, complemented
113C4×#237D311yescharacteristic
114#5519—32no—
115#5519—34no—
116#5470—32no—
117#5470—31no—
118C2×#869—32no—
119C2×#869—31no—
120C2×C32×D4C2311yescharacteristic
121C22×C32×C4C2312yes—
122C22×C3⋊Dic3C2314yes—
123C2×#634—44no—
124C2×#634C2312yes—
125C2×#634C2311yescharacteristic
126C2×#634C2314yes—
127C2×C3×#67C2312yes—
128C22×C3×Dic3C2312yes—
129C22×C3×Dic3C2314yes—
130C22×C3×Dic3C2312yes—
131C3×#237Q818yescomplemented
132C2×C3×C4×D3C2311yescharacteristic
133C2×C3×C4×D3C2311yescharacteristic
134C2×C3×C4×D3C2311yescharacteristic
135C2×C3×Dic6—44no—
136C2×C3×Dic6C2312yes—
137C2×C3×Dic6C2311yescharacteristic
138C2×C3×Dic6C2314yes—
139C2×C3×Dic6C2311yescharacteristic
140C2×#627C2312yes—
141C2×#627C2314yes—
142C2×D3×Dic3C2314yes—
143D3×Dic6—44no—
144C32×C4⋊C4C2311yescharacteristic
145C32×C22⋊C4C2312yes—
146C32×C42C2311yescharacteristic
147#3757C2314yes—
148C4⋊(C3⋊Dic3)C2311yescharacteristic
149C4⋊(C3⋊Dic3)C2312yes—
150C4⋊(C3⋊Dic3)C2312yes—
151#3750C2312yes—
152#3750C2314yes—
153C4×C3⋊Dic3C2312yes—
154C3×#217C2312yes—
155C3×#217C2314yes—
156C3×(C2×D3)⋊C4C2312yes—
157C3×C4⋊Dic3C2312yes—
158C3×C4⋊Dic3C2312yes—
159C3×C4⋊Dic3C2311yescharacteristic
160C3×C4⋊Dic3C2311yescharacteristic
161C3×Dic3⋊C4C2312yes—
162C3×Dic3⋊C4C2312yes—
163C3×Dic3⋊C4C2312yes—
164C3×Dic3⋊C4C2314yes—
165C3×C4×Dic3C2311yescharacteristic
166C3×C4×Dic3C2312yes—
167C3×C4×Dic3C2312yes—
168C3×C4×Dic3C2311yescharacteristic
169C3×C4×Dic3C2312yes—
170C3×C4×Dic3C2311yescharacteristic
171C3×C4×Dic3C2312yes—
172#3724C2312yes—
173#3724C2314yes—
174Dic3⋊Dic3C2314yes—
175Dic3⋊Dic3C2314yes—
176Dic3⋊Dic3C2312yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2312yes—
182Dic3⋊Dic3C2312yes—
183Dic3⋊Dic3C2312yes—
184Dic3⋊Dic3C2314yes—
185(C2×D3)⋊Dic3C2312yes—
186(C2×D3)⋊Dic3C2312yes—
187Dic32C2314yes—
188Dic32C2314yes—
189#3503—91noSylow
190C2×C3×#41—31no—
191C22×C3×Q8—32no—
192C2×D3×Q8—32no—
193C2×#237C2×D311yescharacteristic
194C22×Dic6—32no—
195C22×Dic6—32no—
196C22×Dic6—32no—
197C22×Dic6—62no—
198C22×Dic6C2×D312yes—
199C3×C4⋊Q8—32no—
200C3×C4⋊Q8—31no—
201C3×C22⋊Q8—32no—
202C3×C22⋊Q8—34no—
203C3×C4×Q8—31no—
204C3×C4×Q8—31no—
205C3×C4×Q8—31no—
206C3×C4×D4—21no—
207C3×C4×D4—32no—
208C3×C4×D4—31no—
209C3×C4×D4—32no—
210C3×C4×D4—32no—
211C3×C4×D4C2×D311yescharacteristic
212C3×C4×D4C2×D311yescharacteristic
213C3×#117—31no—
214C3×#117—32no—
215C2×C3×C42—32no—
216C2×C3×C42—31no—
217#946—31no—
218#946—34no—
219Q8×Dic3—32no—
220Q8×Dic3—32no—
221Q8×Dic3—32no—
222#944—34no—
223#944—32no—
224#944—34no—
225#944—32no—
226#944—34no—
227#944—31no—
228#944—32no—
229D4×Dic3—32no—
230D4×Dic3—32no—
231D4×Dic3—34no—
232D4×Dic3—34no—
233D4×Dic3—62no—
234D4×Dic3C2×D311yescharacteristic
235D4×Dic3C2×D312yes—
236C4×#67—34no—
237C4×#67C2×D312yes—
238#926—34no—
239#926—32no—
240C2×C4⋊Dic3—34no—
241C2×C4⋊Dic3—34no—
242C2×C4⋊Dic3—32no—
243C2×C4⋊Dic3—32no—
244#924—32no—
245#924—32no—
246#924—31no—
247#924—34no—
248#924—34no—
249#924—31no—
250#924—32no—
251#924—62no—
252#924C2×D312yes—
253C2×Dic3⋊C4—34no—
254C2×Dic3⋊C4—34no—
255C2×C4×Dic3C2×D312yes—
256#897—31no—
257#896—32no—
258#896—34no—
259#892C2×D311yescharacteristic
260D3×C4⋊C4—32no—
261D3×C4⋊C4—32no—
262#890—32no—
263#890—34no—
264#890—32no—
265#890—34no—
266#890—32no—
267#889—34no—
268#889—34no—
269#889—34no—
270#889—32no—
271#888—34no—
272#888—32no—
273#888—32no—
274#888—34no—
275#888—34no—
276#888—32no—
277#888—32no—
278#888—31no—
279#888—62no—
280#888C2×D312yes—
281#887—32no—
282#887—32no—
283#887—34no—
284#887C2×D311yescharacteristic
285#67⋊C4—34no—
286#67⋊C4C2×D312yes—
287#878—34no—
288#878—34no—
289#878—34no—
290#878—34no—
291#878—34no—
292#878—34no—
293#878—34no—
294#878—34no—
295#878—64no—
296#878C2×D314yes—
297#877—34no—
298#877C2×D312yes—
299#872—32no—
300C42×D3C2×D311yescharacteristic
301#870—32no—
302#870—34no—
303#870—32no—
304#869—32no—
305#869—31no—
306#869—34no—
307#869—32no—
308#869—32no—
309#869—34no—
310#869—31no—
311#869—31no—
312#869—32no—
313#869—32no—
314#869—31no—
315#869—61no—
316#869C2×D311yescharacteristic
317C4×Dic6—32no—
318C4×Dic6—32no—
319C4×Dic6—31no—
320C4×Dic6—31no—
321C4×Dic6—32no—
322C4×Dic6—34no—
323C4×Dic6—32no—
324C4×Dic6—32no—
325C4×Dic6—61no—
326C4×Dic6C2×D311yescharacteristic
327C4×Dic6C2×D311yescharacteristic
328C23×C32C2412yes—
329C22×C3×D3C2411yescharacteristic
330C32×D4C2×Q814yescomplemented
331C2×C32×C4—24no—
332C2×C32×C4C2412yes—
333C2×C32×C4C2411yescharacteristic
334C2×C32×C4C2411yescharacteristic
335C2×C32×C4C2411yescharacteristic
336C2×C3⋊Dic3—44no—
337C2×C3⋊Dic3C2412yes—
338C2×C3⋊Dic3C2414yes—
339C2×C3⋊Dic3C2412yes—
340#634—22no—
341#634—24no—
342#634—44no—
343C3×#67C2×Q818yescomplemented
344C2×C3×Dic3—24no—
345C2×C3×Dic3—44no—
346C2×C3×Dic3C2×Q818yescomplemented
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2414yes—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2411yescharacteristic
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2411yescharacteristic
354C2×C3×Dic3C2411yescharacteristic
355C3×C4×D3—22no—
356C3×C4×D3—22no—
357C3×C4×D3C2×Q814yescomplemented
358C3×Dic6—24no—
359C3×Dic6—22no—
360C3×Dic6—44no—
361C3×Dic6C2×Q814yescomplemented
362#627—24no—
363#627—44no—
364D3×Dic3—44no—
365Q82—92no—
366#557—91no—
367#557—91no—
368#554—92no—
369#554—94no—
370D4×Q8—31no—
371D4×Q8—92no—
372D4×Q8—92no—
373D4×Q8—91no—
374#544—94no—
375#544—92no—
376#533—91no—
377#533—92no—
378C2×C4⋊Q8—91no—
379C2×C4⋊Q8—92no—
380#520—92no—
381C4×#41—31no—
382C3×#41—38no—
383C2×C3×Q8—31no—
384C2×C3×Q8—31no—
385C2×C3×Q8—32no—
386C2×C3×Q8—34no—
387C2×C3×Q8—124no—
388C2×C3×D4—21no—
389C2×C3×D4—32no—
390C2×C3×D4C22×D311yescharacteristic
391C2×C3×D4C22×D311yescharacteristic
392C22×C3×C4—22no—
393C22×C3×C4—32no—
394C22×C3×C4—31no—
395C22×C3×C4—32no—
396C22×C3×C4—34no—
397C22×C3×C4—31no—
398C22×C3×C4—31no—
399C22×C3×C4C22×D312yes—
400C22×C3×C4C22×D312yes—
401C2×#67C22×D312yes—
402C22×Dic3—34no—
403C22×Dic3—34no—
404C22×Dic3—34no—
405C22×Dic3—64no—
406C22×Dic3C22×D312yes—
407C22×Dic3C22×D314yes—
408C22×Dic3C22×D312yes—
409D3×Q8—124no—
410#237Dic618yescomplemented
411C2×C4×D3—34no—
412C2×C4×D3C22×D311yescharacteristic
413C2×C4×D3C22×D311yescharacteristic
414C2×C4×D3C22×D311yescharacteristic
415C2×Dic6—31no—
416C2×Dic6—32no—
417C2×Dic6—31no—
418C2×Dic6—32no—
419C2×Dic6—32no—
420C2×Dic6—32no—
421C2×Dic6—34no—
422C2×Dic6—34no—
423C2×Dic6—34no—
424C2×Dic6—34no—
425C2×Dic6—44no—
426C2×Dic6—61no—
427C2×Dic6—62no—
428C2×Dic6—64no—
429C2×Dic6—124no—
430C2×Dic6—124no—
431C2×Dic6—124no—
432C2×Dic6—128no—
433C2×Dic6C22×D312yes—
434C2×Dic6C22×D311yescharacteristic
435C2×Dic6C22×D314yes—
436C2×Dic6C22×D311yescharacteristic
437C3×C4⋊C4—21no—
438C3×C4⋊C4—31no—
439C3×C4⋊C4—34no—
440C3×C4⋊C4—32no—
441C3×C4⋊C4—32no—
442C3×C4⋊C4—32no—
443C3×C4⋊C4—32no—
444C3×C4⋊C4—32no—
445C3×C4⋊C4—31no—
446C3×C4⋊C4C22×D311yescharacteristic
447C3×C4⋊C4C22×D311yescharacteristic
448C3×C22⋊C4—22no—
449C3×C22⋊C4—34no—
450C3×C22⋊C4—32no—
451C3×C22⋊C4—32no—
452C3×C22⋊C4C22×D312yes—
453C3×C22⋊C4C22×D312yes—
454C3×C42—21no—
455C3×C42—32no—
456C3×C42—32no—
457C3×C42—31no—
458C3×C42—32no—
459C3×C42—31no—
460C3×C42—32no—
461C3×C42—31no—
462C3×C42C22×D311yescharacteristic
463C3×C42C22×D311yescharacteristic
464#217—34no—
465#217—34no—
466#217—32no—
467#217—32no—
468#217—64no—
469#217C22×D312yes—
470#217C22×D314yes—
471(C2×D3)⋊C4—32no—
472(C2×D3)⋊C4—32no—
473(C2×D3)⋊C4C22×D312yes—
474C4⋊Dic3—31no—
475C4⋊Dic3—32no—
476C4⋊Dic3—31no—
477C4⋊Dic3—32no—
478C4⋊Dic3—32no—
479C4⋊Dic3—32no—
480C4⋊Dic3—34no—
481C4⋊Dic3—32no—
482C4⋊Dic3—32no—
483C4⋊Dic3—34no—
484C4⋊Dic3—32no—
485C4⋊Dic3—34no—
486C4⋊Dic3—34no—
487C4⋊Dic3—34no—
488C4⋊Dic3—34no—
489C4⋊Dic3—32no—
490C4⋊Dic3—34no—
491C4⋊Dic3—61no—
492C4⋊Dic3—62no—
493C4⋊Dic3—62no—
494C4⋊Dic3C22×D311yescharacteristic
495C4⋊Dic3C22×D311yescharacteristic
496C4⋊Dic3C22×D312yes—
497C4⋊Dic3C22×D312yes—
498Dic3⋊C4—34no—
499Dic3⋊C4—32no—
500Dic3⋊C4—32no—
501Dic3⋊C4—34no—
502Dic3⋊C4—32no—
503Dic3⋊C4—32no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4—32no—
508Dic3⋊C4—32no—
509Dic3⋊C4—34no—
510Dic3⋊C4—34no—
511Dic3⋊C4—32no—
512Dic3⋊C4—32no—
513Dic3⋊C4—34no—
514Dic3⋊C4—34no—
515Dic3⋊C4—34no—
516Dic3⋊C4—34no—
517Dic3⋊C4—62no—
518Dic3⋊C4—64no—
519Dic3⋊C4C22×D314yes—
520Dic3⋊C4C22×D312yes—
521Dic3⋊C4C22×D312yes—
522Dic3⋊C4C22×D312yes—
523C4×Dic3—32no—
524C4×Dic3—32no—
525C4×Dic3—34no—
526C4×Dic3—34no—
527C4×Dic3—34no—
528C4×Dic3—34no—
529C4×Dic3—62no—
530C4×Dic3C22×D311yescharacteristic
531C4×Dic3C22×D312yes—
532C4×Dic3C22×D312yes—
533C4×Dic3C22×D311yescharacteristic
534C4×Dic3C22×D311yescharacteristic
535C4×Dic3C22×D312yes—
536C4×Dic3C22×D312yes—
537C22×C32—22no—
538C22×C32—22no—
539C22×C32C22×Q814yes—
540C22×C32C2511yescharacteristic
541C2×C3×D3—21no—
542C2×C3×D3—21no—
543C2×C3×D3C22×Q812yes—
544C32×C4—22no—
545C32×C4—21no—
546C32×C4C22×Q812yes—
547C32×C4H(5,𝔽2)12yes—
548C3⋊Dic3—22no—
549C3⋊Dic3—24no—
550C3⋊Dic3—22no—
551C3×Dic3—24no—
552C3×Dic3—21no—
553C3×Dic3—22no—
554C3×Dic3—22no—
555C3×Dic3—22no—
556C3×Dic3C22×Q814yes—
557C3×Dic3C22×Q812yes—
558C3×Dic32−1+412yes—
559C2×#41—31no—
560C22×Q8—32no—
561C22×Q8—92no—
562C22×Q8—92no—
563C4⋊Q8—32no—
564C4⋊Q8—31no—
565C4⋊Q8—92no—
566C4⋊Q8—92no—
567C4⋊Q8—91no—
568C4⋊Q8—91no—
569C4⋊Q8—92no—
570C4⋊Q8—94no—
571C4⋊Q8—92no—
572C4⋊Q8—92no—
573C4⋊Q8—94no—
574C4⋊Q8—94no—
575C4⋊Q8—94no—
576C4⋊Q8—92no—
577C4⋊Q8—91no—
578#125—92no—
579#125—94no—
580#125—92no—
581#125—94no—
582#125—94no—
583#125—92no—
584C22⋊Q8—32no—
585C22⋊Q8—34no—
586C22⋊Q8—94no—
587C22⋊Q8—94no—
588C22⋊Q8—94no—
589C22⋊Q8—94no—
590C22⋊Q8—94no—
591C22⋊Q8—91no—
592C22⋊Q8—92no—
593C22⋊Q8—91no—
594C22⋊Q8—92no—
595C22⋊Q8—94no—
596C4×Q8—31no—
597C4×Q8—31no—
598C4×Q8—31no—
599C4×Q8—92no—
600C4×Q8—92no—
601C4×Q8—94no—
602C4×Q8—92no—
603C4×Q8—92no—
604C4×Q8—92no—
605C4×Q8—91no—
606C4×D4—31no—
607C4×D4—32no—
608C4×D4—32no—
609C4×D4—32no—
610C4×D4—94no—
611C4×D4—94no—
612C4×D4—92no—
613C4×D4D3211yescharacteristic
614#117—31no—
615#117—32no—
616#117—92no—
617#117—94no—
618C2×C4⋊C4—92no—
619C2×C4⋊C4—92no—
620C2×C4⋊C4—94no—
621C2×C4⋊C4—94no—
622C2×C42—32no—
623C2×C42—31no—
624C23×C3—22no—
625C23×C3—31no—
626C23×C3C23×D312yes—
627C23×C3C23×D312yes—
628C22×D3C23×D311yescharacteristic
629C3×Q8—34no—
630C3×Q8—64no—
631C3×Q8—62no—
632C3×Q8—124no—
633C3×D4—24no—
634C3×D4—38no—
635C3×D4C2×Dic614yescomplemented
636C3×D4D3×Q814yescomplemented
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—38no—
644C2×C3×C4—32no—
645C2×C3×C4—31no—
646C2×C3×C4—31no—
647C2×C3×C4—34no—
648C2×C3×C4—32no—
649C2×C3×C4—34no—
650C2×C3×C4—32no—
651C2×C3×C4—32no—
652C2×C3×C4—31no—
653C2×C3×C4—44no—
654C2×C3×C4—62no—
655C2×C3×C4—64no—
656C2×C3×C4—62no—
657C2×C3×C4—124no—
658C2×C3×C4C23×D312yes—
659C2×C3×C4C23×D311yescharacteristic
660C2×C3×C4C23×D311yescharacteristic
661C2×C3×C4C23×D312yes—
662C2×C3×C4C23×D311yescharacteristic
663C2×C3×C4C23×D311yescharacteristic
664C2×C3×C4C23×D311yescharacteristic
665C2×C3×C4C23×D311yescharacteristic
666#67C2×Dic618yescomplemented
667C2×Dic3—24no—
668C2×Dic3—32no—
669C2×Dic3—32no—
670C2×Dic3—32no—
671C2×Dic3—34no—
672C2×Dic3—34no—
673C2×Dic3—32no—
674C2×Dic3—44no—
675C2×Dic3—62no—
676C2×Dic3—62no—
677C2×Dic3—64no—
678C2×Dic3—124no—
679C2×Dic3—124no—
680C2×Dic3—124no—
681C2×Dic3—128no—
682C2×Dic3C2×Dic618yescomplemented
683C2×Dic3C23×D312yes—
684C2×Dic3C23×D314yes—
685C2×Dic3C23×D312yes—
686C2×Dic3C23×D311yescharacteristic
687C2×Dic3C23×D312yes—
688C2×Dic3C23×D312yes—
689C2×Dic3C23×D311yescharacteristic
690C2×Dic3C23×D311yescharacteristic
691C4×D3—22no—
692C4×D3—22no—
693C4×D3—124no—
694C4×D3C2×Dic614yescomplemented
695Dic6—22no—
696Dic6—24no—
697Dic6—44no—
698Dic6—64no—
699Dic6—64no—
700Dic6—62no—
701Dic6—64no—
702Dic6—62no—
703Dic6—64no—
704Dic6—64no—
705Dic6—124no—
706Dic6—124no—
707Dic6—124no—
708Dic6—124no—
709Dic6—124no—
710Dic6—128no—
711Dic6C2×Dic614yescomplemented
712C2×C32—24no—
713C2×C32C23×Q811yescharacteristic
714C2×C32C2×H(5,𝔽2)11yescharacteristic
715C2×C32C2×2−1+411yescharacteristic
716C3×D3—22no—
717#41—38no—
718C2×Q8—31no—
719C2×Q8—31no—
720C2×Q8—32no—
721C2×Q8—34no—
722C2×Q8—92no—
723C2×Q8—94no—
724C2×Q8—91no—
725C2×Q8—92no—
726C2×Q8—94no—
727C2×Q8—124no—
728C2×Q8—364no—
729C2×Q8—364no—
730C2×D4—32no—
731C2×D4C2×D3211yescharacteristic
732C22×C4—32no—
733C22×C4—31no—
734C22×C4—32no—
735C22×C4—34no—
736C22×C4—31no—
737C22×C4—31no—
738C22×C4—94no—
739C22×C4—94no—
740C22×C4C2×D3212yes—
741C4⋊C4—32no—
742C4⋊C4—32no—
743C4⋊C4—32no—
744C4⋊C4—31no—
745C4⋊C4—32no—
746C4⋊C4—31no—
747C4⋊C4—32no—
748C4⋊C4—34no—
749C4⋊C4—92no—
750C4⋊C4—94no—
751C4⋊C4—92no—
752C4⋊C4—94no—
753C4⋊C4—94no—
754C4⋊C4—94no—
755C4⋊C4—94no—
756C4⋊C4—94no—
757C4⋊C4—92no—
758C4⋊C4—94no—
759C4⋊C4—94no—
760C4⋊C4—92no—
761C4⋊C4—92no—
762C4⋊C4—92no—
763C4⋊C4—92no—
764C4⋊C4—91no—
765C4⋊C4—92no—
766C4⋊C4—94no—
767C4⋊C4C2×D3211yescharacteristic
768C22⋊C4—32no—
769C22⋊C4—34no—
770C22⋊C4—32no—
771C22⋊C4—92no—
772C22⋊C4—92no—
773C22⋊C4—94no—
774C22⋊C4C2×D3212yes—
775C42—31no—
776C42—32no—
777C42—31no—
778C42—32no—
779C42—31no—
780C42—32no—
781C42—32no—
782C42—94no—
783C42—94no—
784C42—92no—
785C42C2×D3211yescharacteristic
786C22×C3—22no—
787C22×C3—22no—
788C22×C3—22no—
789C22×C3—22no—
790C22×C3—24no—
791C22×C3—21no—
792C22×C3—32no—
793C22×C3—42no—
794C22×C3—42no—
795C22×C3—61no—
796C22×C3—61no—
797C22×C3C22×Dic614yes—
798C22×C3C2×D3×Q814yes—
799C22×C3C24×D311yescharacteristic
800C22×C3C24×D311yescharacteristic
801C2×D3—21no—
802C2×D3—21no—
803C2×D3C22×Dic612yes—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—21no—
807C3×C4—21no—
808C3×C4—22no—
809C3×C4—22no—
810C3×C4—32no—
811C3×C4—34no—
812C3×C4—32no—
813C3×C4—42no—
814C3×C4—41no—
815C3×C4—61no—
816C3×C4—64no—
817C3×C4—62no—
818C3×C4—62no—
819C3×C4—62no—
820C3×C4C22×Dic612yes—
821C3×C4#100412yes—
822C3×C4C2×D3×Q812yes—
823C3×C4#100912yes—
824Dic3—22no—
825Dic3—24no—
826Dic3—21no—
827Dic3—22no—
828Dic3—22no—
829Dic3—64no—
830Dic3—62no—
831Dic3—64no—
832Dic3—64no—
833Dic3—62no—
834Dic3—62no—
835Dic3—62no—
836Dic3—124no—
837Dic3—122no—
838Dic3C22×Dic614yes—
839Dic3C22×Dic612yes—
840Dic3#101012yes—
841C32#350311yescharacteristic, complemented, Sylow
842C23—31no—
843C23C22×D3212yes—
844Q8—34no—
845Q8—62no—
846Q8—64no—
847Q8—124no—
848Q8—184no—
849Q8—182no—
850Q8—184no—
851Q8—364no—
852Q8—364no—
853D4—38no—
854D4D3×Dic614yescomplemented
855C2×C4—24no—
856C2×C4—38no—
857C2×C4—31no—
858C2×C4—31no—
859C2×C4—32no—
860C2×C4—34no—
861C2×C4—32no—
862C2×C4—31no—
863C2×C4—32no—
864C2×C4—32no—
865C2×C4—34no—
866C2×C4—62no—
867C2×C4—64no—
868C2×C4—62no—
869C2×C4—92no—
870C2×C4—92no—
871C2×C4—94no—
872C2×C4—124no—
873C2×C4—364no—
874C2×C4—364no—
875C2×C4C22×D3212yes—
876C2×C4C22×D3211yescharacteristic
877C2×C4C22×D3211yescharacteristic
878C2×C4C22×D3211yescharacteristic
879C2×C3—24no—
880C2×C3—24no—
881C2×C3—21no—
882C2×C3—21no—
883C2×C3—21no—
884C2×C3—44no—
885C2×C3—62no—
886C2×C3C23×Dic611yescharacteristic
887C2×C3C2×#100411yescharacteristic
888C2×C3C22×D3×Q811yescharacteristic
889C2×C3C2×#100911yescharacteristic
890C2×C3C2×#101011yescharacteristic
891C2×C3D3×2−1+411yescharacteristic
892D3—22no—
893C22—22no—
894C22—22no—
895C22—32no—
896C22—61no—
897C22—61no—
898C22C2×D3×Dic614yes—
899C22C23×D3211yescharacteristic
900C4—22no—
901C4—21no—
902C4—32no—
903C4—34no—
904C4—32no—
905C4—61no—
906C4—62no—
907C4—64no—
908C4—62no—
909C4—62no—
910C4—182no—
911C4—184no—
912C4—182no—
913C4C2×D3×Dic612yes—
914C4#6431412yes—
915C3—21no—
916C3#8582811yescharacteristic, complemented
917C3#8674711yescharacteristic, complemented
918C2—24no—
919C2—62no—
920C2C22×D3×Dic611yescharacteristic
921C2C2×#6431411yescharacteristic
922C2D3×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
prime radicalC2×C3×#237C22
hypercenterC4×D4D32
hypocenterC32#3503
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
2. C3×D4×Dic6C2semidirect
4. #10595272C2semidirect
6. #10594915C2semidirect
7. Dic6×#67C2semidirect
8. C2×#63866C2semidirect
9. #10594808C2semidirect
10. #10594502C2semidirect
11. #10594312C2semidirect
12. #10594146C2semidirect
13. #10594035C2semidirect
14. D3×#869C2semidirect
15. #10593873C2semidirect
16. #10593861C2semidirect
17. #10593860C2semidirect
112. D4×Dic6D3semidirect
131. C3×#237Q8semidirect
330. C32×D4C2×Q8semidirect
343. C3×#67C2×Q8semidirect
346. C2×C3×Dic3C2×Q8semidirect
357. C3×C4×D3C2×Q8semidirect
361. C3×Dic6C2×Q8semidirect
410. #237Dic6semidirect
635. C3×D4C2×Dic6semidirect
636. C3×D4D3×Q8semidirect
666. #67C2×Dic6semidirect
682. C2×Dic3C2×Dic6semidirect
694. C4×D3C2×Dic6semidirect
711. Dic6C2×Dic6semidirect
841. C32#3503semidirect
854. D4D3×Dic6semidirect
916. C3#85828semidirect
917. C3#86747semidirect

Maximal subgroups

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

subgroupindex
D4×#6342
C3×D4×Dic62
C3×C4×#2372
#105952722
#105952222
#105949152
Dic6×#672
C2×#638662
#105948082
#105945022
#105943122
#105941462
#105940352
D3×#8692
#105938732
#105938612
#105938602
#867473
#858283