Finite Group Databasebeta

← #11906231

Subgroups — #11906231

Order 1152.

2369 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595992C211yesmaximal, characteristic
2C3×#5519C211yesmaximal, characteristic, complemented
3C3×#5517C211yesmaximal, characteristic, complemented
4#10595051C211yesmaximal, characteristic, complemented
5#10595049C211yesmaximal, characteristic, complemented
6#10594996C211yesmaximal, characteristic
7C2×#63894C211yesmaximal, characteristic
8#10594484C212yesmaximal, complemented
9#10594470C212yesmaximal, complemented
10#10594470C212yesmaximal, complemented
11#10594379C212yesmaximal, complemented
12#10594180C214yesmaximal, complemented
13#10594067C214yesmaximal, complemented
14#10593958C212yesmaximal, complemented
15#10593938C212yesmaximal, complemented
16#10593938C212yesmaximal, complemented
17#10593903C212yesmaximal, complemented
18#86599—31nomaximal
19#86280—31nomaximal
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×#624C2212yes—
22C2×#3797C2214yescomplemented
23C32×#117C2211yescharacteristic
24#64135C2211yescharacteristic
25#64102C2212yes—
26#64102C2212yes—
27C22⋊C4×C3⋊D3C2214yes—
28C4×C4⋊(C3⋊D3)C2212yes—
29C4×C4⋊(C3⋊D3)C2212yes—
30C3×#926C2211yescharacteristic
31C3×#926C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C3×#890C2211yescharacteristic, complemented
35C3×#890C2211yescharacteristic, complemented
36C3×#890C2212yescomplemented
37C3×#888C2211yescharacteristic, complemented
38C3×#888C2211yescharacteristic, complemented
39C3×#888C2212yescomplemented
40C3×#878C2212yes—
41C3×#878C2214yes—
42C3×#878C2212yes—
43C3×#870C2212yescomplemented
44C3×#869C2212yescomplemented
45C3×C4×Dic6C2212yescomplemented
46C3×C4×Dic6C2212yescomplemented
47#63974C2214yes—
48#63964C2212yes—
49#63964C2214yes—
50#63964C2212yes—
51C2×#3722C2212yes—
52#63919C2212yescomplemented
53#63918C2211yescharacteristic, complemented
54#63918C2212yescomplemented
55#63918C2211yescharacteristic, complemented
56C4×#627C2212yescomplemented
57C4×#627C2212yescomplemented
58#63900C2214yescomplemented
59#63895C2214yescomplemented
60#63895C2214yescomplemented
61#63895C2214yescomplemented
62#63895C2214yescomplemented
63#63894C2212yes—
64#63894C2212yes—
65#63894C2212yes—
66#63894C2212yes—
67#63894C2212yes—
68#63894C2212yes—
69#63894C2212yes—
70#63894C2212yes—
71#63888C2214yescomplemented
72#63888C2214yescomplemented
73#63888C2214yescomplemented
74#63888C2214yescomplemented
75#63883C2214yescomplemented
76#63883C2214yescomplemented
77#63872C2212yescomplemented
78#63871C2214yescomplemented
79#63871C2214yescomplemented
80#63869C2211yescharacteristic, complemented
81#63869C2212yescomplemented
82#63869C2211yescharacteristic, complemented
83#63865C2214yescomplemented
84#63865C2214yescomplemented
85C3×#544—31no—
86C3×#533—31no—
87#5730—32no—
88#5730—32no—
89#5730—32no—
90#5727—32no—
91#5727—32no—
92#5727—32no—
93#5690—32no—
94#5690—32no—
95#5690—32no—
96#5690—32no—
97#5690—32no—
98#5690—32no—
99#5634—34no—
100#5634—34no—
101D3×C22⋊Q8—34no—
102D3×C22⋊Q8—34no—
103#5579—32no—
104#5579—32no—
105#5579—32no—
106Q8×D12—32no—
107#5521—31no—
108#5521—31no—
109#5521—31no—
110#5521—31no—
111#5521—61no—
112#5519—31no—
113#5519D311yescharacteristic, complemented
114#5517—31no—
115#5517D311yescharacteristic, complemented
116C2×#893—31no—
117#5500—31no—
118C2×C4×D12—31no—
119#5470—31no—
120C23×C3⋊D3C2312yes—
121C22×C32×C4C2311yescharacteristic
122C2×C4⋊(C3⋊D3)Q818yescomplemented
123C2×C4⋊(C3⋊D3)C2312yes—
124C2×C4⋊(C3⋊D3)C2312yes—
125C2×C4×C3⋊D3C2314yes—
126C2×C4×C3⋊D3C2314yes—
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2312yes—
130C2×C3×Dic6C2312yes—
131C2×C3×Dic6C2314yes—
132C2×C3×Dic6C2312yes—
133C2×#627C2312yes—
134C2×#627C2314yes—
135C2×#627C2312yes—
136C2×#624—44no—
137C2×#624C2314yes—
138C2×#624C2314yes—
139C2×#624C2314yes—
140C2×#624C2314yes—
141#3797—48no—
142C32×C4⋊C4C2311yescharacteristic
143C32×C4⋊C4C2311yescharacteristic
144C32×C22⋊C4C2312yes—
145C32×C42C2312yes—
146#3757C2312yes—
147#3752C2314yes—
148#3752C2314yes—
149C4⋊(C3⋊Dic3)C2311yescharacteristic
150C4⋊(C3⋊Dic3)C2311yescharacteristic
151C4×C3⋊Dic3C2312yes—
152C3×#217C2312yes—
153C3×#217C2312yes—
154C3×C4⋊Dic3C2312yes—
155C3×C4⋊Dic3C2314yes—
156C3×C4⋊Dic3C2312yes—
157C3×C4⋊Dic3C2312yes—
158C3×C4⋊Dic3C2311yescharacteristic
159C3×C4⋊Dic3C2311yescharacteristic
160C3×C4⋊Dic3C2312yes—
161C3×C4⋊Dic3C2311yescharacteristic
162C3×C4⋊Dic3C2311yescharacteristic
163C3×Dic3⋊C4C2312yes—
164C3×Dic3⋊C4C2314yes—
165C3×Dic3⋊C4C2312yes—
166C3×Dic3⋊C4C2312yes—
167C3×Dic3⋊C4C2314yes—
168C3×Dic3⋊C4C2312yes—
169C3×C4×Dic3C2311yescharacteristic
170C3×C4×Dic3C2312yes—
171C3×C4×Dic3C2311yescharacteristic
172C3×C4×Dic3C2311yescharacteristic
173C3×C4×Dic3C2311yescharacteristic
174C3×C4×Dic3C2312yes—
175#3724C2312yes—
176#3724C2314yes—
177#3724C2312yes—
178Dic3⋊Dic3C2312yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2312yes—
181Dic3⋊Dic3C2312yes—
182Dic3⋊Dic3C2314yes—
183Dic3⋊Dic3C2312yes—
184#3722C2314yes—
185#3722C2314yes—
186#3722C2314yes—
187#3722C2314yes—
188#3501—91noSylow
189C2×D3×Q8—34no—
190C2×D3×Q8—34no—
191C22×D12—31no—
192C22×D12—31no—
193C22×D12—61no—
194C22×C4×D3—32no—
195C22×C4×D3—32no—
196C3×C4⋊Q8—31no—
197C3×C4⋊Q8—32no—
198C3×C4⋊Q8—31no—
199C3×C4⋊Q8—32no—
200C3×#125—31no—
201C3×#125—31no—
202C3×#125—32no—
203C3×#125—32no—
204C3×C22⋊Q8—32no—
205C3×C22⋊Q8—34no—
206C3×C22⋊Q8—32no—
207C3×C4×Q8—32no—
208C3×C4×Q8—32no—
209C3×#117—21no—
210C3×#117—31no—
211C3×#117—31no—
212C3×#117C2×D311yescharacteristic
213C3×#117C2×D311yescharacteristic
214C2×C3×C4⋊C4—31no—
215C2×C3×C42—31no—
216#946—34no—
217#946—34no—
218#946—34no—
219#946—34no—
220#946—34no—
221#946—34no—
222C2×(C2×D3)⋊C4—32no—
223C2×(C2×D3)⋊C4—32no—
224#926—31no—
225#926—31no—
226#926—61no—
227#926C2×D311yescharacteristic
228#926C2×D311yescharacteristic
229C2×C4⋊Dic3C2×D311yescharacteristic
230#924—32no—
231#924—34no—
232#924—32no—
233C2×C4×Dic3C2×D311yescharacteristic
234#897—34no—
235#897—34no—
236#897—34no—
237#897—34no—
238#897—34no—
239#897—34no—
240#896—34no—
241#896—34no—
242#896—34no—
243#896—34no—
244#896—34no—
245#896—34no—
246#896—34no—
247#896—34no—
248#896—34no—
249#896—34no—
250#896—34no—
251#896—34no—
252#893—32no—
253#893—32no—
254#893—32no—
255#893—32no—
256#893—32no—
257#893—32no—
258#893—32no—
259#893—32no—
260#893—32no—
261#893—32no—
262#893—32no—
263#893—32no—
264#893—62no—
265#893—62no—
266D3×C4⋊C4—34no—
267D3×C4⋊C4—34no—
268D3×C4⋊C4—34no—
269D3×C4⋊C4—34no—
270D3×C4⋊C4—34no—
271D3×C4⋊C4—34no—
272#890—32no—
273#890—32no—
274#890—31no—
275#890—32no—
276#890—31no—
277#890C2×D311yescharacteristic, complemented
278#890C2×D312yescomplemented
279#890C2×D311yescharacteristic, complemented
280#888—32no—
281#888—32no—
282#888—31no—
283#888—32no—
284#888—31no—
285#888C2×D311yescharacteristic, complemented
286#888C2×D312yescomplemented
287#888C2×D311yescharacteristic, complemented
288D3×C22⋊C4—34no—
289D3×C22⋊C4—34no—
290D3×C22⋊C4—34no—
291D3×C22⋊C4—34no—
292D3×C22⋊C4—64no—
293#878—32no—
294#878—34no—
295#878—32no—
296#878C2×D312yes—
297#878C2×D314yes—
298#878C2×D312yes—
299C4×D12—32no—
300C4×D12—32no—
301C4×D12—32no—
302C4×D12—32no—
303C4×D12—32no—
304C4×D12—32no—
305C4×D12—32no—
306C4×D12—32no—
307C4×D12—32no—
308C4×D12—32no—
309C4×D12—32no—
310C4×D12—32no—
311C4×D12—62no—
312C4×D12—62no—
313#870—31no—
314#870—31no—
315#870—32no—
316#870C2×D312yescomplemented
317#869—31no—
318#869—31no—
319#869—32no—
320#869C2×D312yescomplemented
321C4×Dic6—32no—
322C4×Dic6—32no—
323C4×Dic6—32no—
324C4×Dic6—32no—
325C4×Dic6C2×D312yescomplemented
326C4×Dic6C2×D312yescomplemented
327C23×C32C2411yescharacteristic
328C22×C3⋊D3—42no—
329C22×C3⋊D3—42no—
330C22×C3⋊D3C2×Q818yescomplemented
331C22×C3⋊D3C2414yes—
332C2×C32×C4C2×Q814yescomplemented
333C2×C32×C4C2412yes—
334C2×C32×C4C2412yes—
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2411yescharacteristic
337C2×C3⋊Dic3C2412yes—
338C2×C3⋊Dic3C2412yes—
339C4⋊(C3⋊D3)C2×Q818yescomplemented
340C4⋊(C3⋊D3)C2×Q818yescomplemented
341C4×C3⋊D3—44no—
342C4×C3⋊D3—44no—
343C2×C3×Dic3—22no—
344C2×C3×Dic3—42no—
345C2×C3×Dic3—41no—
346C2×C3×Dic3C2411yescharacteristic
347C2×C3×Dic3C2411yescharacteristic
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2414yes—
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2411yescharacteristic
354C2×C3×Dic3C2411yescharacteristic
355C3×Dic6—24no—
356C3×Dic6—44no—
357C3×Dic6—42no—
358#627—24no—
359#627—44no—
360#627—42no—
361#624—28no—
362#624—44no—
363#624—44no—
364#624—44no—
365#554—92no—
366#554—92no—
367#554—92no—
368#554—92no—
369#554—92no—
370#554—92no—
371D4×Q8—92no—
372D4×Q8—92no—
373#544—31no—
374#544—91no—
375#543—94no—
376#533—31no—
377#533—91no—
378C2×C22⋊Q8—94no—
379#518—91no—
380#518—91no—
381C2×C4×D4—91no—
382C23×D3—32no—
383C23×D3—32no—
384C23×D3—62no—
385C2×C3×Q8—32no—
386C2×C3×Q8—32no—
387C2×C3×Q8—34no—
388C22×C3×C4—21no—
389C22×C3×C4—31no—
390C22×C3×C4—31no—
391C22×C3×C4—32no—
392C22×C3×C4C22×D311yescharacteristic
393C22×C3×C4C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C22×Dic3C22×D311yescharacteristic
396C22×Dic3C22×D312yes—
397D3×Q8—128no—
398D3×Q8—128no—
399C2×D12—38no—
400C2×D12—38no—
401C2×D12—32no—
402C2×D12—32no—
403C2×D12—32no—
404C2×D12—32no—
405C2×D12—62no—
406C2×D12—62no—
407C2×D12—68no—
408C2×C4×D3—34no—
409C2×C4×D3—34no—
410C2×C4×D3—34no—
411C2×C4×D3—34no—
412C2×C4×D3—34no—
413C2×C4×D3—34no—
414C2×C4×D3—34no—
415C2×C4×D3—34no—
416C2×C4×D3—34no—
417C2×C4×D3—34no—
418C2×C4×D3—34no—
419C2×C4×D3—34no—
420C2×C4×D3—64no—
421C2×C4×D3—64no—
422C2×C4×D3—124no—
423C2×C4×D3—124no—
424C2×Dic6—32no—
425C2×Dic6—32no—
426C2×Dic6—32no—
427C2×Dic6—32no—
428C2×Dic6—34no—
429C2×Dic6—34no—
430C2×Dic6C22×D312yes—
431C2×Dic6C22×D312yes—
432C2×Dic6C22×D314yes—
433C3×C4⋊C4—21no—
434C3×C4⋊C4—21no—
435C3×C4⋊C4—31no—
436C3×C4⋊C4—32no—
437C3×C4⋊C4—32no—
438C3×C4⋊C4—31no—
439C3×C4⋊C4—31no—
440C3×C4⋊C4—31no—
441C3×C4⋊C4—32no—
442C3×C4⋊C4—32no—
443C3×C4⋊C4—32no—
444C3×C4⋊C4—34no—
445C3×C4⋊C4—34no—
446C3×C4⋊C4—34no—
447C3×C4⋊C4—32no—
448C3×C4⋊C4—32no—
449C3×C4⋊C4—32no—
450C3×C4⋊C4C22×D311yescharacteristic
451C3×C4⋊C4C22×D311yescharacteristic
452C3×C4⋊C4C22×D311yescharacteristic
453C3×C4⋊C4C22×D311yescharacteristic
454C3×C22⋊C4—22no—
455C3×C22⋊C4—32no—
456C3×C22⋊C4—32no—
457C3×C22⋊C4C22×D312yes—
458C3×C22⋊C4C22×D312yes—
459C3×C42—22no—
460C3×C42—31no—
461C3×C42—31no—
462C3×C42—32no—
463C3×C42—31no—
464C3×C42—32no—
465C3×C42—31no—
466C3×C42C22×D312yes—
467C3×C42C22×D312yes—
468#217—32no—
469#217—32no—
470#217—62no—
471#217C22×D312yes—
472#217C22×D312yes—
473(C2×D3)⋊C4—34no—
474(C2×D3)⋊C4—34no—
475(C2×D3)⋊C4—34no—
476(C2×D3)⋊C4—34no—
477(C2×D3)⋊C4—34no—
478(C2×D3)⋊C4—34no—
479(C2×D3)⋊C4—34no—
480(C2×D3)⋊C4—34no—
481(C2×D3)⋊C4—34no—
482(C2×D3)⋊C4—34no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4—34no—
485(C2×D3)⋊C4—64no—
486(C2×D3)⋊C4—64no—
487C4⋊Dic3—31no—
488C4⋊Dic3—31no—
489C4⋊Dic3—31no—
490C4⋊Dic3—31no—
491C4⋊Dic3—32no—
492C4⋊Dic3—32no—
493C4⋊Dic3—32no—
494C4⋊Dic3—32no—
495C4⋊Dic3—34no—
496C4⋊Dic3—34no—
497C4⋊Dic3—61no—
498C4⋊Dic3—61no—
499C4⋊Dic3C22×D312yes—
500C4⋊Dic3C22×D312yes—
501C4⋊Dic3C22×D311yescharacteristic
502C4⋊Dic3C22×D312yes—
503C4⋊Dic3C22×D311yescharacteristic
504C4⋊Dic3C22×D314yes—
505C4⋊Dic3C22×D311yescharacteristic
506C4⋊Dic3C22×D312yes—
507C4⋊Dic3C22×D311yescharacteristic
508Dic3⋊C4—32no—
509Dic3⋊C4—32no—
510Dic3⋊C4—32no—
511Dic3⋊C4—32no—
512Dic3⋊C4—32no—
513Dic3⋊C4—32no—
514Dic3⋊C4—32no—
515Dic3⋊C4—32no—
516Dic3⋊C4—34no—
517Dic3⋊C4—34no—
518Dic3⋊C4—34no—
519Dic3⋊C4—34no—
520Dic3⋊C4C22×D312yes—
521Dic3⋊C4C22×D312yes—
522Dic3⋊C4C22×D312yes—
523Dic3⋊C4C22×D312yes—
524Dic3⋊C4C22×D314yes—
525Dic3⋊C4C22×D314yes—
526C4×Dic3—32no—
527C4×Dic3—32no—
528C4×Dic3—62no—
529C4×Dic3C22×D311yescharacteristic
530C4×Dic3C22×D312yes—
531C4×Dic3C22×D311yescharacteristic
532C4×Dic3C22×D311yescharacteristic
533C4×Dic3C22×D312yes—
534C4×Dic3C22×D311yescharacteristic
535C22×C32—21no—
536C22×C32—21no—
537C22×C32C22×Q812yes—
538C22×C32C2511yescharacteristic
539C2×C3⋊D3—24no—
540C2×C3⋊D3—24no—
541C2×C3⋊D3—48no—
542C2×C3⋊D3C22×Q818yes—
543C32×C4—22no—
544C32×C4—22no—
545C32×C4C22×Q812yes—
546C32×C4C22×Q812yes—
547C3⋊Dic3—22no—
548C3⋊Dic3—22no—
549C3×Dic3—24no—
550C3×Dic3—21no—
551C3×Dic3—22no—
552C3×Dic3—22no—
553C3×Dic3—22no—
554C3×Dic3—22no—
555C3×Dic3—21no—
556C3×Dic3—21no—
557C3×Dic3H(5,𝔽2)12yes—
558C22×Q8—94no—
559C22×D4—91no—
560C23×C4—92no—
561C4⋊Q8—31no—
562C4⋊Q8—31no—
563C4⋊Q8—32no—
564C4⋊Q8—32no—
565C4⋊Q8—91no—
566C4⋊Q8—91no—
567C4⋊Q8—92no—
568C4⋊Q8—92no—
569#125—31no—
570#125—31no—
571#125—32no—
572#125—32no—
573#125—91no—
574#125—91no—
575#125—92no—
576#125—92no—
577C22⋊Q8—32no—
578C22⋊Q8—34no—
579C22⋊Q8—32no—
580C22⋊Q8—92no—
581C22⋊Q8—94no—
582C22⋊Q8—92no—
583C22⋊Q8—94no—
584C22⋊Q8—94no—
585C22⋊Q8—94no—
586C22⋊Q8—94no—
587C22⋊Q8—94no—
588C22⋊Q8—94no—
589C22⋊Q8—94no—
590C22⋊Q8—94no—
591C22⋊Q8—94no—
592C22⋊Q8—94no—
593C22⋊Q8—94no—
594C22⋊Q8—94no—
595C4×Q8—32no—
596C4×Q8—32no—
597C4×Q8—92no—
598C4×Q8—92no—
599C4×D4—92no—
600C4×D4—92no—
601C4×D4—92no—
602C4×D4—92no—
603C4×D4—92no—
604C4×D4—92no—
605C4×D4—92no—
606C4×D4—92no—
607C4×D4—92no—
608C4×D4—92no—
609C4×D4—92no—
610C4×D4—92no—
611#117—31no—
612#117—31no—
613#117—91no—
614#117D3211yescharacteristic
615C2×C4⋊C4—31no—
616C2×C4⋊C4—94no—
617C2×C4⋊C4—94no—
618C2×C4⋊C4—94no—
619C2×C22⋊C4—94no—
620C2×C22⋊C4—92no—
621C2×C22⋊C4—94no—
622C2×C42—31no—
623C23×C3—21no—
624C23×C3C23×D311yescharacteristic
625C23×C3C23×D311yescharacteristic
626C22×D3—34no—
627C22×D3—34no—
628C22×D3—38no—
629C22×D3—38no—
630C22×D3—64no—
631C22×D3—68no—
632C22×D3—122no—
633C22×D3—122no—
634C22×D3—122no—
635C22×D3—122no—
636C22×D3—242no—
637C22×D3—242no—
638C3×Q8—64no—
639C3×Q8—124no—
640C3×Q8—122no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—22no—
644C2×C3×C4—22no—
645C2×C3×C4—24no—
646C2×C3×C4—31no—
647C2×C3×C4—31no—
648C2×C3×C4—31no—
649C2×C3×C4—32no—
650C2×C3×C4—32no—
651C2×C3×C4—32no—
652C2×C3×C4—34no—
653C2×C3×C4—32no—
654C2×C3×C4—31no—
655C2×C3×C4—62no—
656C2×C3×C4—122no—
657C2×C3×C4—121no—
658C2×C3×C4D3×Q814yescomplemented
659C2×C3×C4D3×Q814yescomplemented
660C2×C3×C4C23×D312yes—
661C2×C3×C4C23×D312yes—
662C2×C3×C4C23×D312yes—
663C2×C3×C4C23×D312yes—
664C2×C3×C4C23×D311yescharacteristic
665C2×C3×C4C23×D311yescharacteristic
666C2×C3×C4C23×D311yescharacteristic
667C2×C3×C4C23×D311yescharacteristic
668C2×Dic3—22no—
669C2×Dic3—32no—
670C2×Dic3—32no—
671C2×Dic3—32no—
672C2×Dic3—32no—
673C2×Dic3—42no—
674C2×Dic3—41no—
675C2×Dic3—62no—
676C2×Dic3—62no—
677C2×Dic3C23×D311yescharacteristic
678C2×Dic3C23×D311yescharacteristic
679C2×Dic3C23×D311yescharacteristic
680C2×Dic3C23×D312yes—
681C2×Dic3C23×D312yes—
682C2×Dic3C23×D312yes—
683C2×Dic3C23×D312yes—
684C2×Dic3C23×D314yes—
685C2×Dic3C23×D311yescharacteristic
686D12—38no—
687D12—38no—
688D12—38no—
689D12—38no—
690D12—68no—
691D12—68no—
692C4×D3—68no—
693C4×D3—68no—
694C4×D3—124no—
695C4×D3—124no—
696C4×D3—124no—
697C4×D3—124no—
698C4×D3—124no—
699C4×D3—124no—
700C4×D3—124no—
701C4×D3—124no—
702C4×D3—124no—
703C4×D3—124no—
704C4×D3—244no—
705C4×D3—244no—
706Dic6—24no—
707Dic6—42no—
708Dic6—44no—
709Dic6—64no—
710Dic6—64no—
711Dic6—122no—
712Dic6—122no—
713Dic6—124no—
714Dic6—124no—
715C2×C32—22no—
716C2×C32C23×Q811yescharacteristic
717C2×C32C2×H(5,𝔽2)11yescharacteristic
718C2×C32#58511yescharacteristic
719C3⋊D3—28no—
720C24—92no—
721C2×Q8—32no—
722C2×Q8—32no—
723C2×Q8—34no—
724C2×Q8—92no—
725C2×Q8—92no—
726C2×Q8—94no—
727C2×Q8—368no—
728C2×D4—92no—
729C2×D4—92no—
730C2×D4—98no—
731C22×C4—31no—
732C22×C4—31no—
733C22×C4—32no—
734C22×C4—94no—
735C22×C4—94no—
736C22×C4—94no—
737C22×C4—94no—
738C22×C4—94no—
739C22×C4—94no—
740C22×C4—364no—
741C22×C4C2×D3211yescharacteristic
742C4⋊C4—32no—
743C4⋊C4—32no—
744C4⋊C4—32no—
745C4⋊C4—32no—
746C4⋊C4—32no—
747C4⋊C4—34no—
748C4⋊C4—34no—
749C4⋊C4—34no—
750C4⋊C4—31no—
751C4⋊C4—31no—
752C4⋊C4—31no—
753C4⋊C4—31no—
754C4⋊C4—32no—
755C4⋊C4—32no—
756C4⋊C4—32no—
757C4⋊C4—92no—
758C4⋊C4—92no—
759C4⋊C4—92no—
760C4⋊C4—94no—
761C4⋊C4—94no—
762C4⋊C4—94no—
763C4⋊C4—92no—
764C4⋊C4—92no—
765C4⋊C4—92no—
766C4⋊C4—91no—
767C4⋊C4—91no—
768C4⋊C4C2×D3211yescharacteristic
769C4⋊C4C2×D3211yescharacteristic
770C22⋊C4—32no—
771C22⋊C4—32no—
772C22⋊C4—94no—
773C22⋊C4—94no—
774C22⋊C4—94no—
775C22⋊C4—94no—
776C22⋊C4—92no—
777C22⋊C4—94no—
778C22⋊C4—94no—
779C22⋊C4C2×D3212yes—
780C42—31no—
781C42—31no—
782C42—31no—
783C42—31no—
784C42—32no—
785C42—32no—
786C42—92no—
787C42C2×D3212yes—
788C22×C3—21no—
789C22×C3—21no—
790C22×C3—21no—
791C22×C3—21no—
792C22×C3—22no—
793C22×C3—21no—
794C22×C3—41no—
795C22×C3—41no—
796C22×C3C2×D3×Q812yes—
797C22×C3C2×D3×Q812yes—
798C22×C3C24×D311yescharacteristic
799C22×C3C24×D311yescharacteristic
800C2×D3—38no—
801C2×D3—38no—
802C2×D3—68no—
803C2×D3—64no—
804C2×D3—64no—
805C2×D3—64no—
806C2×D3—64no—
807C2×D3—124no—
808C2×D3—124no—
809C2×D3—128no—
810C2×D3—128no—
811C2×D3—248no—
812C3×C4—22no—
813C3×C4—22no—
814C3×C4—22no—
815C3×C4—22no—
816C3×C4—22no—
817C3×C4—22no—
818C3×C4—32no—
819C3×C4—42no—
820C3×C4—42no—
821C3×C4—62no—
822C3×C4—64no—
823C3×C4—62no—
824C3×C4—62no—
825C3×C4—61no—
826C3×C4—61no—
827C3×C4—62no—
828C3×C4—61no—
829C3×C4C2×D3×Q812yes—
830C3×C4C2×D3×Q812yes—
831C3×C4C2×D3×Q812yes—
832C3×C4C2×D3×Q812yes—
833Dic3—22no—
834Dic3—21no—
835Dic3—21no—
836Dic3—22no—
837Dic3—21no—
838Dic3—22no—
839Dic3—24no—
840Dic3—22no—
841Dic3—62no—
842Dic3—62no—
843Dic3—62no—
844Dic3—62no—
845Dic3—122no—
846Dic3—122no—
847Dic3#100912yes—
848C32#350111yescharacteristic, complemented, Sylow
849C23—94no—
850C23—98no—
851C23—362no—
852C23—362no—
853C23C22×D3211yescharacteristic
854Q8—64no—
855Q8—124no—
856Q8—122no—
857Q8—184no—
858Q8—364no—
859Q8—362no—
860D4—98no—
861D4—98no—
862C2×C4—31no—
863C2×C4—31no—
864C2×C4—31no—
865C2×C4—31no—
866C2×C4—32no—
867C2×C4—32no—
868C2×C4—32no—
869C2×C4—32no—
870C2×C4—34no—
871C2×C4—62no—
872C2×C4—92no—
873C2×C4—92no—
874C2×C4—122no—
875C2×C4—121no—
876C2×C4—188no—
877C2×C4—364no—
878C2×C4—364no—
879C2×C4—364no—
880C2×C4—364no—
881C2×C4—364no—
882C2×C4#379714yescomplemented
883C2×C4C22×D3212yes—
884C2×C4C22×D3212yes—
885C2×C4C22×D3211yescharacteristic
886C2×C4C22×D3211yescharacteristic
887C2×C3—22no—
888C2×C3—22no—
889C2×C3—21no—
890C2×C3—21no—
891C2×C3—21no—
892C2×C3—42no—
893C2×C3C22×D3×Q811yescharacteristic
894C2×C3C22×D3×Q811yescharacteristic
895C2×C3C2×#100911yescharacteristic
896C2×C3#596411yescharacteristic
897C2×C3D3×H(5,𝔽2)11yescharacteristic
898C2×C3#596811yescharacteristic
899D3—68no—
900D3—68no—
901D3—128no—
902C22—21no—
903C22—21no—
904C22—98no—
905C22—184no—
906C22—184no—
907C22—368no—
908C22C2×#379712yes—
909C22C23×D3211yescharacteristic
910C4—22no—
911C4—22no—
912C4—32no—
913C4—61no—
914C4—64no—
915C4—62no—
916C4—62no—
917C4—61no—
918C4—61no—
919C4—62no—
920C4—62no—
921C4—182no—
922C4—182no—
923C4C2×#379712yes—
924C4C2×#379712yes—
925C3—21no—
926C3#8628011yescharacteristic, complemented
927C3#8659911yescharacteristic, complemented
928C2—22no—
929C2—188no—
930C2C22×#379711yescharacteristic
931C2D3×#100911yescharacteristic
932C2#1059669711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenter#117D32
hypocenterC32#3501
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×#5519C2semidirect
3. C3×#5517C2semidirect
4. #10595051C2semidirect
5. #10595049C2semidirect
8. #10594484C2semidirect
9. #10594470C2semidirect
10. #10594470C2semidirect
11. #10594379C2semidirect
12. #10594180C2semidirect
13. #10594067C2semidirect
14. #10593958C2semidirect
15. #10593938C2semidirect
16. #10593938C2semidirect
17. #10593903C2semidirect
22. C2×#3797C22semidirect
34. C3×#890C22semidirect
35. C3×#890C22semidirect
36. C3×#890C22semidirect
37. C3×#888C22semidirect
38. C3×#888C22semidirect
39. C3×#888C22semidirect
43. C3×#870C22semidirect
44. C3×#869C22semidirect
45. C3×C4×Dic6C22semidirect
46. C3×C4×Dic6C22semidirect
52. #63919C22semidirect
53. #63918C22semidirect
54. #63918C22semidirect
55. #63918C22semidirect
56. C4×#627C22semidirect
57. C4×#627C22semidirect
58. #63900C22semidirect
59. #63895C22semidirect
60. #63895C22semidirect
61. #63895C22semidirect
62. #63895C22semidirect
71. #63888C22semidirect
72. #63888C22semidirect
73. #63888C22semidirect
74. #63888C22semidirect
75. #63883C22semidirect
76. #63883C22semidirect
77. #63872C22semidirect
78. #63871C22semidirect
79. #63871C22semidirect
80. #63869C22semidirect
81. #63869C22semidirect
82. #63869C22semidirect
83. #63865C22semidirect
84. #63865C22semidirect
113. #5519D3semidirect
115. #5517D3semidirect
122. C2×C4⋊(C3⋊D3)Q8semidirect
277. #890C2×D3semidirect
278. #890C2×D3semidirect
279. #890C2×D3semidirect
285. #888C2×D3semidirect
286. #888C2×D3semidirect
287. #888C2×D3semidirect
316. #870C2×D3semidirect
320. #869C2×D3semidirect
325. C4×Dic6C2×D3semidirect
326. C4×Dic6C2×D3semidirect
330. C22×C3⋊D3C2×Q8semidirect
332. C2×C32×C4C2×Q8semidirect
339. C4⋊(C3⋊D3)C2×Q8semidirect
340. C4⋊(C3⋊D3)C2×Q8semidirect
658. C2×C3×C4D3×Q8semidirect
659. C2×C3×C4D3×Q8semidirect
848. C32#3501semidirect
882. C2×C4#3797semidirect
926. C3#86280semidirect
927. C3#86599semidirect

Maximal subgroups

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

subgroupindex
#105959922
C3×#55192
C3×#55172
#105950512
#105950492
#105949962
C2×#638942
#105944842
#105944702
#105943792
#105941802
#105940672
#105939582
#105939382
#105939032
#865993
#862803