Finite Group Databasebeta

← #11903243

Subgroups — #11903243

Order 1152.

2609 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C3×#5511C212yesmaximal, complemented
3C4×#3811C211yesmaximal, characteristic
4C4×#3811C212yesmaximal
5#10594993C212yesmaximal, complemented
6#10594959C214yesmaximal, complemented
7#10594925C211yesmaximal, characteristic, complemented
8#10594925C212yesmaximal, complemented
9#10594631C211yesmaximal, characteristic, complemented
10#10594624C212yesmaximal, complemented
11D32×C4⋊C4C211yesmaximal, characteristic, complemented
12#10594536C212yesmaximal, complemented
13#10594399C212yesmaximal, complemented
14#10594394C214yesmaximal, complemented
15#10594393C212yesmaximal, complemented
16#10594374C211yesmaximal, characteristic, complemented
17#10594363C211yesmaximal, characteristic, complemented
18D3×#554—32nomaximal
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3C2212yes—
21C2×#3811C2211yescharacteristic
22C2×C4×D32C2211yescharacteristic
23C2×C4×D32C2212yes—
24C2×#3797C2211yescharacteristic
25C2×#3797C2212yes—
26C2×C32×C4⋊C4C2211yescharacteristic, complemented
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
28C2×#3750C2212yescomplemented
29C4⋊C4×C3⋊D3C2211yescharacteristic
30C4⋊C4×C3⋊D3C2212yes—
31C4⋊C4×C3⋊D3C2211yescharacteristic
32C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
33C4⋊C4×C3⋊D3C2212yescomplemented
34C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
35C3×C4×#67C2214yes—
36C3×C4×#67C2212yes—
37C3×#924C2214yescomplemented
38C3×#924C2212yescomplemented
39C3×#897C2212yescomplemented
40C3×#896C2214yescomplemented
41C3×D3×C4⋊C4C2212yescomplemented
42C3×#889C2214yescomplemented
43C3×#888C2212yescomplemented
44C3×#887C2212yescomplemented
45#63982C2212yescomplemented
46#63982C2214yescomplemented
47#63974C2211yescharacteristic
48#63974C2212yes—
49#67⋊Dic3C2212yes—
50#67⋊Dic3C2214yes—
51#63921C2211yescharacteristic
52#63921C2212yes—
53#63918C2212yescomplemented
54C4×#626C2212yes—
55C4×#626C2214yes—
56#63900C2211yescharacteristic
57#63900C2212yes—
58#63899C2214yescomplemented
59#63893C2214yescomplemented
60D3×C4⋊Dic3C2212yescomplemented
61#63887C2214yescomplemented
62#63883C2212yes—
63#63883C2212yes—
64#63883C2212yes—
65#63883C2212yes—
66#63883C2211yescharacteristic
67C4×#624C2211yescharacteristic
68C4×#624C2212yes—
69#63881C2214yes—
70#63881C2212yes—
71D3×Dic3⋊C4C2214yescomplemented
72#63871C2214yescomplemented
73#63871C2212yescomplemented
74#63867C2214yescomplemented
75#63865C2212yescomplemented
76#63865C2214yescomplemented
77#63856C2212yescomplemented
78#63851C2214yescomplemented
79#63846C2214yescomplemented
80#63845C2214yescomplemented
81Dic3×Dic6C2212yescomplemented
82#63839C2214yescomplemented
83#63837C2214yescomplemented
84C3×#554—32no—
85#5730—32no—
86D3×C4⋊Q8—32no—
87#5690—34no—
88D3×#125—34no—
89#5636—34no—
90#5636—34no—
91#5635—32no—
92#5635—32no—
93D3×C22⋊Q8—34no—
94D3×C22⋊Q8—32no—
95D3×C22⋊Q8—32no—
96D3×C22⋊Q8—34no—
97#5579—32no—
98C4×D3×Q8—32no—
99C4×D3×D4—34no—
100C4×D3×D4—32no—
101#5543—32no—
102#5539—34no—
103#5511—32no—
104#5511D312yescomplemented
105C2×D3×C4⋊C4—32no—
106C2×D3×C4⋊C4—32no—
107C2×D3×C4⋊C4—61no—
108C23×C3⋊D3C2311yescharacteristic
109C22×D32C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C32×C4C2312yes—
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2312yes—
114C2×C4×C3⋊D3—24no—
115C2×C4×C3⋊D3—44no—
116C2×C4×C3⋊D3C2312yes—
117C2×C4×C3⋊D3C2312yes—
118C2×C4×C3⋊D3C2311yescharacteristic
119C2×C4×C3⋊D3C2311yescharacteristic
120C2×C4×C3⋊D3C2311yescharacteristic
121C2×C4×C3⋊D3C2312yes—
122C2×C4×C3⋊D3C2312yes—
123C2×C4×C3⋊D3C2311yescharacteristic
124C2×C3×#67C2312yes—
125C2×C3×C4×D3C2312yes—
126C2×C3×C4×D3C2314yes—
127C2×C3×Dic6C2312yes—
128C2×C3×Dic6C2314yes—
129#3811Q818yescomplemented
130C2×#627C2312yes—
131C2×#627C2314yes—
132C2×#626C2312yes—
133C2×#624C2311yescharacteristic
134C2×#624C2312yes—
135C2×#624C2312yes—
136C2×#624C2311yescharacteristic
137C2×#624C2311yescharacteristic
138C2×D3×Dic3C2312yes—
139C2×D3×Dic3C2314yes—
140C4×D32—24no—
141C4×D32—44no—
142#3797—24no—
143#3797—44no—
144C32×C4⋊C4C2311yescharacteristic
145C32×C4⋊C4C2311yescharacteristic
146C32×C4⋊C4C2312yes—
147C4⋊(C3⋊Dic3)C2311yescharacteristic
148C4⋊(C3⋊Dic3)C2312yes—
149C4⋊(C3⋊Dic3)C2311yescharacteristic
150#3750C2312yes—
151#3750C2312yes—
152#3750C2312yes—
153#3750C2312yes—
154C3×#217C2314yes—
155C3×#217C2312yes—
156C3×(C2×D3)⋊C4C2312yes—
157C3×(C2×D3)⋊C4C2314yes—
158C3×C4⋊Dic3C2312yes—
159C3×C4⋊Dic3C2314yes—
160C3×Dic3⋊C4C2314yes—
161C3×Dic3⋊C4C2314yes—
162C3×Dic3⋊C4C2312yes—
163C3×Dic3⋊C4C2314yes—
164C3×Dic3⋊C4C2314yes—
165C3×C4×Dic3C2312yes—
166C3×C4×Dic3C2314yes—
167#3724C2312yes—
168#3724C2314yes—
169Dic3⋊Dic3C2314yes—
170Dic3⋊Dic3C2314yes—
171Dic3⋊Dic3C2314yes—
172Dic3⋊Dic3C2312yes—
173Dic3⋊Dic3C2314yes—
174#3722C2314yes—
175#3722C2312yes—
176(C2×D3)⋊Dic3C2312yes—
177(C2×D3)⋊Dic3C2314yes—
178Dic32C2312yes—
179Dic32C2314yes—
180C2×#554—91noSylow
181C2×D3×Q8—32no—
182C2×D3×Q8—34no—
183C2×D3×D4—32no—
184C22×C4×D3—32no—
185C22×C4×D3—34no—
186C22×C4×D3—32no—
187C22×C4×D3—34no—
188C22×C4×D3—61no—
189C22×C4×D3—62no—
190C3×C4⋊Q8—32no—
191C3×#125—34no—
192C3×C22⋊Q8—32no—
193C3×C22⋊Q8—34no—
194C3×C22⋊Q8—32no—
195C3×C22⋊Q8—34no—
196C3×C4×Q8—32no—
197C3×C4×D4—34no—
198C3×C4×D4—32no—
199C2×C3×C4⋊C4—21no—
200C2×C3×C4⋊C4—32no—
201C2×C3×C4⋊C4C2×D312yescomplemented
202#946—32no—
203#946—34no—
204#946—32no—
205#946—34no—
206Q8×Dic3—32no—
207#944—34no—
208D4×Dic3—32no—
209D4×Dic3—34no—
210C4×#67—32no—
211C4×#67—34no—
212C4×#67C2×D312yes—
213C4×#67C2×D314yes—
214C2×C4⋊Dic3—32no—
215C2×C4⋊Dic3—32no—
216C2×C4⋊Dic3—61no—
217#924—32no—
218#924—34no—
219#924C2×D314yescomplemented
220#924C2×D312yescomplemented
221C2×Dic3⋊C4—34no—
222C2×Dic3⋊C4—34no—
223C2×Dic3⋊C4—62no—
224#897—34no—
225#897—32no—
226#897—34no—
227#897C2×D312yescomplemented
228#896—34no—
229#896—34no—
230#896—34no—
231#896—34no—
232#896—34no—
233#896C2×D314yescomplemented
234#893—32no—
235#893—34no—
236D3×C4⋊C4—32no—
237D3×C4⋊C4—34no—
238D3×C4⋊C4—32no—
239D3×C4⋊C4—34no—
240D3×C4⋊C4—34no—
241D3×C4⋊C4—32no—
242D3×C4⋊C4—32no—
243D3×C4⋊C4—32no—
244D3×C4⋊C4—34no—
245D3×C4⋊C4—32no—
246D3×C4⋊C4—32no—
247D3×C4⋊C4—34no—
248D3×C4⋊C4—34no—
249D3×C4⋊C4—34no—
250D3×C4⋊C4—34no—
251D3×C4⋊C4—61no—
252D3×C4⋊C4—62no—
253D3×C4⋊C4—61no—
254D3×C4⋊C4—61no—
255D3×C4⋊C4—62no—
256D3×C4⋊C4—61no—
257D3×C4⋊C4C2×D312yescomplemented
258#890—34no—
259#890—34no—
260#889—34no—
261#889—34no—
262#889—34no—
263#889C2×D314yescomplemented
264#888—34no—
265#888—32no—
266#888C2×D312yescomplemented
267#887—34no—
268#887C2×D312yescomplemented
269#67⋊C4—34no—
270#67⋊C4—32no—
271#67⋊C4—34no—
272#67⋊C4—32no—
273D3×C22⋊C4—34no—
274D3×C22⋊C4—32no—
275D3×C22⋊C4—34no—
276D3×C22⋊C4—32no—
277#878—34no—
278#878—34no—
279#878—34no—
280#878—34no—
281#878—34no—
282#878—34no—
283C4×D12—34no—
284C4×D12—32no—
285C42×D3—34no—
286C42×D3—32no—
287#870—34no—
288#869—32no—
289C4×Dic6—32no—
290C4×Dic6—34no—
291C23×C32C2411yescharacteristic
292C22×C3⋊D3—22no—
293C22×C3⋊D3—22no—
294C22×C3⋊D3C2×Q814yes—
295C22×C3⋊D3C2411yescharacteristic
296C22×C3⋊D3C2411yescharacteristic
297C22×C3×D3C2412yes—
298C2×D32—22no—
299C2×D32—22no—
300C2×D32C2×Q814yes—
301C2×C32×C4—22no—
302C2×C32×C4—42no—
303C2×C32×C4C2412yes—
304C2×C32×C4C2411yescharacteristic
305C2×C32×C4C2412yes—
306C2×C32×C4C2411yescharacteristic
307C2×C3⋊Dic3—22no—
308C2×C3⋊Dic3—42no—
309C2×C3⋊Dic3C2412yes—
310C2×C3⋊Dic3C2411yescharacteristic
311C2×C3⋊Dic3C2412yes—
312C2×C3⋊Dic3C2411yescharacteristic
313C4×C3⋊D3—22no—
314C4×C3⋊D3—22no—
315C4×C3⋊D3—22no—
316C4×C3⋊D3—24no—
317C4×C3⋊D3—24no—
318C4×C3⋊D3—42no—
319C4×C3⋊D3—42no—
320C4×C3⋊D3#4114yes—
321C3×#67C2×Q818yescomplemented
322C2×C3×Dic3C2414yes—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2414yes—
326C2×C3×Dic3C2412yes—
327C3×C4×D3—24no—
328C3×C4×D3—44no—
329C3×Dic6—24no—
330C3×Dic6—44no—
331#627—24no—
332#627—44no—
333#626C2×Q818yescomplemented
334#624—24no—
335#624—22no—
336#624—22no—
337#624—24no—
338#624C2×Q814yes—
339D3×Dic3—24no—
340D3×Dic3—44no—
341#554—32no—
342#554—92no—
343#554—92no—
344#554—94no—
345#554—94no—
346#554—92no—
347C2×C4⋊Q8—91no—
348C2×#125—92no—
349C2×C22⋊Q8—92no—
350C2×C22⋊Q8—91no—
351C2×C22⋊Q8—92no—
352C2×C22⋊Q8—91no—
353C2×C4×Q8—91no—
354C2×C4×D4—92no—
355C2×C4×D4—91no—
356C22×C4⋊C4—91no—
357C22×C4⋊C4—91no—
358C23×D3—32no—
359C23×D3—32no—
360C23×D3—61no—
361C2×C3×Q8—32no—
362C2×C3×Q8—34no—
363C2×C3×D4—32no—
364C22×C3×C4—21no—
365C22×C3×C4—22no—
366C22×C3×C4—32no—
367C22×C3×C4—34no—
368C22×C3×C4C22×D312yes—
369C22×C3×C4C22×D314yes—
370C2×#67—32no—
371C2×#67C22×D312yes—
372C22×Dic3—32no—
373C22×Dic3—34no—
374C22×Dic3—32no—
375C22×Dic3—34no—
376C22×Dic3—61no—
377C22×Dic3—62no—
378D3×Q8—68no—
379D3×Q8—128no—
380D3×D4—316no—
381C2×D12—32no—
382C2×C4×D3—32no—
383C2×C4×D3—32no—
384C2×C4×D3—32no—
385C2×C4×D3—34no—
386C2×C4×D3—32no—
387C2×C4×D3—32no—
388C2×C4×D3—34no—
389C2×C4×D3—32no—
390C2×C4×D3—34no—
391C2×C4×D3—32no—
392C2×C4×D3—32no—
393C2×C4×D3—34no—
394C2×C4×D3—34no—
395C2×C4×D3—34no—
396C2×C4×D3—34no—
397C2×C4×D3—61no—
398C2×C4×D3—61no—
399C2×C4×D3—61no—
400C2×C4×D3—61no—
401C2×C4×D3—62no—
402C2×C4×D3—62no—
403C2×C4×D3—62no—
404C2×C4×D3—62no—
405C2×C4×D3—68no—
406C2×C4×D3—68no—
407C2×C4×D3—68no—
408C2×C4×D3—128no—
409C2×C4×D3—128no—
410C2×C4×D3—128no—
411C2×C4×D3C22×D312yes—
412C2×C4×D3C22×D314yes—
413C2×Dic6—34no—
414C2×Dic6—34no—
415C2×Dic6—34no—
416C2×Dic6C22×D312yes—
417C2×Dic6C22×D314yes—
418C3×C4⋊C4—21no—
419C3×C4⋊C4—22no—
420C3×C4⋊C4—21no—
421C3×C4⋊C4—34no—
422C3×C4⋊C4—34no—
423C3×C4⋊C4—32no—
424C3×C4⋊C4—34no—
425C3×C4⋊C4—34no—
426C3×C4⋊C4—34no—
427C3×C4⋊C4—32no—
428C3×C4⋊C4C22×D312yes—
429C3×C4⋊C4C22×D312yes—
430C3×C4⋊C4C22×D314yes—
431C3×C22⋊C4—34no—
432C3×C22⋊C4—32no—
433C3×C22⋊C4—34no—
434C3×C22⋊C4—32no—
435C3×C42—32no—
436C3×C42—34no—
437#217—32no—
438#217—34no—
439#217C22×D314yes—
440#217C22×D312yes—
441(C2×D3)⋊C4—34no—
442(C2×D3)⋊C4—32no—
443(C2×D3)⋊C4—34no—
444(C2×D3)⋊C4—32no—
445(C2×D3)⋊C4—32no—
446(C2×D3)⋊C4—34no—
447(C2×D3)⋊C4C22×D314yes—
448(C2×D3)⋊C4C22×D312yes—
449C4⋊Dic3—32no—
450C4⋊Dic3—32no—
451C4⋊Dic3—34no—
452C4⋊Dic3—34no—
453C4⋊Dic3—34no—
454C4⋊Dic3—32no—
455C4⋊Dic3—34no—
456C4⋊Dic3—34no—
457C4⋊Dic3—61no—
458C4⋊Dic3—62no—
459C4⋊Dic3—61no—
460C4⋊Dic3C22×D312yes—
461C4⋊Dic3C22×D314yes—
462Dic3⋊C4—34no—
463Dic3⋊C4—34no—
464Dic3⋊C4—34no—
465Dic3⋊C4—34no—
466Dic3⋊C4—34no—
467Dic3⋊C4—34no—
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—34no—
471Dic3⋊C4—34no—
472Dic3⋊C4—34no—
473Dic3⋊C4—32no—
474Dic3⋊C4—62no—
475Dic3⋊C4—62no—
476Dic3⋊C4—62no—
477Dic3⋊C4—62no—
478Dic3⋊C4C22×D314yes—
479Dic3⋊C4C22×D314yes—
480Dic3⋊C4C22×D314yes—
481Dic3⋊C4C22×D314yes—
482Dic3⋊C4C22×D312yes—
483C4×Dic3—32no—
484C4×Dic3—34no—
485C4×Dic3—32no—
486C4×Dic3—34no—
487C4×Dic3C22×D314yes—
488C4×Dic3C22×D312yes—
489C22×C32—21no—
490C22×C32—21no—
491C22×C32C22×Q812yes—
492C22×C32C2511yescharacteristic
493C2×C3⋊D3—21no—
494C2×C3⋊D3—21no—
495C2×C3⋊D3—28no—
496C2×C3⋊D3C22×Q812yes—
497C2×C3⋊D3C22×Q812yes—
498C2×C3⋊D3C2×#4112yes—
499C2×C3⋊D3H(5,𝔽2)12yes—
500C2×C3×D3—22no—
501C2×C3×D3—22no—
502C2×C3×D3C22×Q814yes—
503D32—28no—
504C32×C4—21no—
505C32×C4—22no—
506C32×C4—22no—
507C32×C4C2×#4112yes—
508C3⋊Dic3—21no—
509C3⋊Dic3—22no—
510C3⋊Dic3—22no—
511C3⋊Dic3C2×#4112yes—
512C3×Dic3—22no—
513C3×Dic3—24no—
514C3×Dic3—24no—
515C3×Dic3—22no—
516C3×Dic3C22×Q814yes—
517C22×Q8—91no—
518C22×Q8—92no—
519C22×D4—91no—
520C23×C4—91no—
521C23×C4—92no—
522C23×C4—91no—
523C23×C4—92no—
524C4⋊Q8—32no—
525C4⋊Q8—92no—
526C4⋊Q8—94no—
527#125—34no—
528#125—94no—
529#125—94no—
530#125—94no—
531C22⋊Q8—34no—
532C22⋊Q8—32no—
533C22⋊Q8—34no—
534C22⋊Q8—32no—
535C22⋊Q8—94no—
536C22⋊Q8—92no—
537C22⋊Q8—94no—
538C22⋊Q8—94no—
539C22⋊Q8—94no—
540C22⋊Q8—94no—
541C22⋊Q8—92no—
542C22⋊Q8—94no—
543C22⋊Q8—92no—
544C22⋊Q8—94no—
545C22⋊Q8—92no—
546C4×Q8—32no—
547C4×Q8—94no—
548C4×Q8—92no—
549C4×D4—34no—
550C4×D4—32no—
551C4×D4—94no—
552C4×D4—92no—
553C4×D4—94no—
554C4×D4—92no—
555C4×D4—94no—
556C4×D4—92no—
557C2×C4⋊C4—32no—
558C2×C4⋊C4—92no—
559C2×C4⋊C4—91no—
560C2×C4⋊C4—91no—
561C2×C4⋊C4—92no—
562C2×C4⋊C4—92no—
563C2×C4⋊C4—92no—
564C2×C4⋊C4—92no—
565C2×C4⋊C4—94no—
566C2×C4⋊C4—92no—
567C2×C4⋊C4—92no—
568C2×C4⋊C4—91no—
569C2×C4⋊C4—91no—
570C2×C4⋊C4—92no—
571C2×C4⋊C4—91no—
572C2×C4⋊C4—92no—
573C2×C4⋊C4—91no—
574C2×C4⋊C4—91no—
575C2×C4⋊C4D3211yescharacteristic, complemented
576C2×C22⋊C4—92no—
577C2×C22⋊C4—91no—
578C2×C22⋊C4—92no—
579C2×C22⋊C4—91no—
580C2×C42—92no—
581C2×C42—91no—
582C23×C3—21no—
583C23×C3—32no—
584C23×C3C23×D312yes—
585C22×D3—32no—
586C22×D3—38no—
587C22×D3—32no—
588C22×D3—38no—
589C22×D3—64no—
590C22×D3—61no—
591C22×D3—61no—
592C22×D3—64no—
593C22×D3—64no—
594C22×D3—64no—
595C22×D3—64no—
596C22×D3—64no—
597C22×D3—64no—
598C22×D3C23×D312yes—
599C3×Q8—64no—
600C3×Q8—124no—
601C3×D4—38no—
602C2×C3×C4—24no—
603C2×C3×C4—24no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—22no—
607C2×C3×C4—22no—
608C2×C3×C4—32no—
609C2×C3×C4—34no—
610C2×C3×C4—32no—
611C2×C3×C4—32no—
612C2×C3×C4—34no—
613C2×C3×C4—44no—
614C2×C3×C4—44no—
615C2×C3×C4—64no—
616C2×C3×C4—124no—
617C2×C3×C4C23×D314yes—
618C2×C3×C4C23×D314yes—
619C2×C3×C4C23×D312yes—
620C2×C3×C4C23×D312yes—
621#67—38no—
622#67D3×Q818yescomplemented
623C2×Dic3—32no—
624C2×Dic3—34no—
625C2×Dic3—32no—
626C2×Dic3—34no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—62no—
630C2×Dic3—62no—
631C2×Dic3—64no—
632C2×Dic3—64no—
633C2×Dic3—64no—
634C2×Dic3—124no—
635C2×Dic3—124no—
636C2×Dic3—124no—
637C2×Dic3C23×D314yes—
638C2×Dic3C23×D312yes—
639C2×Dic3C23×D312yes—
640C2×Dic3C23×D314yes—
641C2×Dic3C23×D312yes—
642D12—38no—
643C4×D3—24no—
644C4×D3—38no—
645C4×D3—38no—
646C4×D3—44no—
647C4×D3—64no—
648C4×D3—64no—
649C4×D3—68no—
650C4×D3—68no—
651C4×D3—64no—
652C4×D3—64no—
653C4×D3—64no—
654C4×D3—64no—
655C4×D3—68no—
656C4×D3—68no—
657C4×D3—64no—
658C4×D3—64no—
659C4×D3—64no—
660C4×D3—64no—
661C4×D3—124no—
662C4×D3—124no—
663C4×D3—124no—
664C4×D3—124no—
665C4×D3—124no—
666C4×D3—124no—
667C4×D3—124no—
668Dic6—24no—
669Dic6—44no—
670Dic6—68no—
671Dic6—124no—
672Dic6—124no—
673C2×C32—22no—
674C2×C32C23×Q811yescharacteristic
675C2×C32C22×#4111yescharacteristic
676C2×C32C2×H(5,𝔽2)11yescharacteristic
677C3⋊D3—22no—
678C3⋊D3#55414yescomplemented
679C3×D3—24no—
680C24—91no—
681C24—91no—
682C2×Q8—32no—
683C2×Q8—34no—
684C2×Q8—92no—
685C2×Q8—94no—
686C2×Q8—184no—
687C2×Q8—364no—
688C2×D4—32no—
689C2×D4—92no—
690C2×D4—98no—
691C22×C4—32no—
692C22×C4—34no—
693C22×C4—91no—
694C22×C4—92no—
695C22×C4—91no—
696C22×C4—91no—
697C22×C4—92no—
698C22×C4—92no—
699C22×C4—94no—
700C22×C4—91no—
701C22×C4—91no—
702C22×C4—92no—
703C22×C4—92no—
704C22×C4—91no—
705C22×C4—92no—
706C22×C4—91no—
707C22×C4—91no—
708C22×C4—92no—
709C22×C4—92no—
710C22×C4—184no—
711C22×C4—184no—
712C22×C4—364no—
713C22×C4—364no—
714C22×C4C2×D3211yescharacteristic
715C22×C4C2×D3212yes—
716C4⋊C4—34no—
717C4⋊C4—32no—
718C4⋊C4—32no—
719C4⋊C4—34no—
720C4⋊C4—34no—
721C4⋊C4—34no—
722C4⋊C4—34no—
723C4⋊C4—94no—
724C4⋊C4—92no—
725C4⋊C4—92no—
726C4⋊C4—94no—
727C4⋊C4—94no—
728C4⋊C4—94no—
729C4⋊C4—94no—
730C4⋊C4—92no—
731C4⋊C4—91no—
732C4⋊C4—92no—
733C4⋊C4—92no—
734C4⋊C4—92no—
735C4⋊C4—92no—
736C4⋊C4—91no—
737C4⋊C4C2×D3211yescharacteristic
738C4⋊C4C2×D3212yes—
739C4⋊C4C2×D3211yescharacteristic
740C22⋊C4—34no—
741C22⋊C4—32no—
742C22⋊C4—34no—
743C22⋊C4—32no—
744C22⋊C4—94no—
745C22⋊C4—92no—
746C22⋊C4—94no—
747C22⋊C4—92no—
748C42—34no—
749C42—32no—
750C42—94no—
751C42—92no—
752C22×C3—22no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—21no—
758C22×C3—34no—
759C22×C3—62no—
760C22×C3—62no—
761C22×C3C2×D3×Q814yes—
762C22×C3C24×D312yes—
763C2×D3—22no—
764C2×D3—22no—
765C2×D3—34no—
766C2×D3—34no—
767C2×D3—34no—
768C2×D3—34no—
769C2×D3—62no—
770C2×D3—62no—
771C2×D3—62no—
772C2×D3—62no—
773C2×D3—616no—
774C2×D3—616no—
775C2×D3—62no—
776C2×D3—62no—
777C2×D3—616no—
778C2×D3—62no—
779C2×D3—62no—
780C2×D3C2×D3×Q814yes—
781C3×C4—22no—
782C3×C4—22no—
783C3×C4—24no—
784C3×C4—24no—
785C3×C4—22no—
786C3×C4—34no—
787C3×C4—42no—
788C3×C4—42no—
789C3×C4—64no—
790C3×C4—62no—
791C3×C4—62no—
792C3×C4—64no—
793C3×C4D3×#4114yes—
794Dic3—24no—
795Dic3—22no—
796Dic3—22no—
797Dic3—24no—
798Dic3—34no—
799Dic3—62no—
800Dic3—62no—
801Dic3—62no—
802Dic3—64no—
803Dic3—64no—
804Dic3—122no—
805Dic3—122no—
806Dic3C2×D3×Q814yes—
807C32C2×#55411yescharacteristic, complemented, Sylow
808C23—32no—
809C23—94no—
810C23—91no—
811C23—94no—
812C23—91no—
813C23—182no—
814C23—182no—
815C23—182no—
816C23—182no—
817C23C22×D3211yescharacteristic
818Q8—64no—
819Q8—124no—
820Q8—184no—
821Q8—364no—
822D4—38no—
823D4—98no—
824C2×C4—22no—
825C2×C4—32no—
826C2×C4—34no—
827C2×C4—32no—
828C2×C4—32no—
829C2×C4—34no—
830C2×C4—42no—
831C2×C4—64no—
832C2×C4—94no—
833C2×C4—91no—
834C2×C4—94no—
835C2×C4—92no—
836C2×C4—91no—
837C2×C4—92no—
838C2×C4—124no—
839C2×C4—182no—
840C2×C4—182no—
841C2×C4—184no—
842C2×C4—184no—
843C2×C4—182no—
844C2×C4—184no—
845C2×C4—184no—
846C2×C4—182no—
847C2×C4—184no—
848C2×C4—182no—
849C2×C4—182no—
850C2×C4—362no—
851C2×C4—362no—
852C2×C4—364no—
853C2×C4—362no—
854C2×C4C22×D3212yes—
855C2×C4C22×D3211yescharacteristic
856C2×C4C22×D3212yes—
857C2×C4C22×D3211yescharacteristic
858C2×C3—24no—
859C2×C3—24no—
860C2×C3—21no—
861C2×C3—21no—
862C2×C3—21no—
863C2×C3—64no—
864C2×C3C22×D3×Q812yes—
865C2×C3C2×D3×#4112yes—
866C2×C3D3×H(5,𝔽2)12yes—
867D3—24no—
868D3—38no—
869D3—64no—
870D3—64no—
871D3—64no—
872C22—21no—
873C22—21no—
874C22—34no—
875C22—62no—
876C22—62no—
877C22—92no—
878C22—92no—
879C22—92no—
880C22—92no—
881C22—188no—
882C22—188no—
883C22—181no—
884C22—181no—
885C22D32×Q812yes—
886C22C23×D3211yescharacteristic
887C4—21no—
888C4—22no—
889C4—22no—
890C4—34no—
891C4—62no—
892C4—64no—
893C4—64no—
894C4—62no—
895C4—92no—
896C4—181no—
897C4—182no—
898C4—182no—
899C4#6430612yes—
900C3—21no—
901C3D3×#55412yescomplemented
902C2—22no—
903C2—64no—
904C2—94no—
905C2—182no—
906C2C2×#6430611yescharacteristic
907C2#1059667511yescharacteristic
908C2C2×D32×Q811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C4⋊C4C22
prime radicalC2×#3811C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#554
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×C3⋊D3C2semidirect
2. C3×#5511C2semidirect
5. #10594993C2semidirect
6. #10594959C2semidirect
7. #10594925C2semidirect
8. #10594925C2semidirect
9. #10594631C2semidirect
10. #10594624C2semidirect
11. D32×C4⋊C4C2semidirect
12. #10594536C2semidirect
13. #10594399C2semidirect
14. #10594394C2semidirect
15. #10594393C2semidirect
16. #10594374C2semidirect
17. #10594363C2semidirect
26. C2×C32×C4⋊C4C22semidirect
27. C2×C4⋊(C3⋊Dic3)C22semidirect
28. C2×#3750C22semidirect
32. C4⋊C4×C3⋊D3C22semidirect
33. C4⋊C4×C3⋊D3C22semidirect
34. C4⋊C4×C3⋊D3C22semidirect
37. C3×#924C22semidirect
38. C3×#924C22semidirect
39. C3×#897C22semidirect
40. C3×#896C22semidirect
41. C3×D3×C4⋊C4C22semidirect
42. C3×#889C22semidirect
43. C3×#888C22semidirect
44. C3×#887C22semidirect
45. #63982C22semidirect
46. #63982C22semidirect
53. #63918C22semidirect
58. #63899C22semidirect
59. #63893C22semidirect
60. D3×C4⋊Dic3C22semidirect
61. #63887C22semidirect
71. D3×Dic3⋊C4C22semidirect
72. #63871C22semidirect
73. #63871C22semidirect
74. #63867C22semidirect
75. #63865C22semidirect
76. #63865C22semidirect
77. #63856C22semidirect
78. #63851C22semidirect
79. #63846C22semidirect
80. #63845C22semidirect
81. Dic3×Dic6C22semidirect
82. #63839C22semidirect
83. #63837C22semidirect
104. #5511D3semidirect
129. #3811Q8semidirect
201. C2×C3×C4⋊C4C2×D3semidirect
219. #924C2×D3semidirect
220. #924C2×D3semidirect
227. #897C2×D3semidirect
233. #896C2×D3semidirect
257. D3×C4⋊C4C2×D3semidirect
263. #889C2×D3semidirect
266. #888C2×D3semidirect
268. #887C2×D3semidirect
321. C3×#67C2×Q8semidirect
333. #626C2×Q8semidirect
575. C2×C4⋊C4D32semidirect
622. #67D3×Q8semidirect
678. C3⋊D3#554semidirect
807. C32C2×#554semidirect
901. C3D3×#554semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C3×#55112
C4×#38112
#105949932
#105949592
#105949252
#105946312
#105946242
D32×C4⋊C42
#105945362
#105943992
#105943942
#105943932
#105943742
#105943632
D3×#5543