Finite Group Databasebeta

← #11909939

Subgroups — #11909939

Order 1152.

2095 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595941C211yesmaximal, characteristic, complemented
2C3×#5479C211yesmaximal, characteristic
3C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
4#10594952C214yesmaximal, complemented
5#10594949C212yesmaximal
6Dic6×#67C212yesmaximal, complemented
7#10594849C212yesmaximal, complemented
8#10594808C212yesmaximal, complemented
9#10593932C212yesmaximal, complemented
10#10593928C214yesmaximal, complemented
11Dic6×D12C211yesmaximal, characteristic, complemented
12#10593885C212yesmaximal, complemented
13#10593880C212yesmaximal, complemented
14#10593879C211yesmaximal, characteristic, complemented
15#10593860C211yesmaximal, characteristic, complemented
16#10593860C211yesmaximal, characteristic, complemented
17#10593852C212yesmaximal, complemented
18#86129—31nomaximal
19#85804—31nomaximal
20C22×C3×Dic6C2211yescharacteristic
21C2×D3×Dic6C2212yes—
22C2×C32×C42C2211yescharacteristic
23#64135C2212yes—
24#64133C2212yes—
25#64133C2212yes—
26#64079C2212yes—
27#64078C2211yescharacteristic
28#64078C2211yescharacteristic
29C4×#634C2212yes—
30C4×#634C2212yes—
31C3×#930C2211yescharacteristic
32C3×#929C2212yes—
33C3×C4×#67C2212yes—
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C3×#924C2211yescharacteristic
36C2×C3×Dic3⋊C4C2212yes—
37C2×C3×C4×Dic3C2212yes—
38C3×#876C2212yes—
39C3×#875C2211yescharacteristic
40C3×C4×D12C2211yescharacteristic
41C3×#872C2212yes—
42C3×#870C2211yescharacteristic
43C3×C4×Dic6C2212yes—
44C3×C4×Dic6C2211yescharacteristic
45C3×C4×Dic6C2211yescharacteristic
46C3×C4×Dic6C2211yescharacteristic
47C3×C4×Dic6C2211yescharacteristic
48C3×C4×Dic6C2211yescharacteristic
49C3×C4×Dic6C2212yes—
50Dic3×#67C2214yes—
51#63964C2214yes—
52#63961C2214yes—
53#63955C2214yes—
54#63918C2212yes—
55#63893C2214yes—
56Dic3×D12C2212yes—
57#63887C2214yes—
58#63878C2214yes—
59#63877C2214yes—
60#63870C2214yes—
61#63869C2212yes—
62#63869C2212yes—
63#63867C2214yes—
64#63866C2212yes—
65#63866C2212yes—
66#63862C2214yes—
67#63861C2214yes—
68#63860C2212yes—
69#63859C2214yes—
70#63858C2214yes—
71#63857C2212yes—
72#63856C2212yes—
73#63847C2214yes—
74#63845C2214yes—
75#63845C2214yes—
76#63844C2212yes—
77#63844C2212yes—
78#63844C2212yes—
79Dic3×Dic6C2212yes—
80Dic3×Dic6C2212yes—
81#63841C2212yes—
82#63839C2214yes—
83#63838C2214yes—
84#63837C2214yes—
85C3×#529—31no—
86C2×C3×C4×Q8—31no—
87Q8×#67—32no—
88#5701—34no—
89#5685—32no—
90#5671—32no—
91#5650—34no—
92#5622—32no—
93#5600—32no—
94#5584—32no—
95#5584—31no—
96#5583—34no—
97#5583—32no—
98Q8×D12—31no—
99#5572—32no—
100#5570—31no—
101#5570—31no—
102#5567—32no—
103#5567—31no—
104#5567—31no—
105#5542—31no—
106#5541—32no—
107D4×Dic6—32no—
108D4×Dic6—31no—
109#5518—32no—
110#5516—32no—
111#5513—34no—
112#5513—32no—
113#5479—32no—
114#5479D311yescharacteristic
115#5470—31no—
116#5470—31no—
117#5470—32no—
118#5470—61no—
119C2×C4×Dic6D311yescharacteristic, complemented
120C22×C32×C4C2311yescharacteristic
121C22×C32×C4C2311yescharacteristic
122C22×C32×C4C2311yescharacteristic
123C2×#634C2312yes—
124C2×#634C2312yes—
125C2×C3×#67C2312yes—
126C22×C3×Dic3C2312yes—
127C22×C3×Dic3C2312yes—
128C2×C3×D12C2311yescharacteristic
129C2×C3×C4×D3C2312yes—
130C2×C3×Dic6—24no—
131C2×C3×Dic6C2311yescharacteristic
132C2×C3×Dic6C2312yes—
133C2×C3×Dic6C2311yescharacteristic
134C2×C3×Dic6C2311yescharacteristic
135C2×#627C2314yes—
136C2×D3×Dic3C2314yes—
137D3×Dic6—28no—
138C32×C42C2311yescharacteristic
139C32×C42C2311yescharacteristic
140C32×C42C2311yescharacteristic
141C32×C42C2311yescharacteristic
142#3757C2314yes—
143C4⋊(C3⋊Dic3)C2312yes—
144C4⋊(C3⋊Dic3)C2312yes—
145C4⋊(C3⋊Dic3)C2312yes—
146C4⋊(C3⋊Dic3)C2312yes—
147#3750C2314yes—
148#3750C2314yes—
149C4×C3⋊Dic3C2314yes—
150C3×#217C2312yes—
151C3×(C2×D3)⋊C4C2312yes—
152C3×(C2×D3)⋊C4C2312yes—
153C3×(C2×D3)⋊C4C2312yes—
154C3×(C2×D3)⋊C4C2312yes—
155C3×C4⋊Dic3C2311yescharacteristic
156C3×C4⋊Dic3C2311yescharacteristic
157C3×C4⋊Dic3C2312yes—
158C3×C4⋊Dic3C2311yescharacteristic
159C3×C4⋊Dic3C2311yescharacteristic
160C3×Dic3⋊C4C2312yes—
161C3×Dic3⋊C4C2312yes—
162C3×Dic3⋊C4C2312yes—
163C3×Dic3⋊C4C2312yes—
164C3×Dic3⋊C4C2312yes—
165C3×Dic3⋊C4C2312yes—
166C3×Dic3⋊C4C2312yes—
167C3×Dic3⋊C4C2312yes—
168C3×C4×Dic3C2312yes—
169C3×C4×Dic3C2312yes—
170C3×C4×Dic3C2312yes—
171C3×C4×Dic3C2312yes—
172C3×C4×Dic3C2312yes—
173#3724C2314yes—
174#3724C2314yes—
175#3724C2314yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181(C2×D3)⋊Dic3C2314yes—
182(C2×D3)⋊Dic3C2314yes—
183(C2×D3)⋊Dic3C2314yes—
184Dic32C2314yes—
185Dic32C2314yes—
186Dic32C2314yes—
187#3523—91noSylow
188C22×C3×Q8—31no—
189C2×D3×Q8—32no—
190C22×Dic6—32no—
191C22×Dic6C2×D311yescharacteristic
192C3×#126—32no—
193C3×#125—31no—
194C3×#124—31no—
195C3×#123—32no—
196C3×C22⋊Q8—31no—
197C3×#121—31no—
198C3×C4×Q8—31no—
199C3×C4×Q8—31no—
200C3×C4×Q8—32no—
201C3×C4×Q8—31no—
202C3×C4×Q8—31no—
203C3×C4×Q8—32no—
204C3×C4×Q8—31no—
205C3×C4×D4—32no—
206C3×C4×D4—31no—
207C3×#117—32no—
208C2×C3×C4⋊C4—32no—
209C2×C3×C4⋊C4—31no—
210C2×C3×C42—21no—
211C2×C3×C42—32no—
212C2×C3×C42C2×D311yescharacteristic
213C2×C3×C42C2×D311yescharacteristic
214#946—32no—
215#946—34no—
216Q8×Dic3—32no—
217Q8×Dic3—32no—
218#944—34no—
219#944—32no—
220#944—32no—
221#936—32no—
222#935—34no—
223D4×Dic3—34no—
224D4×Dic3—32no—
225#930C2×D311yescharacteristic
226#929—34no—
227#929C2×D312yes—
228C4×#67—34no—
229C4×#67C2×D312yes—
230#926—32no—
231#926—32no—
232#926—34no—
233#926—32no—
234#926—62no—
235C2×C4⋊Dic3C2×D311yescharacteristic
236#924—32no—
237#924—32no—
238#924—32no—
239#924—32no—
240#924—32no—
241#924—34no—
242#924—32no—
243#924—62no—
244#924—62no—
245#924C2×D311yescharacteristic
246C2×Dic3⋊C4C2×D312yes—
247C2×C4×Dic3C2×D312yes—
248#898—34no—
249#898—34no—
250#898—34no—
251#897—32no—
252#897—34no—
253#892—32no—
254#892—34no—
255#890—34no—
256#890—34no—
257#890—32no—
258#890—32no—
259#889—34no—
260#889—34no—
261#889—34no—
262#889—34no—
263#889—34no—
264#889—34no—
265#889—34no—
266#888—34no—
267#888—32no—
268#887—34no—
269#887—34no—
270#887—32no—
271#887—32no—
272#887—34no—
273#887—32no—
274#879—34no—
275#879—34no—
276#879—34no—
277#879—34no—
278#878—34no—
279#878—34no—
280#878—34no—
281#877—34no—
282#877—34no—
283#877—34no—
284#876—34no—
285#876C2×D312yes—
286#875—32no—
287#875C2×D311yescharacteristic
288C4×D12—32no—
289C4×D12C2×D311yescharacteristic
290#872—34no—
291#872C2×D312yes—
292#870—32no—
293#870—32no—
294#870—32no—
295#870—32no—
296#870—34no—
297#870—62no—
298#870C2×D311yescharacteristic
299#869—32no—
300#869—32no—
301#869—31no—
302#869—31no—
303#869—31no—
304#869—31no—
305#869—32no—
306#869—61no—
307#869—61no—
308C4×Dic6—32no—
309C4×Dic6—32no—
310C4×Dic6—32no—
311C4×Dic6—32no—
312C4×Dic6—32no—
313C4×Dic6—32no—
314C4×Dic6—32no—
315C4×Dic6—32no—
316C4×Dic6—32no—
317C4×Dic6—34no—
318C4×Dic6—62no—
319C4×Dic6—62no—
320C4×Dic6C2×D312yes—
321C4×Dic6C2×D312yes—
322C4×Dic6C2×D311yescharacteristic
323C4×Dic6C2×D311yescharacteristic
324C4×Dic6C2×D311yescharacteristic
325C4×Dic6C2×D311yescharacteristic
326C4×Dic6C2×D311yescharacteristic
327C23×C32C2411yescharacteristic
328C22×C3×D3C2412yes—
329C2×C32×C4—22no—
330C2×C32×C4—22no—
331C2×C32×C4—22no—
332C2×C32×C4C2411yescharacteristic
333C2×C32×C4C2411yescharacteristic
334C2×C32×C4C2411yescharacteristic
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2411yescharacteristic
337C2×C32×C4C2411yescharacteristic
338C2×C3⋊Dic3C2414yes—
339C2×C3⋊Dic3C2414yes—
340#634—24no—
341#634—24no—
342C3×#67—24no—
343C2×C3×Dic3—24no—
344C2×C3×Dic3—24no—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2412yes—
352C3×D12—22no—
353C3×C4×D3—24no—
354C3×Dic6—22no—
355C3×Dic6—22no—
356C3×Dic6—24no—
357C3×Dic6#4114yes—
358#627—28no—
359D3×Dic3—28no—
360#557—91no—
361#557—91no—
362#557—92no—
363#556—91no—
364#556—92no—
365#552—92no—
366#552—94no—
367D4×Q8—91no—
368D4×Q8—92no—
369#541—92no—
370#541—94no—
371#533—92no—
372#533—91no—
373#529—31no—
374#529—92no—
375#519—92no—
376C2×C4×Q8—31no—
377C2×C3×Q8—31no—
378C2×C3×Q8—31no—
379C2×C3×Q8—32no—
380C2×C3×Q8—31no—
381C2×C3×Q8—64no—
382C2×C3×D4—32no—
383C2×C3×D4—31no—
384C22×C3×C4—21no—
385C22×C3×C4—21no—
386C22×C3×C4—21no—
387C22×C3×C4—32no—
388C22×C3×C4—32no—
389C22×C3×C4—32no—
390C22×C3×C4C22×D311yescharacteristic
391C22×C3×C4C22×D311yescharacteristic
392C22×C3×C4C22×D311yescharacteristic
393C22×C3×C4C22×D311yescharacteristic
394C22×C3×C4C22×D311yescharacteristic
395C22×C3×C4C22×D311yescharacteristic
396C2×#67C22×D312yes—
397C22×Dic3—34no—
398C22×Dic3C22×D312yes—
399C22×Dic3C22×D312yes—
400D3×Q8—68no—
401C2×D12C22×D311yescharacteristic
402C2×C4×D3—34no—
403C2×C4×D3C22×D312yes—
404C2×Dic6—24no—
405C2×Dic6—32no—
406C2×Dic6—32no—
407C2×Dic6—32no—
408C2×Dic6—32no—
409C2×Dic6—34no—
410C2×Dic6—34no—
411C2×Dic6—62no—
412C2×Dic6—62no—
413C2×Dic6—68no—
414C2×Dic6C22×D311yescharacteristic
415C2×Dic6C22×D311yescharacteristic
416C2×Dic6C22×D312yes—
417C2×Dic6C22×D311yescharacteristic
418C3×C4⋊C4—31no—
419C3×C4⋊C4—32no—
420C3×C4⋊C4—32no—
421C3×C4⋊C4—31no—
422C3×C4⋊C4—32no—
423C3×C4⋊C4—31no—
424C3×C4⋊C4—32no—
425C3×C4⋊C4—32no—
426C3×C4⋊C4—32no—
427C3×C4⋊C4—32no—
428C3×C4⋊C4—32no—
429C3×C4⋊C4—32no—
430C3×C4⋊C4—31no—
431C3×C22⋊C4—32no—
432C3×C22⋊C4—32no—
433C3×C22⋊C4—32no—
434C3×C22⋊C4—32no—
435C3×C22⋊C4—32no—
436C3×C42—21no—
437C3×C42—21no—
438C3×C42—21no—
439C3×C42—21no—
440C3×C42—32no—
441C3×C42—32no—
442C3×C42—32no—
443C3×C42—32no—
444C3×C42—32no—
445C3×C42C22×D311yescharacteristic
446C3×C42C22×D311yescharacteristic
447C3×C42C22×D311yescharacteristic
448C3×C42C22×D311yescharacteristic
449C3×C42C22×D311yescharacteristic
450C3×C42C22×D311yescharacteristic
451C3×C42C22×D311yescharacteristic
452C3×C42C22×D311yescharacteristic
453#217—34no—
454#217—34no—
455#217—34no—
456#217—34no—
457#217—34no—
458#217—64no—
459#217C22×D312yes—
460(C2×D3)⋊C4—34no—
461(C2×D3)⋊C4—34no—
462(C2×D3)⋊C4—34no—
463(C2×D3)⋊C4C22×D312yes—
464(C2×D3)⋊C4C22×D312yes—
465(C2×D3)⋊C4C22×D312yes—
466(C2×D3)⋊C4C22×D312yes—
467C4⋊Dic3—32no—
468C4⋊Dic3—32no—
469C4⋊Dic3—32no—
470C4⋊Dic3—32no—
471C4⋊Dic3—32no—
472C4⋊Dic3—32no—
473C4⋊Dic3—32no—
474C4⋊Dic3—32no—
475C4⋊Dic3—34no—
476C4⋊Dic3—34no—
477C4⋊Dic3—34no—
478C4⋊Dic3—34no—
479C4⋊Dic3—34no—
480C4⋊Dic3—62no—
481C4⋊Dic3—62no—
482C4⋊Dic3—62no—
483C4⋊Dic3—62no—
484C4⋊Dic3C22×D311yescharacteristic
485C4⋊Dic3C22×D311yescharacteristic
486C4⋊Dic3C22×D311yescharacteristic
487C4⋊Dic3C22×D311yescharacteristic
488C4⋊Dic3C22×D312yes—
489Dic3⋊C4—34no—
490Dic3⋊C4—34no—
491Dic3⋊C4—34no—
492Dic3⋊C4—34no—
493Dic3⋊C4—34no—
494Dic3⋊C4—34no—
495Dic3⋊C4—34no—
496Dic3⋊C4—34no—
497Dic3⋊C4—34no—
498Dic3⋊C4—34no—
499Dic3⋊C4—34no—
500Dic3⋊C4—34no—
501Dic3⋊C4—34no—
502Dic3⋊C4—34no—
503Dic3⋊C4—34no—
504Dic3⋊C4—64no—
505Dic3⋊C4—64no—
506Dic3⋊C4C22×D312yes—
507Dic3⋊C4C22×D312yes—
508Dic3⋊C4C22×D312yes—
509Dic3⋊C4C22×D312yes—
510Dic3⋊C4C22×D312yes—
511Dic3⋊C4C22×D312yes—
512Dic3⋊C4C22×D312yes—
513Dic3⋊C4C22×D312yes—
514C4×Dic3—34no—
515C4×Dic3—34no—
516C4×Dic3—34no—
517C4×Dic3—34no—
518C4×Dic3—34no—
519C4×Dic3—34no—
520C4×Dic3—34no—
521C4×Dic3—34no—
522C4×Dic3—64no—
523C4×Dic3C22×D312yes—
524C4×Dic3C22×D312yes—
525C4×Dic3C22×D312yes—
526C4×Dic3C22×D312yes—
527C4×Dic3C22×D312yes—
528C22×C32—21no—
529C22×C32—21no—
530C22×C322−1+412yes—
531C22×C32C2511yescharacteristic
532C2×C3×D3—22no—
533C2×C3×D3—22no—
534C2×C3×D3—22no—
535C32×C4—21no—
536C32×C4—21no—
537C32×C4—21no—
538C32×C4—21no—
539C32×C4C2×#4112yes—
540C32×C42−1+412yes—
541C3⋊Dic3—24no—
542C3⋊Dic3—24no—
543C3×Dic3—22no—
544C3×Dic3—22no—
545C3×Dic3—22no—
546C3×Dic3—22no—
547C3×Dic3—22no—
548C3×Dic3—22no—
549C3×Dic3C2×#4114yes—
550C22×Q8—31no—
551C22×Q8—92no—
552C4⋊Q8—92no—
553C4⋊Q8—92no—
554C4⋊Q8—92no—
555C4⋊Q8—94no—
556C4⋊Q8—91no—
557C4⋊Q8—91no—
558#126—32no—
559#126—94no—
560#126—94no—
561#126—94no—
562#126—94no—
563#125—31no—
564#125—92no—
565#125—94no—
566#125—92no—
567#125—94no—
568#125—94no—
569#125—94no—
570#125—94no—
571#125—92no—
572#124—31no—
573#124—92no—
574#123—32no—
575#123—94no—
576C22⋊Q8—31no—
577C22⋊Q8—94no—
578C22⋊Q8—94no—
579C22⋊Q8—94no—
580C22⋊Q8—92no—
581C22⋊Q8—92no—
582C22⋊Q8—92no—
583C22⋊Q8—92no—
584#121—31no—
585C4×Q8—31no—
586C4×Q8—32no—
587C4×Q8—31no—
588C4×Q8—31no—
589C4×Q8—32no—
590C4×Q8—31no—
591C4×Q8—31no—
592C4×Q8—94no—
593C4×Q8—92no—
594C4×Q8—92no—
595C4×Q8—92no—
596C4×Q8—92no—
597C4×Q8—92no—
598C4×Q8—94no—
599C4×Q8—92no—
600C4×Q8—92no—
601C4×D4—32no—
602C4×D4—31no—
603C4×D4—92no—
604C4×D4—94no—
605#117—32no—
606#117—94no—
607#117—94no—
608#117—94no—
609#117—92no—
610#117—92no—
611C2×C4⋊C4—32no—
612C2×C4⋊C4—31no—
613C2×C42—32no—
614C2×C42D3211yescharacteristic
615C23×C3—21no—
616C23×C3—32no—
617C23×C3C23×D311yescharacteristic
618C23×C3C23×D311yescharacteristic
619C22×D3C23×D312yes—
620C3×Q8—34no—
621C3×Q8—64no—
622C3×Q8—62no—
623C3×Q8—62no—
624C3×D4—64no—
625C3×D4—62no—
626C2×C3×C4—24no—
627C2×C3×C4—22no—
628C2×C3×C4—22no—
629C2×C3×C4—22no—
630C2×C3×C4—22no—
631C2×C3×C4—22no—
632C2×C3×C4—22no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
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—42no—
647C2×C3×C4—42no—
648C2×C3×C4—64no—
649C2×C3×C4—64no—
650C2×C3×C4—64no—
651C2×C3×C4C23×D311yescharacteristic
652C2×C3×C4C23×D311yescharacteristic
653C2×C3×C4C23×D311yescharacteristic
654C2×C3×C4C23×D311yescharacteristic
655C2×C3×C4C23×D311yescharacteristic
656C2×C3×C4C23×D311yescharacteristic
657C2×C3×C4C23×D311yescharacteristic
658C2×C3×C4C23×D311yescharacteristic
659C2×C3×C4C23×D311yescharacteristic
660C2×C3×C4C23×D311yescharacteristic
661C2×C3×C4C23×D311yescharacteristic
662C2×C3×C4C23×D311yescharacteristic
663#67—24no—
664C2×Dic3—24no—
665C2×Dic3—24no—
666C2×Dic3—34no—
667C2×Dic3—34no—
668C2×Dic3—34no—
669C2×Dic3—34no—
670C2×Dic3—64no—
671C2×Dic3—64no—
672C2×Dic3—68no—
673C2×Dic3C23×D312yes—
674C2×Dic3C23×D312yes—
675C2×Dic3C23×D312yes—
676C2×Dic3C23×D312yes—
677C2×Dic3C23×D312yes—
678C2×Dic3C23×D312yes—
679C2×Dic3C23×D312yes—
680D12—22no—
681C4×D3—24no—
682C4×D3—68no—
683Dic6—22no—
684Dic6—22no—
685Dic6—24no—
686Dic6—68no—
687Dic6—64no—
688Dic6—64no—
689Dic6—64no—
690Dic6—64no—
691Dic6—68no—
692Dic6—124no—
693Dic6—124no—
694Dic6#23514yes—
695C2×C32—22no—
696C2×C32C22×#4111yescharacteristic
697C2×C32C2×2−1+411yescharacteristic
698C2×C32C2×2−1+411yescharacteristic
699C3×D3—42no—
700C2×Q8—31no—
701C2×Q8—32no—
702C2×Q8—31no—
703C2×Q8—31no—
704C2×Q8—64no—
705C2×Q8—94no—
706C2×Q8—92no—
707C2×Q8—92no—
708C2×Q8—188no—
709C2×D4—32no—
710C2×D4—31no—
711C22×C4—32no—
712C22×C4—32no—
713C22×C4—32no—
714C22×C4—94no—
715C22×C4C2×D3211yescharacteristic
716C22×C4C2×D3211yescharacteristic
717C22×C4C2×D3211yescharacteristic
718C4⋊C4—32no—
719C4⋊C4—31no—
720C4⋊C4—32no—
721C4⋊C4—31no—
722C4⋊C4—32no—
723C4⋊C4—32no—
724C4⋊C4—32no—
725C4⋊C4—32no—
726C4⋊C4—32no—
727C4⋊C4—31no—
728C4⋊C4—32no—
729C4⋊C4—31no—
730C4⋊C4—32no—
731C4⋊C4—94no—
732C4⋊C4—94no—
733C4⋊C4—94no—
734C4⋊C4—94no—
735C4⋊C4—94no—
736C4⋊C4—94no—
737C4⋊C4—94no—
738C4⋊C4—94no—
739C4⋊C4—92no—
740C4⋊C4—94no—
741C4⋊C4—92no—
742C4⋊C4—92no—
743C4⋊C4—92no—
744C4⋊C4—94no—
745C22⋊C4—32no—
746C22⋊C4—32no—
747C22⋊C4—32no—
748C22⋊C4—32no—
749C22⋊C4—32no—
750C22⋊C4—94no—
751C22⋊C4—94no—
752C22⋊C4—94no—
753C22⋊C4—94no—
754C42—32no—
755C42—32no—
756C42—32no—
757C42—32no—
758C42—32no—
759C42—94no—
760C42—94no—
761C42—94no—
762C42—94no—
763C42C2×D3211yescharacteristic
764C42C2×D3211yescharacteristic
765C42C2×D3211yescharacteristic
766C42C2×D3211yescharacteristic
767C22×C3—21no—
768C22×C3—21no—
769C22×C3—21no—
770C22×C3—21no—
771C22×C3—22no—
772C22×C3—21no—
773C22×C3—41no—
774C22×C3—41no—
775C22×C3—62no—
776C22×C3—62no—
777C22×C3—62no—
778C22×C3#101012yes—
779C22×C3#101012yes—
780C22×C3C24×D311yescharacteristic
781C22×C3C24×D311yescharacteristic
782C2×D3—22no—
783C2×D3—22no—
784C2×D3—22no—
785C3×C4—22no—
786C3×C4—22no—
787C3×C4—21no—
788C3×C4—21no—
789C3×C4—21no—
790C3×C4—21no—
791C3×C4—21no—
792C3×C4—21no—
793C3×C4—21no—
794C3×C4—21no—
795C3×C4—22no—
796C3×C4—22no—
797C3×C4—34no—
798C3×C4—41no—
799C3×C4—41no—
800C3×C4—62no—
801C3×C4—62no—
802C3×C4—62no—
803C3×C4—62no—
804C3×C4—62no—
805C3×C4—62no—
806C3×C4C2×#23512yes—
807C3×C4#100712yes—
808C3×C4D3×#4112yes—
809C3×C4#101012yes—
810Dic3—22no—
811Dic3—22no—
812Dic3—22no—
813Dic3—22no—
814Dic3—22no—
815Dic3—22no—
816Dic3—64no—
817Dic3—64no—
818Dic3—64no—
819Dic3—64no—
820Dic3—124no—
821Dic3—124no—
822Dic3C2×#23514yes—
823C32#352311yescharacteristic, complemented, Sylow
824C23—32no—
825C23C22×D3211yescharacteristic
826Q8—34no—
827Q8—64no—
828Q8—62no—
829Q8—62no—
830Q8—188no—
831Q8—184no—
832Q8—184no—
833D4—64no—
834D4—62no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—32no—
839C2×C4—32no—
840C2×C4—32no—
841C2×C4—32no—
842C2×C4—32no—
843C2×C4—32no—
844C2×C4—32no—
845C2×C4—64no—
846C2×C4—64no—
847C2×C4—64no—
848C2×C4—94no—
849C2×C4—94no—
850C2×C4—188no—
851C2×C4C22×D3211yescharacteristic
852C2×C4C22×D3211yescharacteristic
853C2×C4C22×D3211yescharacteristic
854C2×C4C22×D3211yescharacteristic
855C2×C4C22×D3211yescharacteristic
856C2×C4C22×D3211yescharacteristic
857C2×C3—22no—
858C2×C3—22no—
859C2×C3—21no—
860C2×C3—21no—
861C2×C3—21no—
862C2×C3—42no—
863C2×C3—122no—
864C2×C3C22×#23511yescharacteristic
865C2×C3C2×#100711yescharacteristic
866C2×C3C2×D3×#4111yescharacteristic
867C2×C3C2×#101011yescharacteristic
868C2×C3C2×#101011yescharacteristic
869C2×C3C2×#101011yescharacteristic
870D3—42no—
871C22—21no—
872C22—21no—
873C22—62no—
874C22—62no—
875C22—62no—
876C22#6429812yes—
877C22C23×D3211yescharacteristic
878C4—21no—
879C4—21no—
880C4—21no—
881C4—21no—
882C4—34no—
883C4—62no—
884C4—62no—
885C4—62no—
886C4—62no—
887C4—62no—
888C4—62no—
889C4—184no—
890C4—184no—
891C4#6429712yes—
892C4D3×#23512yes—
893C3—21no—
894C3#8580411yescharacteristic, complemented
895C3#8612911yescharacteristic, complemented
896C2—22no—
897C2—122no—
898C2C2×#6429711yescharacteristic
899C2C2×#6429811yescharacteristic
900C2C2×D3×#23511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C42C22
prime radicalC3×#930C22
hypercenterC2×C42D32
hypocenterC32#3523
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #10595941C2semidirect
3. C2×C3×C4×Dic6C2semidirect
4. #10594952C2semidirect
6. Dic6×#67C2semidirect
7. #10594849C2semidirect
8. #10594808C2semidirect
9. #10593932C2semidirect
10. #10593928C2semidirect
11. Dic6×D12C2semidirect
12. #10593885C2semidirect
13. #10593880C2semidirect
14. #10593879C2semidirect
15. #10593860C2semidirect
16. #10593860C2semidirect
17. #10593852C2semidirect
119. C2×C4×Dic6D3semidirect
823. C32#3523semidirect
894. C3#85804semidirect
895. C3#86129semidirect

Maximal subgroups

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

subgroupindex
#105959412
C3×#54792
C2×C3×C4×Dic62
#105949522
#105949492
Dic6×#672
#105948492
#105948082
#105939322
#105939282
Dic6×D122
#105938852
#105938802
#105938792
#105938602
#105938522
#861293
#858043