Finite Group Databasebeta

← #11909312

Subgroups — #11909312

Order 1152.

2365 conjugacy classes of subgroups.

The subgroup lattice has 999 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596028C211yesmaximal, characteristic, complemented
2C3×#5555C211yesmaximal, characteristic, complemented
3C3×#5551C211yesmaximal, characteristic, complemented
4#10595301C212yesmaximal, complemented
5#10595157C212yesmaximal, complemented
6#10595070C212yesmaximal, complemented
7#10594991C212yesmaximal, complemented
8#10594986C212yesmaximal, complemented
9#10594984C212yesmaximal, complemented
10D3×#897C212yesmaximal, complemented
11#10594551C212yesmaximal, complemented
12#10594304C214yesmaximal, complemented
13#10594123C214yesmaximal, complemented
14C4×#3802C211yesmaximal, characteristic, complemented
15#10593904C211yesmaximal, characteristic, complemented
16#10593866C211yesmaximal, characteristic, complemented
17#10593863C211yesmaximal, characteristic, complemented
18#86686—31nomaximal
19#86685—31nomaximal
20C2×C3×#237C2212yescomplemented
21C2×C3×#235C2212yes—
22C2×#3802C2211yescharacteristic
23C2×C4×D32C2212yes—
24C2×D3×Dic6C2212yescomplemented
25C32×C4×D4C2211yescharacteristic, complemented
26#64147C2211yescharacteristic
27#64145C2211yescharacteristic, complemented
28C4×#638C2212yes—
29#64135C2212yescomplemented
30#64106C2211yescharacteristic
31#64099C2211yescharacteristic, complemented
32#64092C2212yes—
33#64088C2212yescomplemented
34C42×C3⋊D3C2211yescharacteristic
35C4×#634C2211yescharacteristic, complemented
36C3×#938C2212yescomplemented
37C3×#930C2212yes—
38C2×C3×C4⋊Dic3C2212yescomplemented
39C3×#924C2212yescomplemented
40C3×#897C2212yescomplemented
41C3×D3×C4⋊C4C2212yescomplemented
42C3×#886C2214yescomplemented
43C3×#883C2214yescomplemented
44C3×C4×D12C2211yescharacteristic
45C3×C4×D12C2211yescharacteristic
46C3×#869C2211yescharacteristic, complemented
47C3×#869C2211yescharacteristic, complemented
48#63983C2214yes—
49Dic3×#67C2214yescomplemented
50Dic3×#67C2214yescomplemented
51#63970C2214yes—
52#63969C2214yescomplemented
53#63964C2214yescomplemented
54#63959C2214yescomplemented
55#63952C2214yes—
56#63921C2212yes—
57D3×(C2×D3)⋊C4C2214yes—
58#63919C2212yescomplemented
59#63905C2214yes—
60#63902C2212yes—
61C4×#625C2212yes—
62#63900C2211yescharacteristic
63#63899C2214yescomplemented
64#63898C2212yes—
65#63898C2211yescharacteristic
66#63898C2211yescharacteristic
67#63895C2214yes—
68#63893C2214yescomplemented
69D3×C4⋊Dic3C2214yescomplemented
70#63872C2212yescomplemented
71#63871C2212yes—
72#63871C2212yes—
73#63863C2212yes—
74#63861C2214yescomplemented
75#63858C2214yescomplemented
76#63857C2212yescomplemented
77#63856C2212yescomplemented
78#63849C2212yes—
79#63847C2214yescomplemented
80#63843C2212yescomplemented
81#63843C2212yescomplemented
82#63843C2212yescomplemented
83#63841C2214yescomplemented
84#63841C2212yescomplemented
85C3×#547—31no—
86C3×#547—31no—
87#5831—32no—
88#5829—32no—
89#5828—32no—
90#5827—32no—
91#5732—31no—
92#5728—31no—
93#5728—31no—
94#5727—31no—
95#5665—34no—
96#5660—34no—
97#5659—34no—
98#5658—34no—
99#5643—32no—
100#5639—32no—
101#5635—32no—
102D3×C22⋊Q8—32no—
103#5612—32no—
104#5606—32no—
105#5603—32no—
106#5598—32no—
107#5557—31no—
108#5557—31no—
109#5557—61no—
110#5555D311yescharacteristic, complemented
111#5551D311yescharacteristic, complemented
112C4×D3×D4—31no—
113C4×D3×D4—31no—
114#5542—31no—
115D4×Dic6—31no—
116#5513—32no—
117#5511—32no—
118C2×#897—32no—
119#5504—32no—
120C22×D32C2312yes—
121C2×C32×D4C2311yescharacteristic
122C22×C32×C4C2312yes—
123C2×#638C2312yes—
124C2×C4×C3⋊D3C2311yescharacteristic
125C2×C4×C3⋊D3C2311yescharacteristic
126C2×C4×C3⋊D3C2311yescharacteristic
127C2×#634C2311yescharacteristic
128C2×C3×#67C2314yes—
129C2×C3×#67C2314yes—
130C22×C3×Dic3C2314yes—
131C3×#237—44no—
132C3×#235—28no—
133C2×C3×D12C2311yescharacteristic
134C2×C3×D12C2311yescharacteristic
135C2×C3×C4×D3C2314yes—
136C2×C3×C4×D3C2312yes—
137C2×C3×C4×D3C2312yes—
138C2×C3×Dic6C2312yes—
139C2×C3×Dic6C2312yes—
140C2×#627C2314yes—
141C2×#625C2312yes—
142C2×#624C2312yes—
143C2×D3×Dic3C2314yes—
144C2×D3×Dic3C2312yes—
145C2×D3×Dic3C2312yes—
146#3802—24no—
147C4×D32—44no—
148D3×Dic6—44no—
149C32×C4⋊C4C2311yescharacteristic
150C32×C22⋊C4C2312yes—
151C32×C42C2311yescharacteristic
152#3757C2312yes—
153#3757C2312yes—
154#3757C2312yes—
155#3752C2312yes—
156C4⋊(C3⋊Dic3)C2311yescharacteristic
157C4⋊(C3⋊Dic3)C2312yes—
158C4⋊(C3⋊Dic3)C2312yes—
159#3750C2312yes—
160#3750C2312yes—
161C4×C3⋊Dic3C2312yes—
162C4×C3⋊Dic3C2311yescharacteristic
163C4×C3⋊Dic3C2311yescharacteristic
164C4×C3⋊Dic3C2311yescharacteristic
165C3×#217C2314yes—
166C3×(C2×D3)⋊C4C2312yes—
167C3×(C2×D3)⋊C4C2312yes—
168C3×(C2×D3)⋊C4C2314yes—
169C3×C4⋊Dic3C2312yes—
170C3×C4⋊Dic3C2312yes—
171C3×C4⋊Dic3C2314yes—
172C3×C4⋊Dic3C2312yes—
173C3×C4⋊Dic3C2311yescharacteristic
174C3×C4⋊Dic3C2311yescharacteristic
175C3×C4⋊Dic3C2312yes—
176C3×Dic3⋊C4C2314yes—
177#3724C2312yes—
178#3724C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2314yes—
182#3722C2314yes—
183(C2×D3)⋊Dic3C2312yes—
184(C2×D3)⋊Dic3C2314yes—
185(C2×D3)⋊Dic3C2314yes—
186(C2×D3)⋊Dic3C2314yes—
187(C2×D3)⋊Dic3C2312yes—
188Dic32C2314yes—
189Dic32C2314yes—
190#3520—91noSylow
191C2×C3×#41—32no—
192C2×C3×#41—32no—
193C2×D3×Q8—32no—
194C2×#237C2×D312yescomplemented
195C2×D3×D4—31no—
196C2×D3×D4—31no—
197C2×#235C2×D312yes—
198C22×C4×D3—32no—
199C22×C4×D3—32no—
200C22×Dic6—32no—
201C3×C4⋊Q8—31no—
202C3×C4⋊Q8—31no—
203C3×#123—34no—
204C3×#123—34no—
205C3×C22⋊Q8—32no—
206C3×C22⋊Q8—32no—
207C3×#121—32no—
208C3×#121—32no—
209C3×C4×D4—21no—
210C3×C4×D4—31no—
211C3×C4×D4—31no—
212C3×C4×D4C2×D311yescharacteristic, complemented
213C3×C4×D4C2×D311yescharacteristic, complemented
214C2×C3×C4⋊C4—32no—
215C2×C3×C4⋊C4—32no—
216#947—32no—
217#946—32no—
218#946—32no—
219#946—32no—
220Q8×Dic3—32no—
221Q8×Dic3—32no—
222Q8×Dic3—32no—
223#939—34no—
224#938—31no—
225#938—31no—
226#938—34no—
227#938—61no—
228#938C2×D312yescomplemented
229#937—34no—
230#937—34no—
231#936—31no—
232#936—31no—
233#936—32no—
234#936—34no—
235#936—61no—
236#935—34no—
237D4×Dic3—34no—
238D4×Dic3—34no—
239D4×Dic3—32no—
240D4×Dic3—31no—
241D4×Dic3—31no—
242#930C2×D312yes—
243#929—34no—
244C4×#67—32no—
245C4×#67—32no—
246C4×#67—34no—
247C4×#67—34no—
248C4×#67—32no—
249C4×#67—32no—
250C4×#67—34no—
251C4×#67—62no—
252C2×(C2×D3)⋊C4—34no—
253#926—32no—
254#926—32no—
255#926—32no—
256#926—34no—
257#926—62no—
258C2×C4⋊Dic3—34no—
259C2×C4⋊Dic3C2×D312yescomplemented
260#924—32no—
261#924—34no—
262#924—32no—
263#924C2×D312yescomplemented
264#898—34no—
265#898—34no—
266#897—32no—
267#897—32no—
268#897—32no—
269#897—31no—
270#897—31no—
271#897—34no—
272#897—34no—
273#897—61no—
274#897C2×D312yescomplemented
275#896—34no—
276#896—34no—
277#893—31no—
278#893—32no—
279#893—31no—
280#892—34no—
281#892—32no—
282#892—32no—
283#892—32no—
284D3×C4⋊C4—34no—
285D3×C4⋊C4—31no—
286D3×C4⋊C4—31no—
287D3×C4⋊C4C2×D312yescomplemented
288#890—31no—
289#890—31no—
290#890—32no—
291#890—32no—
292#890—61no—
293#889—34no—
294#889—34no—
295#888—32no—
296#888—32no—
297#887—32no—
298#887—32no—
299#887—32no—
300#886C2×D314yescomplemented
301#885—34no—
302#883—34no—
303#883—34no—
304#883—32no—
305#883—32no—
306#883—62no—
307#883C2×D314yescomplemented
308#67⋊C4—34no—
309#67⋊C4—32no—
310#67⋊C4—32no—
311D3×C22⋊C4—34no—
312D3×C22⋊C4—32no—
313D3×C22⋊C4—32no—
314#879—32no—
315#879—32no—
316#879—34no—
317#879—34no—
318#879—62no—
319#878—34no—
320#878—34no—
321#878—34no—
322C4×D12C2×D311yescharacteristic
323C4×D12C2×D311yescharacteristic
324C42×D3—31no—
325C42×D3—31no—
326C42×D3—61no—
327#869C2×D311yescharacteristic, complemented
328#869C2×D311yescharacteristic, complemented
329C4×Dic6—31no—
330C4×Dic6—31no—
331C4×Dic6—61no—
332C23×C32C2412yes—
333C22×C3⋊D3C2411yescharacteristic
334C22×C3×D3C2412yes—
335C22×C3×D3C2412yes—
336C2×D32—24no—
337C2×D32—24no—
338C2×D32—42no—
339C32×D4—22no—
340C2×C32×C4—24no—
341C2×C32×C4C2412yes—
342C2×C32×C4C2411yescharacteristic
343C2×C32×C4C2411yescharacteristic
344C2×C32×C4C2411yescharacteristic
345#638—24no—
346C2×C3⋊Dic3C2411yescharacteristic
347C2×C3⋊Dic3C2412yes—
348C2×C3⋊Dic3C2412yes—
349C2×C3⋊Dic3C2411yescharacteristic
350C2×C3⋊Dic3C2411yescharacteristic
351C4×C3⋊D3—22no—
352C4×C3⋊D3—22no—
353C4×C3⋊D3—22no—
354#634—22no—
355C3×#67—28no—
356C3×#67—44no—
357C2×C3×Dic3—44no—
358C2×C3×Dic3C2414yes—
359C2×C3×Dic3C2412yes—
360C2×C3×Dic3C2414yes—
361C2×C3×Dic3C2412yes—
362C3×D12—22no—
363C3×D12#4114yescomplemented
364C3×C4×D3—28no—
365C3×C4×D3—24no—
366C3×C4×D3—24no—
367C3×Dic6—24no—
368C3×Dic6—24no—
369#627—44no—
370#625—24no—
371#624—42no—
372D3×Dic3—44no—
373D3×Dic3—42no—
374D3×Dic3—42no—
375#556—91no—
376#554—92no—
377#552—92no—
378#551—94no—
379D4×Q8—91no—
380#548—92no—
381#547—31no—
382#547—31no—
383#546—92no—
384#542—92no—
385#539—94no—
386#533—91no—
387#529—91no—
388#525—92no—
389C2×C22⋊Q8—92no—
390#520—92no—
391C2×C4×D4—91no—
392C23×D3—32no—
393C23×D3—32no—
394C3×#41—68no—
395C3×#41—124no—
396C2×C3×Q8—32no—
397C2×C3×Q8—32no—
398C2×C3×D4—21no—
399C2×C3×D4—34no—
400C2×C3×D4—34no—
401C2×C3×D4—31no—
402C2×C3×D4—31no—
403C2×C3×D4C22×D311yescharacteristic
404C2×C3×D4C22×D311yescharacteristic
405C22×C3×C4—22no—
406C22×C3×C4—34no—
407C22×C3×C4—32no—
408C22×C3×C4—32no—
409C22×C3×C4—34no—
410C22×C3×C4C22×D312yes—
411C22×C3×C4C22×D312yes—
412C2×#67—32no—
413C2×#67—32no—
414C2×#67—32no—
415C2×#67—32no—
416C2×#67—62no—
417C2×#67C22×D314yes—
418C2×#67C22×D314yes—
419C22×Dic3—32no—
420C22×Dic3—34no—
421C22×Dic3—32no—
422C22×Dic3C22×D314yes—
423D3×Q8—124no—
424#237—44no—
425D3×D4—64no—
426D3×D4—64no—
427#235—28no—
428C2×D12C22×D311yescharacteristic
429C2×D12C22×D311yescharacteristic
430C2×C4×D3—31no—
431C2×C4×D3—31no—
432C2×C4×D3—31no—
433C2×C4×D3—31no—
434C2×C4×D3—31no—
435C2×C4×D3—31no—
436C2×C4×D3—34no—
437C2×C4×D3—32no—
438C2×C4×D3—32no—
439C2×C4×D3—32no—
440C2×C4×D3—32no—
441C2×C4×D3—61no—
442C2×C4×D3—61no—
443C2×C4×D3—61no—
444C2×C4×D3—124no—
445C2×C4×D3—124no—
446C2×C4×D3C22×D312yes—
447C2×C4×D3C22×D312yes—
448C2×C4×D3C22×D314yes—
449C2×Dic6—31no—
450C2×Dic6—31no—
451C2×Dic6—34no—
452C2×Dic6—34no—
453C2×Dic6—61no—
454C2×Dic6—124no—
455C2×Dic6C22×D312yes—
456C2×Dic6C22×D312yes—
457C3×C4⋊C4—21no—
458C3×C4⋊C4—31no—
459C3×C4⋊C4—32no—
460C3×C4⋊C4—32no—
461C3×C4⋊C4—31no—
462C3×C4⋊C4—34no—
463C3×C4⋊C4—34no—
464C3×C4⋊C4—32no—
465C3×C4⋊C4—32no—
466C3×C4⋊C4C22×D311yescharacteristic
467C3×C4⋊C4C22×D311yescharacteristic
468C3×C22⋊C4—22no—
469C3×C22⋊C4—34no—
470C3×C22⋊C4—32no—
471C3×C22⋊C4—34no—
472C3×C22⋊C4—32no—
473C3×C22⋊C4C22×D312yes—
474C3×C22⋊C4C22×D312yes—
475C3×C42—21no—
476C3×C42C22×D311yescharacteristic
477C3×C42C22×D311yescharacteristic
478#217—32no—
479#217—32no—
480#217—32no—
481#217—32no—
482#217—32no—
483#217—32no—
484#217—34no—
485#217—34no—
486#217—32no—
487#217—34no—
488#217—32no—
489#217—62no—
490#217—62no—
491#217—62no—
492#217C22×D314yes—
493(C2×D3)⋊C4—32no—
494(C2×D3)⋊C4—32no—
495(C2×D3)⋊C4—34no—
496(C2×D3)⋊C4—34no—
497(C2×D3)⋊C4—34no—
498(C2×D3)⋊C4—32no—
499(C2×D3)⋊C4—32no—
500(C2×D3)⋊C4—34no—
501(C2×D3)⋊C4—34no—
502(C2×D3)⋊C4—62no—
503(C2×D3)⋊C4C22×D312yes—
504(C2×D3)⋊C4C22×D312yes—
505(C2×D3)⋊C4C22×D314yes—
506C4⋊Dic3—31no—
507C4⋊Dic3—31no—
508C4⋊Dic3—32no—
509C4⋊Dic3—32no—
510C4⋊Dic3—32no—
511C4⋊Dic3—32no—
512C4⋊Dic3—34no—
513C4⋊Dic3—34no—
514C4⋊Dic3—34no—
515C4⋊Dic3—61no—
516C4⋊Dic3—62no—
517C4⋊Dic3—62no—
518C4⋊Dic3C22×D312yes—
519C4⋊Dic3C22×D312yes—
520C4⋊Dic3C22×D312yes—
521C4⋊Dic3C22×D312yes—
522C4⋊Dic3C22×D311yescharacteristic
523C4⋊Dic3C22×D311yescharacteristic
524C4⋊Dic3C22×D314yes—
525Dic3⋊C4—32no—
526Dic3⋊C4—32no—
527Dic3⋊C4—32no—
528Dic3⋊C4—32no—
529Dic3⋊C4—32no—
530Dic3⋊C4—34no—
531Dic3⋊C4—34no—
532Dic3⋊C4—34no—
533Dic3⋊C4—34no—
534Dic3⋊C4—34no—
535Dic3⋊C4—32no—
536Dic3⋊C4—62no—
537Dic3⋊C4—62no—
538Dic3⋊C4C22×D314yes—
539C4×Dic3—32no—
540C4×Dic3—32no—
541C4×Dic3—31no—
542C4×Dic3—31no—
543C4×Dic3—31no—
544C4×Dic3—31no—
545C4×Dic3—31no—
546C4×Dic3—31no—
547C4×Dic3—34no—
548C4×Dic3—34no—
549C4×Dic3—34no—
550C4×Dic3—34no—
551C4×Dic3—62no—
552C4×Dic3—61no—
553C4×Dic3—61no—
554C4×Dic3—61no—
555C22×C32—22no—
556C22×C32—22no—
557C22×C32—22no—
558C22×C32C2511yescharacteristic
559C2×C3⋊D3—21no—
560C2×C3⋊D3—21no—
561C2×C3⋊D32−1+412yes—
562C2×C3×D3—22no—
563C2×C3×D3—22no—
564C2×C3×D3—22no—
565C2×C3×D3—22no—
566C2×C3×D3—22no—
567C2×C3×D3C2×#4114yes—
568D32—48no—
569C32×C4—22no—
570C32×C4—21no—
571C32×C4C2×#4112yes—
572C32×C4H(5,𝔽2)12yes—
573C3⋊Dic3—21no—
574C3⋊Dic3—21no—
575C3⋊Dic3—22no—
576C3⋊Dic3—21no—
577C3⋊Dic3—22no—
578C3×Dic3—24no—
579C3×Dic3—22no—
580C3×Dic3—22no—
581C3×Dic3—24no—
582C2×#41—32no—
583C2×#41—32no—
584C22×Q8—92no—
585C22×D4—91no—
586C23×C4—92no—
587C4⋊Q8—31no—
588C4⋊Q8—31no—
589C4⋊Q8—92no—
590#126—94no—
591#126—94no—
592#126—92no—
593#125—92no—
594#125—94no—
595#125—91no—
596#124—94no—
597#124—92no—
598#124—91no—
599#123—34no—
600#123—34no—
601#123—94no—
602#123—94no—
603#123—92no—
604C22⋊Q8—32no—
605C22⋊Q8—32no—
606C22⋊Q8—94no—
607C22⋊Q8—94no—
608C22⋊Q8—94no—
609C22⋊Q8—94no—
610C22⋊Q8—92no—
611C22⋊Q8—92no—
612C22⋊Q8—92no—
613C22⋊Q8—92no—
614C22⋊Q8—91no—
615#121—32no—
616#121—32no—
617#121—94no—
618#121—91no—
619#120—94no—
620C4×Q8—92no—
621C4×Q8—92no—
622C4×Q8—92no—
623C4×Q8—91no—
624C4×D4—31no—
625C4×D4—31no—
626C4×D4—92no—
627C4×D4—94no—
628C4×D4—91no—
629C4×D4—91no—
630C4×D4—92no—
631C4×D4—92no—
632C4×D4—94no—
633C4×D4—94no—
634C4×D4—92no—
635C4×D4D3211yescharacteristic, complemented
636#117—92no—
637#117—94no—
638#117—92no—
639#117—92no—
640C2×C4⋊C4—32no—
641C2×C4⋊C4—32no—
642C2×C4⋊C4—91no—
643C2×C4⋊C4—94no—
644C2×C22⋊C4—92no—
645C2×C22⋊C4—94no—
646C2×C42—91no—
647C23×C3—22no—
648C23×C3—32no—
649C23×C3—32no—
650C23×C3C23×D312yes—
651C23×C3C23×D312yes—
652C22×D3—31no—
653C22×D3—31no—
654C22×D3—61no—
655C22×D3—64no—
656C22×D3—64no—
657C22×D3—64no—
658C22×D3—64no—
659C22×D3—122no—
660C22×D3—122no—
661C22×D3C23×D312yes—
662C22×D3C23×D312yes—
663C3×Q8—64no—
664C3×Q8—64no—
665C3×D4—22no—
666C3×D4—22no—
667C3×D4—34no—
668C3×D4—42no—
669C3×D4—68no—
670C3×D4—62no—
671C3×D4—124no—
672C2×C3×C4—24no—
673C2×C3×C4—24no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—22no—
678C2×C3×C4—32no—
679C2×C3×C4—34no—
680C2×C3×C4—34no—
681C2×C3×C4—32no—
682C2×C3×C4—44no—
683C2×C3×C4—68no—
684C2×C3×C4—64no—
685C2×C3×C4—64no—
686C2×C3×C4—124no—
687C2×C3×C4C23×D311yescharacteristic
688C2×C3×C4C23×D311yescharacteristic
689C2×C3×C4C23×D312yes—
690C2×C3×C4C23×D312yes—
691C2×C3×C4C23×D311yescharacteristic
692C2×C3×C4C23×D311yescharacteristic
693C2×C3×C4C23×D311yescharacteristic
694C2×C3×C4C23×D311yescharacteristic
695#67—28no—
696#67—44no—
697#67—64no—
698#67—64no—
699#67—64no—
700#67—64no—
701#67—124no—
702C2×Dic3—31no—
703C2×Dic3—31no—
704C2×Dic3—32no—
705C2×Dic3—32no—
706C2×Dic3—31no—
707C2×Dic3—31no—
708C2×Dic3—31no—
709C2×Dic3—31no—
710C2×Dic3—32no—
711C2×Dic3—32no—
712C2×Dic3—44no—
713C2×Dic3—61no—
714C2×Dic3—61no—
715C2×Dic3—61no—
716C2×Dic3—62no—
717C2×Dic3—62no—
718C2×Dic3—124no—
719C2×Dic3—122no—
720C2×Dic3—122no—
721C2×Dic3C23×D314yes—
722C2×Dic3C23×D312yes—
723C2×Dic3C23×D314yes—
724C2×Dic3C23×D312yes—
725D12—22no—
726D12#23714yescomplemented
727C4×D3—28no—
728C4×D3—24no—
729C4×D3—24no—
730C4×D3—62no—
731C4×D3—62no—
732C4×D3—62no—
733C4×D3—62no—
734C4×D3—62no—
735C4×D3—62no—
736C4×D3—122no—
737C4×D3—122no—
738C4×D3—122no—
739C4×D3—122no—
740C4×D3—122no—
741C4×D3—122no—
742C4×D3—122no—
743C4×D3—124no—
744Dic6—24no—
745Dic6—24no—
746Dic6—62no—
747Dic6—62no—
748Dic6—122no—
749Dic6—124no—
750Dic6—124no—
751C2×C32—42no—
752C2×C32C22×#4111yescharacteristic
753C2×C32C2×H(5,𝔽2)11yescharacteristic
754C2×C32C2×2−1+411yescharacteristic
755C3⋊D3—22no—
756C3×D3—24no—
757C3×D3—42no—
758C24—92no—
759#41—68no—
760#41—124no—
761C2×Q8—32no—
762C2×Q8—32no—
763C2×Q8—94no—
764C2×Q8—91no—
765C2×Q8—364no—
766C2×D4—34no—
767C2×D4—34no—
768C2×D4—31no—
769C2×D4—31no—
770C2×D4—92no—
771C2×D4—92no—
772C2×D4—184no—
773C2×D4C2×D3211yescharacteristic
774C22×C4—34no—
775C22×C4—34no—
776C22×C4—32no—
777C22×C4—32no—
778C22×C4—92no—
779C22×C4—94no—
780C22×C4—92no—
781C22×C4—92no—
782C22×C4—91no—
783C22×C4—91no—
784C22×C4—91no—
785C22×C4—364no—
786C22×C4C2×D3212yes—
787C4⋊C4—31no—
788C4⋊C4—34no—
789C4⋊C4—32no—
790C4⋊C4—32no—
791C4⋊C4—34no—
792C4⋊C4—31no—
793C4⋊C4—32no—
794C4⋊C4—32no—
795C4⋊C4—92no—
796C4⋊C4—94no—
797C4⋊C4—94no—
798C4⋊C4—94no—
799C4⋊C4—94no—
800C4⋊C4—92no—
801C4⋊C4—92no—
802C4⋊C4—91no—
803C4⋊C4—92no—
804C4⋊C4—92no—
805C4⋊C4C2×D3211yescharacteristic
806C22⋊C4—34no—
807C22⋊C4—32no—
808C22⋊C4—32no—
809C22⋊C4—34no—
810C22⋊C4—94no—
811C22⋊C4—92no—
812C22⋊C4—92no—
813C22⋊C4—94no—
814C22⋊C4—94no—
815C22⋊C4—94no—
816C22⋊C4—92no—
817C22⋊C4—92no—
818C22⋊C4—92no—
819C22⋊C4—92no—
820C22⋊C4C2×D3212yes—
821C42—94no—
822C42—94no—
823C42—91no—
824C42—91no—
825C42—91no—
826C42—92no—
827C42C2×D3211yescharacteristic
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—22no—
831C22×C3—22no—
832C22×C3—22no—
833C22×C3—22no—
834C22×C3—21no—
835C22×C3—34no—
836C22×C3—42no—
837C22×C3—42no—
838C22×C3—42no—
839C22×C3—62no—
840C22×C3—62no—
841C22×C3—62no—
842C22×C3—62no—
843C22×C3—62no—
844C22×C3C24×D311yescharacteristic
845C22×C3C24×D311yescharacteristic
846C2×D3—22no—
847C2×D3—22no—
848C2×D3—22no—
849C2×D3—22no—
850C2×D3—22no—
851C2×D3—32no—
852C2×D3—32no—
853C2×D3—62no—
854C2×D3—61no—
855C2×D3—61no—
856C2×D3—61no—
857C2×D3—61no—
858C2×D3—121no—
859C2×D3—121no—
860C2×D3—128no—
861C2×D3—128no—
862C2×D3C2×#23714yes—
863C3×C4—22no—
864C3×C4—22no—
865C3×C4—21no—
866C3×C4—21no—
867C3×C4—22no—
868C3×C4—22no—
869C3×C4—41no—
870C3×C4—42no—
871C3×C4—62no—
872C3×C4—64no—
873C3×C4—64no—
874C3×C4—62no—
875C3×C4C2×#23712yes—
876C3×C4#100412yes—
877C3×C4D3×#4112yes—
878C3×C4#100912yes—
879Dic3—24no—
880Dic3—24no—
881Dic3—22no—
882Dic3—22no—
883Dic3—61no—
884Dic3—62no—
885Dic3—61no—
886Dic3—61no—
887Dic3—62no—
888Dic3—61no—
889Dic3—61no—
890Dic3—61no—
891Dic3—62no—
892Dic3—62no—
893Dic3—122no—
894Dic3—121no—
895Dic3—121no—
896Dic3—121no—
897Dic3—122no—
898C32#352011yescharacteristic, complemented, Sylow
899C23—32no—
900C23—32no—
901C23—91no—
902C23—184no—
903C23—184no—
904C23—362no—
905C23C22×D3212yes—
906Q8—64no—
907Q8—64no—
908Q8—182no—
909Q8—364no—
910D4—22no—
911D4—34no—
912D4—68no—
913D4—62no—
914D4—124no—
915D4—184no—
916D4—184no—
917C2×C4—24no—
918C2×C4—34no—
919C2×C4—32no—
920C2×C4—34no—
921C2×C4—32no—
922C2×C4—68no—
923C2×C4—64no—
924C2×C4—64no—
925C2×C4—91no—
926C2×C4—92no—
927C2×C4—91no—
928C2×C4—91no—
929C2×C4—92no—
930C2×C4—124no—
931C2×C4—182no—
932C2×C4—182no—
933C2×C4—182no—
934C2×C4—362no—
935C2×C4—362no—
936C2×C4—362no—
937C2×C4—364no—
938C2×C4C22×D3211yescharacteristic
939C2×C4C22×D3212yes—
940C2×C4C22×D3211yescharacteristic
941C2×C4C22×D3211yescharacteristic
942C2×C3—21no—
943C2×C3—21no—
944C2×C3—21no—
945C2×C3—42no—
946C2×C3—42no—
947C2×C3—64no—
948C2×C3—82no—
949C2×C3—122no—
950C2×C3C22×#23711yescharacteristic
951C2×C3C2×#100411yescharacteristic
952C2×C3C2×D3×#4111yescharacteristic
953C2×C3C2×#100911yescharacteristic
954C2×C3D3×2−1+411yescharacteristic
955C2×C3D3×2−1+411yescharacteristic
956D3—24no—
957D3—42no—
958D3—62no—
959D3—62no—
960D3—122no—
961C22—22no—
962C22—22no—
963C22—22no—
964C22—34no—
965C22—62no—
966C22—62no—
967C22—62no—
968C22—62no—
969C22—62no—
970C22—92no—
971C22—181no—
972C22—181no—
973C22—368no—
974C22C23×D3211yescharacteristic
975C4—22no—
976C4—21no—
977C4—62no—
978C4—62no—
979C4—64no—
980C4—64no—
981C4—181no—
982C4—182no—
983C4—181no—
984C4—181no—
985C4—182no—
986C4#6430712yes—
987C4D3×#23712yes—
988C3—21no—
989C3#8668511yescharacteristic, complemented
990C3#8668611yescharacteristic, complemented
991C2—42no—
992C2—64no—
993C2—122no—
994C2—182no—
995C2C2×#6430711yescharacteristic
996C2C2×D3×#23711yescharacteristic
997C2#1059669411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
hypercenterC4×D4D32
hypocenterC32#3520
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596028C2semidirect
2. C3×#5555C2semidirect
3. C3×#5551C2semidirect
4. #10595301C2semidirect
5. #10595157C2semidirect
6. #10595070C2semidirect
7. #10594991C2semidirect
8. #10594986C2semidirect
9. #10594984C2semidirect
10. D3×#897C2semidirect
11. #10594551C2semidirect
12. #10594304C2semidirect
13. #10594123C2semidirect
14. C4×#3802C2semidirect
15. #10593904C2semidirect
16. #10593866C2semidirect
17. #10593863C2semidirect
20. C2×C3×#237C22semidirect
24. C2×D3×Dic6C22semidirect
25. C32×C4×D4C22semidirect
27. #64145C22semidirect
29. #64135C22semidirect
31. #64099C22semidirect
33. #64088C22semidirect
35. C4×#634C22semidirect
36. C3×#938C22semidirect
38. C2×C3×C4⋊Dic3C22semidirect
39. C3×#924C22semidirect
40. C3×#897C22semidirect
41. C3×D3×C4⋊C4C22semidirect
42. C3×#886C22semidirect
43. C3×#883C22semidirect
46. C3×#869C22semidirect
47. C3×#869C22semidirect
49. Dic3×#67C22semidirect
50. Dic3×#67C22semidirect
52. #63969C22semidirect
53. #63964C22semidirect
54. #63959C22semidirect
58. #63919C22semidirect
63. #63899C22semidirect
68. #63893C22semidirect
69. D3×C4⋊Dic3C22semidirect
70. #63872C22semidirect
74. #63861C22semidirect
75. #63858C22semidirect
76. #63857C22semidirect
77. #63856C22semidirect
79. #63847C22semidirect
80. #63843C22semidirect
81. #63843C22semidirect
82. #63843C22semidirect
83. #63841C22semidirect
84. #63841C22semidirect
110. #5555D3semidirect
111. #5551D3semidirect
194. C2×#237C2×D3semidirect
212. C3×C4×D4C2×D3semidirect
213. C3×C4×D4C2×D3semidirect
228. #938C2×D3semidirect
259. C2×C4⋊Dic3C2×D3semidirect
263. #924C2×D3semidirect
274. #897C2×D3semidirect
287. D3×C4⋊C4C2×D3semidirect
300. #886C2×D3semidirect
307. #883C2×D3semidirect
327. #869C2×D3semidirect
328. #869C2×D3semidirect
363. C3×D12#41semidirect
635. C4×D4D32semidirect
726. D12#237semidirect
898. C32#3520semidirect
989. C3#86685semidirect
990. C3#86686semidirect

Maximal subgroups

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

subgroupindex
#105960282
C3×#55552
C3×#55512
#105953012
#105951572
#105950702
#105949912
#105949862
#105949842
D3×#8972
#105945512
#105943042
#105941232
C4×#38022
#105939042
#105938662
#105938632
#866863
#866853