Finite Group Databasebeta

← #11909347

Subgroups — #11909347

Order 1152.

2354 conjugacy classes of subgroups.

The subgroup lattice has 977 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596013C211yesmaximal, characteristic, complemented
2C3×#5551C211yesmaximal, characteristic, complemented
3C3×C4×D3×D4C211yesmaximal, characteristic, complemented
4#10595228C212yesmaximal, complemented
5#10595124C212yesmaximal, complemented
6#10595022C212yesmaximal, complemented
7#10594942C212yesmaximal, complemented
8#10594899C212yesmaximal, complemented
9D3×#924C212yesmaximal, complemented
10#10594531C212yesmaximal, complemented
11#10594359C212yesmaximal, complemented
12#10594193C214yesmaximal, complemented
13#10594091C214yesmaximal, complemented
14#10593974C211yesmaximal, characteristic, complemented
15#10593904C211yesmaximal, characteristic, complemented
16#10593895C211yesmaximal, characteristic, complemented
17#10593859C211yesmaximal, characteristic, complemented
18#86686—31nomaximal
19#85767—31nomaximal
20C2×C3×D3×D4C2211yescharacteristic
21C2×C3×#235C2212yescomplemented
22C22×C3×C4×D3C2212yes—
23C2×#3795C2212yes—
24C2×D3×Dic6C2212yescomplemented
25C32×C4×D4C2211yescharacteristic
26#64145C2212yes—
27#64135C2212yescomplemented
28#64133C2212yescomplemented
29#64096C2212yescomplemented
30#64088C2214yescomplemented
31#64078C2211yescharacteristic, complemented
32C4×#634C2211yescharacteristic, complemented
33C3×#938C2212yes—
34C3×D4×Dic3C2211yescharacteristic
35C3×C4×#67C2212yes—
36C3×#924C2212yescomplemented
37C3×#893C2211yescharacteristic
38C3×D3×C4⋊C4C2211yescharacteristic
39C3×D3×C4⋊C4C2212yescomplemented
40C3×#883C2214yescomplemented
41C3×#67⋊C4C2212yes—
42C3×D3×C22⋊C4C2212yes—
43C3×C4×D12C2211yescharacteristic
44C3×C4×D12C2211yescharacteristic, complemented
45C3×C42×D3C2211yescharacteristic
46C3×#869C2211yescharacteristic, complemented
47#63976C2214yes—
48#63970C2214yes—
49#63969C2214yes—
50D3×#217C2214yes—
51#63964C2214yescomplemented
52#63961C2214yescomplemented
53#63959C2214yescomplemented
54#63956C2214yescomplemented
55#63919C2212yescomplemented
56#63908C2211yescharacteristic
57#63908C2212yescomplemented
58#63905C2212yes—
59C4×#625C2214yes—
60C4×#625C2212yes—
61C4×#625C2214yescomplemented
62#63899C2214yescomplemented
63#63898C2212yes—
64#63891C2214yescomplemented
65D3×C4⋊Dic3C2212yescomplemented
66#63879C2214yescomplemented
67#63878C2214yescomplemented
68D3×Dic3⋊C4C2214yescomplemented
69#63870C2214yescomplemented
70#63869C2212yescomplemented
71#63869C2211yescharacteristic, complemented
72#63860C2211yescharacteristic, complemented
73#63859C2212yescomplemented
74#63857C2212yes—
75#63857C2211yescharacteristic
76#63857C2212yescomplemented
77#63856C2212yes—
78#63856C2212yescomplemented
79#63855C2212yescomplemented
80#63851C2214yes—
81#63851C2214yescomplemented
82#63844C2212yescomplemented
83Dic3×Dic6C2212yescomplemented
84#63841C2212yes—
85C3×#547—31no—
86C2×C3×C4×D4—31no—
87#5831—32no—
88#5828—32no—
89#5806—32no—
90#5791—32no—
91C2×#924—32no—
92#5728—31no—
93#5727—31no—
94#5660—34no—
95#5659—34no—
96#5639—32no—
97D3×C22⋊Q8—32no—
98#5612—32no—
99#5603—32no—
100#5564—34no—
101#5561—32no—
102#5557—31no—
103#5555—31no—
104#5552—32no—
105#5551—31no—
106#5551D311yescharacteristic, complemented
107#5546—32no—
108C4×D3×D4D311yescharacteristic, complemented
109#5542—31no—
110#5542—31no—
111#5542—61no—
112#5541—32no—
113D4×Dic6—31no—
114#5511—32no—
115#5511—32no—
116#5504—32no—
117#5495—34no—
118#5479—31no—
119#5470—31no—
120C23×C3×D3C2312yes—
121C2×C32×D4C2311yescharacteristic
122C22×C32×C4C2312yes—
123C2×#634C2311yescharacteristic
124C2×#634C2312yes—
125C2×C3×#67C2312yes—
126C2×C3×#67C2314yes—
127C22×C3×Dic3C2312yes—
128C3×D3×D4—24no—
129C3×#235—44no—
130C2×C3×D12C2311yescharacteristic
131C2×C3×D12C2311yescharacteristic
132C2×C3×C4×D3—44no—
133C2×C3×C4×D3C2311yescharacteristic
134C2×C3×C4×D3C2311yescharacteristic
135C2×C3×C4×D3C2312yes—
136C2×C3×C4×D3C2312yes—
137C2×C3×C4×D3C2311yescharacteristic
138C2×C3×C4×D3C2312yes—
139C2×C3×C4×D3C2312yes—
140C2×C3×C4×D3C2314yes—
141C2×C3×Dic6C2312yes—
142C2×#627C2314yes—
143C2×#625C2314yes—
144C2×#625C2312yes—
145C2×D3×Dic3C2314yes—
146C2×D3×Dic3C2314yes—
147#3795—28no—
148D3×Dic6—44no—
149C32×C4⋊C4C2311yescharacteristic
150C32×C22⋊C4C2312yes—
151C32×C42C2311yescharacteristic
152#3757C2314yes—
153#3757C2314yes—
154C4⋊(C3⋊Dic3)C2311yescharacteristic
155C4⋊(C3⋊Dic3)C2312yes—
156C4⋊(C3⋊Dic3)C2312yes—
157#3750C2312yes—
158#3750C2314yes—
159C4×C3⋊Dic3C2312yes—
160C4×C3⋊Dic3C2314yes—
161C3×#217C2312yes—
162C3×#217C2314yes—
163C3×(C2×D3)⋊C4C2312yes—
164C3×(C2×D3)⋊C4C2312yes—
165C3×(C2×D3)⋊C4C2312yes—
166C3×C4⋊Dic3C2312yes—
167C3×C4⋊Dic3C2311yescharacteristic
168C3×C4⋊Dic3C2312yes—
169C3×C4⋊Dic3C2311yescharacteristic
170C3×Dic3⋊C4C2312yes—
171C3×Dic3⋊C4C2314yes—
172C3×C4×Dic3C2311yescharacteristic
173C3×C4×Dic3C2311yescharacteristic
174C3×C4×Dic3C2311yescharacteristic
175#3724C2314yes—
176#3724C2314yes—
177#3724C2312yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2312yes—
181Dic3⋊Dic3C2312yes—
182(C2×D3)⋊Dic3C2314yes—
183(C2×D3)⋊Dic3C2312yes—
184(C2×D3)⋊Dic3C2312yes—
185(C2×D3)⋊Dic3C2314yes—
186(C2×D3)⋊Dic3C2312yes—
187(C2×D3)⋊Dic3C2312yes—
188(C2×D3)⋊Dic3C2314yes—
189Dic32C2314yes—
190#3520—91noSylow
191C2×C3×#41—32no—
192C22×C3×D4—31no—
193C23×C3×C4—32no—
194C2×D3×Q8—32no—
195C2×#237—32no—
196C2×D3×D4C2×D311yescharacteristic
197C2×#235—32no—
198C2×#235C2×D312yescomplemented
199C22×C4×D3C2×D312yes—
200C22×Dic6—32no—
201C3×C4⋊Q8—31no—
202C3×#123—34no—
203C3×C22⋊Q8—32no—
204C3×#121—32no—
205C3×C4×D4—21no—
206C3×C4×D4—31no—
207C3×C4×D4—32no—
208C3×C4×D4—31no—
209C3×C4×D4—32no—
210C3×C4×D4—31no—
211C3×C4×D4—31no—
212C3×C4×D4C2×D311yescharacteristic
213C3×C4×D4C2×D311yescharacteristic
214C2×C3×C4⋊C4—31no—
215C2×C3×C4⋊C4—32no—
216C2×C3×C22⋊C4—32no—
217C2×C3×C42—31no—
218#953—34no—
219C2×#217—34no—
220#946—32no—
221#946—32no—
222Q8×Dic3—32no—
223#939—34no—
224#938—34no—
225#938—31no—
226#938—32no—
227#938C2×D312yes—
228#937—34no—
229#936—32no—
230#936—32no—
231#936—34no—
232#936—31no—
233#936—62no—
234#935—34no—
235#935—34no—
236D4×Dic3—32no—
237D4×Dic3C2×D311yescharacteristic
238#930—31no—
239#930—32no—
240#929—34no—
241#929—32no—
242C4×#67—34no—
243C4×#67—34no—
244C4×#67—32no—
245C4×#67—34no—
246C4×#67—32no—
247C4×#67—34no—
248C4×#67—34no—
249C4×#67C2×D312yes—
250#926—32no—
251#926—32no—
252#926—32no—
253#926—32no—
254#926—62no—
255C2×C4⋊Dic3—32no—
256#924—32no—
257#924—32no—
258#924—32no—
259#924—32no—
260#924—34no—
261#924—32no—
262#924—31no—
263#924—32no—
264#924—34no—
265#924—34no—
266#924—62no—
267#924C2×D312yescomplemented
268C2×Dic3⋊C4—34no—
269#897—32no—
270#897—31no—
271#897—32no—
272#896—34no—
273#896—34no—
274#896—34no—
275#893—32no—
276#893C2×D311yescharacteristic
277#892—32no—
278#892—34no—
279D3×C4⋊C4—32no—
280D3×C4⋊C4—34no—
281D3×C4⋊C4C2×D311yescharacteristic
282D3×C4⋊C4C2×D312yescomplemented
283#890—31no—
284#890—32no—
285#889—34no—
286#889—34no—
287#888—32no—
288#888—32no—
289#887—32no—
290#887—32no—
291#887—32no—
292#887—62no—
293#886—34no—
294#885—34no—
295#883—34no—
296#883—32no—
297#883—34no—
298#883C2×D314yescomplemented
299#67⋊C4—34no—
300#67⋊C4C2×D312yes—
301D3×C22⋊C4—34no—
302D3×C22⋊C4C2×D312yes—
303#879—34no—
304#879—34no—
305#879—34no—
306#879—34no—
307#879—32no—
308#879—64no—
309#878—34no—
310#878—34no—
311#877—34no—
312#876—32no—
313#875—31no—
314C4×D12C2×D311yescharacteristic
315C4×D12C2×D311yescharacteristic, complemented
316#872—32no—
317C42×D3C2×D311yescharacteristic
318#870—32no—
319#870—31no—
320#869—31no—
321#869—31no—
322#869—61no—
323#869C2×D311yescharacteristic, complemented
324C4×Dic6—32no—
325C4×Dic6—31no—
326C4×Dic6—31no—
327C4×Dic6—32no—
328C4×Dic6—61no—
329C23×C32C2412yes—
330C22×C3×D3—24no—
331C22×C3×D3—24no—
332C22×C3×D3—42no—
333C22×C3×D3C2412yes—
334C22×C3×D3C2412yes—
335C22×C3×D3C2411yescharacteristic
336C32×D4—22no—
337C2×C32×C4—24no—
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2412yes—
340C2×C32×C4C2411yescharacteristic
341C2×C32×C4C2411yescharacteristic
342C2×C3⋊Dic3C2414yes—
343C2×C3⋊Dic3C2412yes—
344C2×C3⋊Dic3C2412yes—
345#634—24no—
346#634—22no—
347C3×#67—24no—
348C3×#67—44no—
349C2×C3×Dic3—42no—
350C2×C3×Dic3C2411yescharacteristic
351C2×C3×Dic3C2414yes—
352C2×C3×Dic3C2411yescharacteristic
353C2×C3×Dic3C2411yescharacteristic
354C2×C3×Dic3C2412yes—
355C2×C3×Dic3C2412yes—
356C3×D12—22no—
357C3×D12#4114yescomplemented
358C3×C4×D3—22no—
359C3×C4×D3—24no—
360C3×C4×D3—22no—
361C3×C4×D3—24no—
362C3×C4×D3—22no—
363C3×C4×D3—42no—
364C3×C4×D3—42no—
365C3×C4×D3—44no—
366C3×Dic6—24no—
367#627—44no—
368#625—28no—
369#625—24no—
370D3×Dic3—28no—
371D3×Dic3—44no—
372#556—91no—
373#554—92no—
374#552—92no—
375#551—94no—
376D4×Q8—91no—
377#548—92no—
378#547—31no—
379#547—91no—
380#546—92no—
381#542—92no—
382#539—94no—
383#533—91no—
384#529—91no—
385#525—92no—
386C2×C22⋊Q8—92no—
387#520—92no—
388C2×C4×D4—31no—
389C24×C3—32no—
390C23×D3C22×D312yes—
391C3×#41—124no—
392C2×C3×Q8—32no—
393C2×C3×D4—21no—
394C2×C3×D4—32no—
395C2×C3×D4—34no—
396C2×C3×D4—31no—
397C2×C3×D4—31no—
398C2×C3×D4—64no—
399C2×C3×D4C22×D311yescharacteristic
400C2×C3×D4C22×D311yescharacteristic
401C22×C3×C4—22no—
402C22×C3×C4—32no—
403C22×C3×C4—31no—
404C22×C3×C4—31no—
405C22×C3×C4—32no—
406C22×C3×C4—32no—
407C22×C3×C4—31no—
408C22×C3×C4—32no—
409C22×C3×C4—32no—
410C22×C3×C4—34no—
411C22×C3×C4—124no—
412C22×C3×C4C22×D312yes—
413C22×C3×C4C22×D312yes—
414C2×#67—34no—
415C2×#67—32no—
416C2×#67—34no—
417C2×#67—32no—
418C2×#67C22×D312yes—
419C2×#67C22×D314yes—
420C22×Dic3—34no—
421C22×Dic3—34no—
422C22×Dic3C22×D312yes—
423D3×Q8—124no—
424#237—68no—
425D3×D4—24no—
426#235—44no—
427#235—68no—
428C2×D12C22×D311yescharacteristic
429C2×D12C22×D311yescharacteristic
430C2×C4×D3—34no—
431C2×C4×D3—34no—
432C2×C4×D3—44no—
433C2×C4×D3C22×D311yescharacteristic
434C2×C4×D3C22×D311yescharacteristic
435C2×C4×D3C22×D311yescharacteristic
436C2×C4×D3C22×D312yes—
437C2×C4×D3C22×D312yes—
438C2×C4×D3C22×D312yes—
439C2×C4×D3C22×D314yes—
440C2×C4×D3C22×D312yes—
441C2×Dic6—32no—
442C2×Dic6—31no—
443C2×Dic6—31no—
444C2×Dic6—32no—
445C2×Dic6—34no—
446C2×Dic6—34no—
447C2×Dic6—61no—
448C2×Dic6—62no—
449C2×Dic6—124no—
450C2×Dic6C22×D312yes—
451C3×C4⋊C4—21no—
452C3×C4⋊C4—32no—
453C3×C4⋊C4—31no—
454C3×C4⋊C4—32no—
455C3×C4⋊C4—34no—
456C3×C4⋊C4—31no—
457C3×C4⋊C4—32no—
458C3×C4⋊C4C22×D311yescharacteristic
459C3×C4⋊C4C22×D311yescharacteristic
460C3×C22⋊C4—22no—
461C3×C22⋊C4—34no—
462C3×C22⋊C4—32no—
463C3×C22⋊C4—32no—
464C3×C22⋊C4—32no—
465C3×C22⋊C4—32no—
466C3×C22⋊C4C22×D312yes—
467C3×C22⋊C4C22×D312yes—
468C3×C42—21no—
469C3×C42—31no—
470C3×C42—31no—
471C3×C42—31no—
472C3×C42C22×D311yescharacteristic
473C3×C42C22×D311yescharacteristic
474#217—34no—
475#217—34no—
476#217—34no—
477#217—34no—
478#217—34no—
479#217—32no—
480#217—32no—
481#217—34no—
482#217—32no—
483#217—34no—
484#217—32no—
485#217—64no—
486#217—64no—
487#217C22×D312yes—
488#217C22×D314yes—
489(C2×D3)⋊C4—32no—
490(C2×D3)⋊C4—32no—
491(C2×D3)⋊C4—32no—
492(C2×D3)⋊C4—32no—
493(C2×D3)⋊C4—34no—
494(C2×D3)⋊C4—34no—
495(C2×D3)⋊C4—34no—
496(C2×D3)⋊C4C22×D312yes—
497(C2×D3)⋊C4C22×D312yes—
498(C2×D3)⋊C4C22×D312yes—
499C4⋊Dic3—32no—
500C4⋊Dic3—31no—
501C4⋊Dic3—31no—
502C4⋊Dic3—32no—
503C4⋊Dic3—32no—
504C4⋊Dic3—32no—
505C4⋊Dic3—32no—
506C4⋊Dic3—32no—
507C4⋊Dic3—34no—
508C4⋊Dic3—34no—
509C4⋊Dic3—61no—
510C4⋊Dic3—62no—
511C4⋊Dic3—62no—
512C4⋊Dic3C22×D312yes—
513C4⋊Dic3C22×D312yes—
514C4⋊Dic3C22×D311yescharacteristic
515C4⋊Dic3C22×D311yescharacteristic
516Dic3⋊C4—32no—
517Dic3⋊C4—32no—
518Dic3⋊C4—34no—
519Dic3⋊C4—34no—
520Dic3⋊C4—34no—
521Dic3⋊C4—34no—
522Dic3⋊C4—32no—
523Dic3⋊C4—32no—
524Dic3⋊C4—32no—
525Dic3⋊C4—34no—
526Dic3⋊C4—34no—
527Dic3⋊C4—34no—
528Dic3⋊C4—32no—
529Dic3⋊C4—34no—
530Dic3⋊C4—62no—
531Dic3⋊C4—64no—
532Dic3⋊C4C22×D314yes—
533Dic3⋊C4C22×D312yes—
534C4×Dic3—32no—
535C4×Dic3—32no—
536C4×Dic3—34no—
537C4×Dic3—34no—
538C4×Dic3—34no—
539C4×Dic3—34no—
540C4×Dic3—62no—
541C4×Dic3—64no—
542C4×Dic3C22×D311yescharacteristic
543C4×Dic3C22×D311yescharacteristic
544C4×Dic3C22×D311yescharacteristic
545C22×C32—22no—
546C22×C32—22no—
547C22×C32—22no—
548C22×C32C2511yescharacteristic
549C2×C3×D3—21no—
550C2×C3×D3—22no—
551C2×C3×D3—21no—
552C2×C3×D3—22no—
553C2×C3×D3—22no—
554C2×C3×D3—22no—
555C2×C3×D3—22no—
556C2×C3×D3—48no—
557C2×C3×D3C2×#4114yes—
558C2×C3×D32−1+412yes—
559C32×C4—22no—
560C32×C4—21no—
561C32×C4C2×#4112yes—
562C32×C4H(5,𝔽2)12yes—
563C3⋊Dic3—24no—
564C3⋊Dic3—22no—
565C3⋊Dic3—22no—
566C3×Dic3—22no—
567C3×Dic3—21no—
568C3×Dic3—24no—
569C3×Dic3—22no—
570C3×Dic3—21no—
571C3×Dic3—21no—
572C2×#41—32no—
573C2×#41—92no—
574C22×Q8—92no—
575C22×D4—31no—
576C23×C4—32no—
577C4⋊Q8—31no—
578C4⋊Q8—92no—
579C4⋊Q8—91no—
580#126—92no—
581#126—94no—
582#126—94no—
583#125—91no—
584#125—92no—
585#125—94no—
586#124—91no—
587#124—94no—
588#124—92no—
589#123—34no—
590#123—94no—
591#123—92no—
592#123—94no—
593#123—94no—
594C22⋊Q8—32no—
595C22⋊Q8—94no—
596C22⋊Q8—94no—
597C22⋊Q8—91no—
598C22⋊Q8—94no—
599C22⋊Q8—92no—
600C22⋊Q8—94no—
601C22⋊Q8—92no—
602C22⋊Q8—92no—
603C22⋊Q8—92no—
604C22⋊Q8—92no—
605#121—32no—
606#121—91no—
607#121—92no—
608#121—94no—
609#120—94no—
610C4×Q8—92no—
611C4×Q8—92no—
612C4×Q8—92no—
613C4×Q8—91no—
614C4×D4—31no—
615C4×D4—32no—
616C4×D4—31no—
617C4×D4—32no—
618C4×D4—31no—
619C4×D4—31no—
620C4×D4—94no—
621C4×D4—92no—
622C4×D4—94no—
623C4×D4—94no—
624C4×D4—92no—
625C4×D4D3211yescharacteristic
626#117—92no—
627#117—94no—
628#117—92no—
629#117—92no—
630C2×C4⋊C4—31no—
631C2×C4⋊C4—32no—
632C2×C4⋊C4—94no—
633C2×C4⋊C4—92no—
634C2×C22⋊C4—32no—
635C2×C22⋊C4—94no—
636C2×C42—31no—
637C23×C3—22no—
638C23×C3—31no—
639C23×C3—32no—
640C23×C3—32no—
641C23×C3—64no—
642C23×C3—64no—
643C23×C3—122no—
644C23×C3C23×D312yes—
645C23×C3C23×D312yes—
646C22×D3—24no—
647C22×D3—24no—
648C22×D3—42no—
649C22×D3C23×D312yes—
650C22×D3C23×D312yes—
651C22×D3C23×D311yescharacteristic
652C3×Q8—64no—
653C3×D4—22no—
654C3×D4—22no—
655C3×D4—34no—
656C3×D4—42no—
657C3×D4—64no—
658C3×D4—62no—
659C3×D4—124no—
660C2×C3×C4—24no—
661C2×C3×C4—24no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—22no—
665C2×C3×C4—21no—
666C2×C3×C4—31no—
667C2×C3×C4—34no—
668C2×C3×C4—31no—
669C2×C3×C4—31no—
670C2×C3×C4—32no—
671C2×C3×C4—32no—
672C2×C3×C4—44no—
673C2×C3×C4—62no—
674C2×C3×C4—64no—
675C2×C3×C4—64no—
676C2×C3×C4—62no—
677C2×C3×C4—62no—
678C2×C3×C4—122no—
679C2×C3×C4—122no—
680C2×C3×C4—124no—
681C2×C3×C4—122no—
682C2×C3×C4C23×D312yes—
683C2×C3×C4C23×D312yes—
684C2×C3×C4C23×D311yescharacteristic
685C2×C3×C4C23×D311yescharacteristic
686C2×C3×C4C23×D311yescharacteristic
687C2×C3×C4C23×D311yescharacteristic
688C2×C3×C4C23×D311yescharacteristic
689C2×C3×C4C23×D311yescharacteristic
690#67—24no—
691#67—44no—
692#67—68no—
693#67—64no—
694#67—68no—
695#67—64no—
696C2×Dic3—32no—
697C2×Dic3—32no—
698C2×Dic3—34no—
699C2×Dic3—34no—
700C2×Dic3—32no—
701C2×Dic3—32no—
702C2×Dic3—42no—
703C2×Dic3—62no—
704C2×Dic3—62no—
705C2×Dic3—64no—
706C2×Dic3—68no—
707C2×Dic3—124no—
708C2×Dic3C23×D311yescharacteristic
709C2×Dic3C23×D314yes—
710C2×Dic3C23×D311yescharacteristic
711C2×Dic3C23×D311yescharacteristic
712C2×Dic3C23×D312yes—
713C2×Dic3C23×D312yes—
714D12—22no—
715D12#23514yescomplemented
716C4×D3—22no—
717C4×D3—22no—
718C4×D3—22no—
719C4×D3—24no—
720C4×D3—24no—
721C4×D3—42no—
722C4×D3—42no—
723C4×D3—44no—
724C4×D3—68no—
725C4×D3—124no—
726Dic6—24no—
727Dic6—64no—
728Dic6—62no—
729Dic6—62no—
730Dic6—64no—
731Dic6—124no—
732Dic6—122no—
733Dic6—124no—
734Dic6—124no—
735C2×C32—42no—
736C2×C32C22×#4111yescharacteristic
737C2×C32C2×H(5,𝔽2)11yescharacteristic
738C2×C32C2×2−1+411yescharacteristic
739C3×D3—22no—
740C3×D3—24no—
741C3×D3—42no—
742C24—32no—
743#41—124no—
744#41—188no—
745C2×Q8—32no—
746C2×Q8—94no—
747C2×Q8—92no—
748C2×Q8—91no—
749C2×Q8—364no—
750C2×D4—32no—
751C2×D4—34no—
752C2×D4—31no—
753C2×D4—31no—
754C2×D4—64no—
755C2×D4—92no—
756C2×D4—94no—
757C2×D4C2×D3211yescharacteristic
758C22×C4—32no—
759C22×C4—31no—
760C22×C4—31no—
761C22×C4—31no—
762C22×C4—32no—
763C22×C4—32no—
764C22×C4—32no—
765C22×C4—34no—
766C22×C4—32no—
767C22×C4—94no—
768C22×C4—94no—
769C22×C4—124no—
770C22×C4C2×D3212yes—
771C4⋊C4—34no—
772C4⋊C4—32no—
773C4⋊C4—31no—
774C4⋊C4—32no—
775C4⋊C4—31no—
776C4⋊C4—32no—
777C4⋊C4—92no—
778C4⋊C4—94no—
779C4⋊C4—94no—
780C4⋊C4—92no—
781C4⋊C4—94no—
782C4⋊C4—92no—
783C4⋊C4—94no—
784C4⋊C4—92no—
785C4⋊C4—94no—
786C4⋊C4—91no—
787C4⋊C4—92no—
788C4⋊C4—92no—
789C4⋊C4C2×D3211yescharacteristic
790C22⋊C4—32no—
791C22⋊C4—34no—
792C22⋊C4—32no—
793C22⋊C4—32no—
794C22⋊C4—32no—
795C22⋊C4—92no—
796C22⋊C4—94no—
797C22⋊C4—94no—
798C22⋊C4—92no—
799C22⋊C4—92no—
800C22⋊C4—92no—
801C22⋊C4—94no—
802C22⋊C4—94no—
803C22⋊C4—94no—
804C22⋊C4C2×D3212yes—
805C42—31no—
806C42—31no—
807C42—31no—
808C42—94no—
809C42—94no—
810C42—92no—
811C42C2×D3211yescharacteristic
812C22×C3—22no—
813C22×C3—22no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—22no—
817C22×C3—22no—
818C22×C3—21no—
819C22×C3—34no—
820C22×C3—32no—
821C22×C3—42no—
822C22×C3—42no—
823C22×C3—42no—
824C22×C3—62no—
825C22×C3—61no—
826C22×C3—61no—
827C22×C3—62no—
828C22×C3—62no—
829C22×C3—62no—
830C22×C3—62no—
831C22×C3—128no—
832C22×C3C24×D311yescharacteristic
833C22×C3C24×D311yescharacteristic
834C2×D3—21no—
835C2×D3—21no—
836C2×D3—22no—
837C2×D3—22no—
838C2×D3—22no—
839C2×D3—22no—
840C2×D3—22no—
841C2×D3—48no—
842C2×D3C2×#23514yes—
843C2×D3#101012yes—
844C3×C4—22no—
845C3×C4—22no—
846C3×C4—21no—
847C3×C4—21no—
848C3×C4—22no—
849C3×C4—22no—
850C3×C4—42no—
851C3×C4—41no—
852C3×C4—62no—
853C3×C4—62no—
854C3×C4—64no—
855C3×C4—61no—
856C3×C4—61no—
857C3×C4—61no—
858C3×C4C2×#23512yes—
859C3×C4#100412yes—
860C3×C4#100412yes—
861C3×C4D3×#4112yes—
862Dic3—21no—
863Dic3—24no—
864Dic3—22no—
865Dic3—21no—
866Dic3—22no—
867Dic3—21no—
868Dic3—64no—
869Dic3—62no—
870Dic3—62no—
871Dic3—64no—
872Dic3—62no—
873Dic3—62no—
874Dic3—124no—
875Dic3—122no—
876Dic3—122no—
877C32#352011yescharacteristic, complemented, Sylow
878C23—32no—
879C23—31no—
880C23—32no—
881C23—64no—
882C23—64no—
883C23—122no—
884C23C22×D3212yes—
885Q8—64no—
886Q8—184no—
887Q8—182no—
888Q8—364no—
889D4—22no—
890D4—34no—
891D4—64no—
892D4—62no—
893D4—124no—
894D4—188no—
895D4—184no—
896C2×C4—24no—
897C2×C4—31no—
898C2×C4—31no—
899C2×C4—31no—
900C2×C4—34no—
901C2×C4—32no—
902C2×C4—32no—
903C2×C4—62no—
904C2×C4—62no—
905C2×C4—64no—
906C2×C4—62no—
907C2×C4—64no—
908C2×C4—92no—
909C2×C4—94no—
910C2×C4—92no—
911C2×C4—122no—
912C2×C4—122no—
913C2×C4—124no—
914C2×C4—122no—
915C2×C4—188no—
916C2×C4—364no—
917C2×C4C22×D3211yescharacteristic
918C2×C4C22×D3212yes—
919C2×C4C22×D3211yescharacteristic
920C2×C4C22×D3211yescharacteristic
921C2×C3—21no—
922C2×C3—21no—
923C2×C3—21no—
924C2×C3—42no—
925C2×C3—42no—
926C2×C3—62no—
927C2×C3—64no—
928C2×C3—82no—
929C2×C3—122no—
930C2×C3C22×#23511yescharacteristic
931C2×C3C2×#100411yescharacteristic
932C2×C3C2×#100411yescharacteristic
933C2×C3C2×D3×#4111yescharacteristic
934C2×C3C2×#101011yescharacteristic
935C2×C3D3×2−1+411yescharacteristic
936D3—22no—
937D3—24no—
938D3—42no—
939C22—22no—
940C22—22no—
941C22—22no—
942C22—34no—
943C22—32no—
944C22—61no—
945C22—61no—
946C22—62no—
947C22—62no—
948C22—62no—
949C22—62no—
950C22—62no—
951C22—128no—
952C22C23×D3211yescharacteristic
953C4—22no—
954C4—21no—
955C4—62no—
956C4—61no—
957C4—61no—
958C4—62no—
959C4—64no—
960C4—61no—
961C4—184no—
962C4—182no—
963C4—182no—
964C4D3×#23512yes—
965C4#6431312yes—
966C3—21no—
967C3#8576711yescharacteristic, complemented
968C3#8668611yescharacteristic, complemented
969C2—42no—
970C2—62no—
971C2—64no—
972C2—122no—
973C2C2×D3×#23511yescharacteristic
974C2C2×#6431311yescharacteristic
975C2D3×#101011yescharacteristic
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. #10596013C2semidirect
2. C3×#5551C2semidirect
3. C3×C4×D3×D4C2semidirect
4. #10595228C2semidirect
5. #10595124C2semidirect
6. #10595022C2semidirect
7. #10594942C2semidirect
8. #10594899C2semidirect
9. D3×#924C2semidirect
10. #10594531C2semidirect
11. #10594359C2semidirect
12. #10594193C2semidirect
13. #10594091C2semidirect
14. #10593974C2semidirect
15. #10593904C2semidirect
16. #10593895C2semidirect
17. #10593859C2semidirect
21. C2×C3×#235C22semidirect
24. C2×D3×Dic6C22semidirect
27. #64135C22semidirect
28. #64133C22semidirect
29. #64096C22semidirect
30. #64088C22semidirect
31. #64078C22semidirect
32. C4×#634C22semidirect
36. C3×#924C22semidirect
39. C3×D3×C4⋊C4C22semidirect
40. C3×#883C22semidirect
44. C3×C4×D12C22semidirect
46. C3×#869C22semidirect
51. #63964C22semidirect
52. #63961C22semidirect
53. #63959C22semidirect
54. #63956C22semidirect
55. #63919C22semidirect
57. #63908C22semidirect
61. C4×#625C22semidirect
62. #63899C22semidirect
64. #63891C22semidirect
65. D3×C4⋊Dic3C22semidirect
66. #63879C22semidirect
67. #63878C22semidirect
68. D3×Dic3⋊C4C22semidirect
69. #63870C22semidirect
70. #63869C22semidirect
71. #63869C22semidirect
72. #63860C22semidirect
73. #63859C22semidirect
76. #63857C22semidirect
78. #63856C22semidirect
79. #63855C22semidirect
81. #63851C22semidirect
82. #63844C22semidirect
83. Dic3×Dic6C22semidirect
106. #5551D3semidirect
108. C4×D3×D4D3semidirect
198. C2×#235C2×D3semidirect
267. #924C2×D3semidirect
282. D3×C4⋊C4C2×D3semidirect
298. #883C2×D3semidirect
315. C4×D12C2×D3semidirect
323. #869C2×D3semidirect
357. C3×D12#41semidirect
715. D12#235semidirect
877. C32#3520semidirect
967. C3#85767semidirect
968. C3#86686semidirect

Maximal subgroups

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

subgroupindex
#105960132
C3×#55512
C3×C4×D3×D42
#105952282
#105951242
#105950222
#105949422
#105948992
D3×#9242
#105945312
#105943592
#105941932
#105940912
#105939742
#105939042
#105938952
#105938592
#866863
#857673