Finite Group Databasebeta

← #11903650

Subgroups — #11903650

Order 1152.

2370 conjugacy classes of subgroups.

The subgroup lattice has 973 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596013C211yesmaximal, characteristic, complemented
2C3×#5563C211yesmaximal, characteristic, complemented
3C3×C4×D3×D4C211yesmaximal, characteristic, complemented
4#10595228C212yesmaximal, complemented
5#10595172C212yesmaximal, complemented
6#10594945C212yesmaximal, complemented
7#10594939C212yesmaximal, complemented
8D3×#926C212yesmaximal, complemented
9#10594892C212yesmaximal, complemented
10#10594550C212yesmaximal, complemented
11#10594358C212yesmaximal, complemented
12#10594092C214yesmaximal, complemented
13#10594087C214yesmaximal, complemented
14#10593956C211yesmaximal, characteristic, complemented
15#10593895C211yesmaximal, characteristic, complemented
16C4×#3795C211yesmaximal, characteristic, complemented
17#10593859C211yesmaximal, characteristic, complemented
18#86958—31nomaximal
19#85764—31nomaximal
20C2×C3×D3×D4C2211yescharacteristic
21C22×C3×C4×D3C2212yes—
22C2×#3795C2212yes—
23C2×#3795C2211yescharacteristic
24C32×C4×D4C2211yescharacteristic
25#64145C2212yes—
26#64135C2212yescomplemented
27#64133C2212yescomplemented
28#64096C2212yescomplemented
29#64088C2214yescomplemented
30#64078C2211yescharacteristic, complemented
31C4×#634C2211yescharacteristic, complemented
32C3×#938C2212yes—
33C3×D4×Dic3C2211yescharacteristic
34C3×#930C2212yescomplemented
35C3×C4×#67C2212yes—
36C3×#926C2212yescomplemented
37C3×#893C2211yescharacteristic
38C3×#892C2212yescomplemented
39C3×D3×C4⋊C4C2211yescharacteristic
40C3×#885C2214yescomplemented
41C3×#67⋊C4C2212yes—
42C3×D3×C22⋊C4C2212yes—
43C3×C4×D12C2211yescharacteristic
44C3×C4×D12C2211yescharacteristic, complemented
45C3×C42×D3C2211yescharacteristic
46C3×#869C2211yescharacteristic, complemented
47#63976C2214yes—
48Dic3×#67C2214yescomplemented
49#63970C2214yes—
50#63969C2214yes—
51#63969C2214yescomplemented
52D3×#217C2214yes—
53#63956C2214yescomplemented
54#63955C2214yescomplemented
55#63908C2212yescomplemented
56#63905C2214yes—
57#63902C2214yescomplemented
58C4×#625C2212yes—
59#63898C2212yes—
60Dic3×D12C2211yescharacteristic, complemented
61#63891C2214yescomplemented
62D3×C4⋊Dic3C2212yescomplemented
63D3×C4⋊Dic3C2212yescomplemented
64#63887C2214yescomplemented
65#63879C2212yes—
66#63879C2214yescomplemented
67#63877C2212yescomplemented
68#63877C2214yescomplemented
69C4×D3×Dic3C2214yescomplemented
70C4×D3×Dic3C2212yescomplemented
71#63872C2212yescomplemented
72#63869C2212yescomplemented
73#63867C2214yescomplemented
74#63862C2214yescomplemented
75#63857C2212yes—
76#63857C2212yescomplemented
77#63857C2212yescomplemented
78#63856C2212yes—
79#63855C2214yes—
80#63844C2212yescomplemented
81#63844C2211yescharacteristic, complemented
82Dic3×Dic6C2212yescomplemented
83#63841C2212yes—
84#63841C2211yescharacteristic
85C3×#555—31no—
86C2×C3×C4×D4—31no—
87#5806—32no—
88#5791—32no—
89C2×#926—32no—
90#5730—31no—
91#5728—31no—
92#5680—34no—
93#5679—34no—
94#5614—32no—
95#5612—32no—
96#5606—32no—
97#5600—32no—
98#5565—32no—
99#5563D311yescharacteristic, complemented
100#5557—32no—
101#5555—31no—
102#5551—31no—
103C4×D3×D4D311yescharacteristic, complemented
104#5543—31no—
105#5542—31no—
106#5542—31no—
107#5542—61no—
108#5541—32no—
109#5538—34no—
110C4×#237—32no—
111C4×#237—31no—
112#5529—32no—
113#5529—32no—
114#5522—32no—
115D3×#117—32no—
116#5513—32no—
117#5495—34no—
118C4×#235—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—
129C2×C3×D12C2311yescharacteristic
130C2×C3×D12C2311yescharacteristic
131C2×C3×C4×D3—28no—
132C2×C3×C4×D3C2312yes—
133C2×C3×C4×D3C2312yes—
134C2×C3×C4×D3C2311yescharacteristic
135C2×C3×C4×D3C2312yes—
136C2×C3×C4×D3C2312yes—
137C2×C3×C4×D3C2311yescharacteristic
138C2×C3×C4×D3C2311yescharacteristic
139C2×C3×Dic6C2312yes—
140C2×#625C2312yes—
141C2×#625C2314yes—
142C2×D3×Dic3C2312yes—
143C2×D3×Dic3C2314yes—
144C2×D3×Dic3C2312yes—
145C2×D3×Dic3C2314yes—
146#3795—28no—
147#3795—24no—
148C32×C4⋊C4C2311yescharacteristic
149C32×C22⋊C4C2312yes—
150C32×C42C2311yescharacteristic
151#3757C2314yes—
152#3757C2314yes—
153C4⋊(C3⋊Dic3)C2311yescharacteristic
154C4⋊(C3⋊Dic3)C2312yes—
155C4⋊(C3⋊Dic3)C2312yes—
156#3750C2312yes—
157#3750C2314yes—
158C4×C3⋊Dic3C2312yes—
159C4×C3⋊Dic3C2314yes—
160C3×#217C2312yes—
161C3×#217C2314yes—
162C3×(C2×D3)⋊C4C2312yes—
163C3×(C2×D3)⋊C4C2312yes—
164C3×(C2×D3)⋊C4C2312yes—
165C3×(C2×D3)⋊C4C2314yes—
166C3×C4⋊Dic3C2311yescharacteristic
167C3×C4⋊Dic3C2312yes—
168C3×C4⋊Dic3C2311yescharacteristic
169C3×C4⋊Dic3C2312yes—
170C3×Dic3⋊C4C2312yes—
171C3×C4×Dic3C2311yescharacteristic
172C3×C4×Dic3C2314yes—
173C3×C4×Dic3C2311yescharacteristic
174C3×C4×Dic3C2311yescharacteristic
175#3724C2314yes—
176#3724C2312yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181(C2×D3)⋊Dic3C2312yes—
182(C2×D3)⋊Dic3C2314yes—
183(C2×D3)⋊Dic3C2314yes—
184(C2×D3)⋊Dic3C2314yes—
185(C2×D3)⋊Dic3C2312yes—
186Dic32C2314yes—
187Dic32C2312yes—
188Dic32C2312yes—
189#3475—91noSylow
190C22×C3×D4—31no—
191C23×C3×C4—32no—
192C2×#237—32no—
193C2×#237—31no—
194C2×D3×D4C2×D311yescharacteristic
195C2×#235—31no—
196C2×#235—32no—
197C22×C4×D3C2×D312yes—
198C3×C4⋊Q8—31no—
199C3×#124—34no—
200C3×#121—32no—
201C3×#121—32no—
202C3×C4×D4—21no—
203C3×C4×D4—31no—
204C3×C4×D4—32no—
205C3×C4×D4—31no—
206C3×C4×D4—32no—
207C3×C4×D4—31no—
208C3×C4×D4—31no—
209C3×C4×D4C2×D311yescharacteristic
210C3×C4×D4C2×D311yescharacteristic
211C3×#117—32no—
212C3×#117—32no—
213C2×C3×C4⋊C4—31no—
214C2×C3×C22⋊C4—32no—
215C2×C3×C42—31no—
216#953—34no—
217C2×#217—34no—
218#946—32no—
219#946—34no—
220Q8×Dic3—32no—
221#939—34no—
222#938—34no—
223#938—32no—
224#938C2×D312yes—
225#937—34no—
226#936—32no—
227#936—32no—
228#936—62no—
229#935—34no—
230#935—34no—
231D4×Dic3—34no—
232D4×Dic3—32no—
233D4×Dic3—31no—
234D4×Dic3C2×D311yescharacteristic
235#930—32no—
236#930C2×D312yescomplemented
237#929—34no—
238C4×#67—34no—
239C4×#67—32no—
240C4×#67—32no—
241C4×#67—32no—
242C4×#67—34no—
243C4×#67C2×D312yes—
244#926—32no—
245#926—32no—
246#926—34no—
247#926—32no—
248#926—31no—
249#926—34no—
250#926—62no—
251#926C2×D312yescomplemented
252C2×C4⋊Dic3—32no—
253C2×C4⋊Dic3—32no—
254#924—32no—
255#924—32no—
256#924—32no—
257#924—32no—
258#924—32no—
259#924—32no—
260#924—62no—
261C2×C4×Dic3—32no—
262C2×C4×Dic3—34no—
263#898—34no—
264#897—32no—
265#897—32no—
266#897—32no—
267#893—32no—
268#893C2×D311yescharacteristic
269#892—32no—
270#892—31no—
271#892C2×D312yescomplemented
272D3×C4⋊C4—32no—
273D3×C4⋊C4—32no—
274D3×C4⋊C4C2×D311yescharacteristic
275#890—32no—
276#890—32no—
277#890—32no—
278#889—34no—
279#887—32no—
280#887—32no—
281#887—32no—
282#887—31no—
283#887—62no—
284#886—34no—
285#885C2×D314yescomplemented
286#883—34no—
287#883—34no—
288#883—34no—
289#883—34no—
290#67⋊C4—32no—
291#67⋊C4—34no—
292#67⋊C4—34no—
293#67⋊C4—34no—
294#67⋊C4C2×D312yes—
295D3×C22⋊C4—34no—
296D3×C22⋊C4C2×D312yes—
297#879—34no—
298#879—34no—
299#879—34no—
300#879—34no—
301#879—34no—
302#879—64no—
303#878—34no—
304#877—34no—
305#877—32no—
306#877—34no—
307C4×D12—31no—
308C4×D12C2×D311yescharacteristic
309C4×D12C2×D311yescharacteristic, complemented
310#872—34no—
311#872—34no—
312#872—32no—
313C42×D3—34no—
314C42×D3—32no—
315C42×D3C2×D311yescharacteristic
316#870—32no—
317#870—34no—
318#869—31no—
319#869—31no—
320#869—61no—
321#869C2×D311yescharacteristic, complemented
322C4×Dic6—32no—
323C4×Dic6—31no—
324C4×Dic6—31no—
325C4×Dic6—32no—
326C4×Dic6—31no—
327C4×Dic6—61no—
328C23×C32C2412yes—
329C22×C3×D3—24no—
330C22×C3×D3—24no—
331C22×C3×D3—42no—
332C22×C3×D3C2412yes—
333C22×C3×D3C2411yescharacteristic
334C22×C3×D3C2412yes—
335C32×D4—22no—
336C2×C32×C4—24no—
337C2×C32×C4C2412yes—
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2411yescharacteristic
340C2×C32×C4C2411yescharacteristic
341C2×C3⋊Dic3C2412yes—
342C2×C3⋊Dic3C2414yes—
343C2×C3⋊Dic3C2412yes—
344#634—24no—
345#634—22no—
346C3×#67—24no—
347C3×#67—44no—
348C2×C3×Dic3—24no—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2411yescharacteristic
351C2×C3×Dic3C2414yes—
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2411yescharacteristic
354C2×C3×Dic3C2411yescharacteristic
355C3×D12—22no—
356C3×D12#4114yescomplemented
357C3×C4×D3—24no—
358C3×C4×D3—24no—
359C3×C4×D3—24no—
360C3×C4×D3—22no—
361C3×C4×D3—24no—
362C3×C4×D3—41no—
363C3×C4×D3#4114yescomplemented
364C3×Dic6—42no—
365#625—24no—
366#625—28no—
367D3×Dic3—28no—
368D3×Dic3—24no—
369D3×Dic3—42no—
370D3×Dic3—44no—
371#556—91no—
372#555—31no—
373#554—91no—
374#553—92no—
375#552—92no—
376#552—92no—
377#551—94no—
378#547—91no—
379#546—92no—
380#533—91no—
381#529—92no—
382#529—94no—
383#525—92no—
384C4×#41—91no—
385C4×#41—92no—
386C2×C4×D4—31no—
387C2×#117—92no—
388C24×C3—32no—
389C23×D3C22×D312yes—
390C2×C3×Q8—32no—
391C2×C3×D4—21no—
392C2×C3×D4—32no—
393C2×C3×D4—34no—
394C2×C3×D4—31no—
395C2×C3×D4—31no—
396C2×C3×D4—64no—
397C2×C3×D4C22×D311yescharacteristic
398C2×C3×D4C22×D311yescharacteristic
399C22×C3×C4—22no—
400C22×C3×C4—31no—
401C22×C3×C4—32no—
402C22×C3×C4—32no—
403C22×C3×C4—32no—
404C22×C3×C4—31no—
405C22×C3×C4—32no—
406C22×C3×C4—32no—
407C22×C3×C4—31no—
408C22×C3×C4—68no—
409C22×C3×C4C22×D312yes—
410C22×C3×C4C22×D312yes—
411C2×#67—34no—
412C2×#67—32no—
413C2×#67—34no—
414C2×#67—32no—
415C2×#67C22×D312yes—
416C2×#67C22×D314yes—
417C22×Dic3—32no—
418C22×Dic3—34no—
419C22×Dic3—34no—
420C22×Dic3—32no—
421C22×Dic3C22×D312yes—
422#237—68no—
423#237—64no—
424D3×D4—24no—
425#235—64no—
426#235—68no—
427C2×D12C22×D311yescharacteristic
428C2×D12C22×D311yescharacteristic
429C2×C4×D3—28no—
430C2×C4×D3—34no—
431C2×C4×D3—32no—
432C2×C4×D3—32no—
433C2×C4×D3—34no—
434C2×C4×D3C22×D312yes—
435C2×C4×D3C22×D312yes—
436C2×C4×D3C22×D311yescharacteristic
437C2×C4×D3C22×D312yes—
438C2×C4×D3C22×D312yes—
439C2×C4×D3C22×D311yescharacteristic
440C2×C4×D3C22×D311yescharacteristic
441C2×Dic6—31no—
442C2×Dic6—32no—
443C2×Dic6—31no—
444C2×Dic6—32no—
445C2×Dic6—61no—
446C2×Dic6—62no—
447C2×Dic6C22×D312yes—
448C3×C4⋊C4—21no—
449C3×C4⋊C4—32no—
450C3×C4⋊C4—31no—
451C3×C4⋊C4—32no—
452C3×C4⋊C4—31no—
453C3×C4⋊C4—32no—
454C3×C4⋊C4C22×D311yescharacteristic
455C3×C4⋊C4C22×D311yescharacteristic
456C3×C22⋊C4—22no—
457C3×C22⋊C4—34no—
458C3×C22⋊C4—32no—
459C3×C22⋊C4—32no—
460C3×C22⋊C4—32no—
461C3×C22⋊C4—32no—
462C3×C22⋊C4—34no—
463C3×C22⋊C4C22×D312yes—
464C3×C22⋊C4C22×D312yes—
465C3×C42—21no—
466C3×C42—31no—
467C3×C42—31no—
468C3×C42—31no—
469C3×C42—34no—
470C3×C42C22×D311yescharacteristic
471C3×C42C22×D311yescharacteristic
472#217—34no—
473#217—34no—
474#217—34no—
475#217—34no—
476#217—34no—
477#217—32no—
478#217—34no—
479#217—34no—
480#217—32no—
481#217—64no—
482#217—64no—
483#217C22×D312yes—
484#217C22×D314yes—
485(C2×D3)⋊C4—32no—
486(C2×D3)⋊C4—32no—
487(C2×D3)⋊C4—34no—
488(C2×D3)⋊C4—34no—
489(C2×D3)⋊C4—34no—
490(C2×D3)⋊C4C22×D312yes—
491(C2×D3)⋊C4C22×D312yes—
492(C2×D3)⋊C4C22×D312yes—
493(C2×D3)⋊C4C22×D314yes—
494C4⋊Dic3—32no—
495C4⋊Dic3—31no—
496C4⋊Dic3—31no—
497C4⋊Dic3—32no—
498C4⋊Dic3—32no—
499C4⋊Dic3—32no—
500C4⋊Dic3—34no—
501C4⋊Dic3—34no—
502C4⋊Dic3—34no—
503C4⋊Dic3—34no—
504C4⋊Dic3—61no—
505C4⋊Dic3—62no—
506C4⋊Dic3—62no—
507C4⋊Dic3C22×D312yes—
508C4⋊Dic3C22×D311yescharacteristic
509C4⋊Dic3C22×D312yes—
510C4⋊Dic3C22×D311yescharacteristic
511Dic3⋊C4—32no—
512Dic3⋊C4—32no—
513Dic3⋊C4—34no—
514Dic3⋊C4—34no—
515Dic3⋊C4—34no—
516Dic3⋊C4—34no—
517Dic3⋊C4—32no—
518Dic3⋊C4—32no—
519Dic3⋊C4—34no—
520Dic3⋊C4—34no—
521Dic3⋊C4—34no—
522Dic3⋊C4—34no—
523Dic3⋊C4—62no—
524Dic3⋊C4—64no—
525Dic3⋊C4C22×D312yes—
526C4×Dic3—32no—
527C4×Dic3—32no—
528C4×Dic3—34no—
529C4×Dic3—34no—
530C4×Dic3—34no—
531C4×Dic3—32no—
532C4×Dic3—32no—
533C4×Dic3—32no—
534C4×Dic3—34no—
535C4×Dic3—32no—
536C4×Dic3—62no—
537C4×Dic3—64no—
538C4×Dic3C22×D311yescharacteristic
539C4×Dic3C22×D311yescharacteristic
540C4×Dic3C22×D311yescharacteristic
541C4×Dic3C22×D314yes—
542C22×C32—22no—
543C22×C32—22no—
544C22×C32—22no—
545C22×C32C2511yescharacteristic
546C2×C3×D3—22no—
547C2×C3×D3—21no—
548C2×C3×D3—22no—
549C2×C3×D3—21no—
550C2×C3×D3—22no—
551C2×C3×D3—22no—
552C2×C3×D3—22no—
553C2×C3×D3—48no—
554C2×C3×D3C2×#4114yes—
555C2×C3×D3C2×#4112yes—
556C32×C4—22no—
557C32×C4—21no—
558C32×C4C2×#4112yes—
559C32×C4C2×#4112yes—
560C3⋊Dic3—24no—
561C3⋊Dic3—22no—
562C3⋊Dic3—22no—
563C3×Dic3—22no—
564C3×Dic3—22no—
565C3×Dic3—21no—
566C3×Dic3—21no—
567C3×Dic3—24no—
568C3×Dic3C2×#4112yes—
569C2×#41—91no—
570C2×#41—92no—
571C22×D4—31no—
572C23×C4—32no—
573C4⋊Q8—31no—
574C4⋊Q8—91no—
575#126—94no—
576#126—94no—
577#126—94no—
578#125—94no—
579#125—92no—
580#125—92no—
581#124—34no—
582#124—92no—
583#123—94no—
584#123—94no—
585#123—94no—
586#123—94no—
587C22⋊Q8—94no—
588C22⋊Q8—92no—
589C22⋊Q8—92no—
590C22⋊Q8—92no—
591C22⋊Q8—92no—
592C22⋊Q8—92no—
593#121—32no—
594#121—32no—
595#121—92no—
596#121—94no—
597#120—94no—
598C4×Q8—92no—
599C4×Q8—91no—
600C4×Q8—92no—
601C4×Q8—92no—
602C4×Q8—91no—
603C4×D4—31no—
604C4×D4—32no—
605C4×D4—31no—
606C4×D4—32no—
607C4×D4—31no—
608C4×D4—31no—
609C4×D4—91no—
610C4×D4—94no—
611C4×D4—94no—
612C4×D4—92no—
613C4×D4—92no—
614C4×D4—92no—
615C4×D4—94no—
616C4×D4D3211yescharacteristic
617#117—32no—
618#117—32no—
619#117—92no—
620#117—94no—
621#117—94no—
622#117—94no—
623#117—91no—
624#117—92no—
625#117—92no—
626C2×C4⋊C4—31no—
627C2×C4⋊C4—92no—
628C2×C4⋊C4—92no—
629C2×C22⋊C4—32no—
630C2×C22⋊C4—94no—
631C2×C42—31no—
632C2×C42—94no—
633C2×C42—92no—
634C23×C3—22no—
635C23×C3—31no—
636C23×C3—32no—
637C23×C3—32no—
638C23×C3—64no—
639C23×C3—64no—
640C23×C3—122no—
641C23×C3C23×D312yes—
642C23×C3C23×D312yes—
643C22×D3—24no—
644C22×D3—24no—
645C22×D3—42no—
646C22×D3C23×D312yes—
647C22×D3C23×D312yes—
648C22×D3C23×D311yescharacteristic
649C3×Q8—122no—
650C3×D4—22no—
651C3×D4—22no—
652C3×D4—34no—
653C3×D4—42no—
654C3×D4—64no—
655C3×D4—62no—
656C3×D4—124no—
657C2×C3×C4—24no—
658C2×C3×C4—24no—
659C2×C3×C4—21no—
660C2×C3×C4—21no—
661C2×C3×C4—22no—
662C2×C3×C4—21no—
663C2×C3×C4—31no—
664C2×C3×C4—34no—
665C2×C3×C4—31no—
666C2×C3×C4—32no—
667C2×C3×C4—34no—
668C2×C3×C4—31no—
669C2×C3×C4—32no—
670C2×C3×C4—44no—
671C2×C3×C4—64no—
672C2×C3×C4—64no—
673C2×C3×C4—64no—
674C2×C3×C4—64no—
675C2×C3×C4—64no—
676C2×C3×C4—62no—
677C2×C3×C4—121no—
678C2×C3×C4C23×D312yes—
679C2×C3×C4C23×D312yes—
680C2×C3×C4C23×D311yescharacteristic
681C2×C3×C4C23×D311yescharacteristic
682C2×C3×C4C23×D311yescharacteristic
683C2×C3×C4C23×D311yescharacteristic
684C2×C3×C4C23×D311yescharacteristic
685C2×C3×C4C23×D311yescharacteristic
686#67—24no—
687#67—44no—
688#67—64no—
689#67—68no—
690#67—68no—
691#67—64no—
692C2×Dic3—24no—
693C2×Dic3—32no—
694C2×Dic3—32no—
695C2×Dic3—32no—
696C2×Dic3—32no—
697C2×Dic3—34no—
698C2×Dic3—34no—
699C2×Dic3—62no—
700C2×Dic3—62no—
701C2×Dic3—64no—
702C2×Dic3—68no—
703C2×Dic3—64no—
704C2×Dic3—122no—
705C2×Dic3—124no—
706C2×Dic3C23×D311yescharacteristic
707C2×Dic3C23×D312yes—
708C2×Dic3C23×D314yes—
709C2×Dic3C23×D311yescharacteristic
710C2×Dic3C23×D312yes—
711C2×Dic3C23×D311yescharacteristic
712D12—22no—
713D12#23514yescomplemented
714C4×D3—24no—
715C4×D3—22no—
716C4×D3—24no—
717C4×D3—24no—
718C4×D3—24no—
719C4×D3—41no—
720C4×D3—64no—
721C4×D3—68no—
722C4×D3—124no—
723C4×D3—122no—
724C4×D3#23714yescomplemented
725Dic6—42no—
726Dic6—64no—
727Dic6—62no—
728Dic6—62no—
729Dic6—64no—
730Dic6—124no—
731Dic6—122no—
732C2×C32—42no—
733C2×C32C22×#4111yescharacteristic
734C2×C32C22×#4111yescharacteristic
735C2×C32#58511yescharacteristic
736C3×D3—22no—
737C3×D3—24no—
738C3×D3—42no—
739C24—32no—
740#41—184no—
741#41—188no—
742C2×Q8—32no—
743C2×Q8—91no—
744C2×Q8—92no—
745C2×D4—32no—
746C2×D4—34no—
747C2×D4—31no—
748C2×D4—31no—
749C2×D4—64no—
750C2×D4—92no—
751C2×D4—94no—
752C2×D4C2×D3211yescharacteristic
753C22×C4—31no—
754C22×C4—32no—
755C22×C4—31no—
756C22×C4—32no—
757C22×C4—32no—
758C22×C4—32no—
759C22×C4—32no—
760C22×C4—31no—
761C22×C4—68no—
762C22×C4—94no—
763C22×C4—92no—
764C22×C4—94no—
765C22×C4—92no—
766C22×C4C2×D3212yes—
767C4⋊C4—31no—
768C4⋊C4—32no—
769C4⋊C4—31no—
770C4⋊C4—32no—
771C4⋊C4—32no—
772C4⋊C4—94no—
773C4⋊C4—94no—
774C4⋊C4—94no—
775C4⋊C4—92no—
776C4⋊C4—94no—
777C4⋊C4—94no—
778C4⋊C4—91no—
779C4⋊C4—92no—
780C4⋊C4—92no—
781C4⋊C4—94no—
782C4⋊C4—92no—
783C4⋊C4C2×D3211yescharacteristic
784C22⋊C4—32no—
785C22⋊C4—34no—
786C22⋊C4—32no—
787C22⋊C4—32no—
788C22⋊C4—34no—
789C22⋊C4—32no—
790C22⋊C4—92no—
791C22⋊C4—94no—
792C22⋊C4—94no—
793C22⋊C4—92no—
794C22⋊C4—94no—
795C22⋊C4—94no—
796C22⋊C4—94no—
797C22⋊C4C2×D3212yes—
798C42—31no—
799C42—31no—
800C42—31no—
801C42—34no—
802C42—92no—
803C42—94no—
804C42—92no—
805C42—94no—
806C42—92no—
807C42C2×D3211yescharacteristic
808C22×C3—22no—
809C22×C3—22no—
810C22×C3—22no—
811C22×C3—22no—
812C22×C3—22no—
813C22×C3—22no—
814C22×C3—21no—
815C22×C3—34no—
816C22×C3—32no—
817C22×C3—42no—
818C22×C3—42no—
819C22×C3—42no—
820C22×C3—62no—
821C22×C3—61no—
822C22×C3—62no—
823C22×C3—61no—
824C22×C3—62no—
825C22×C3—62no—
826C22×C3—62no—
827C22×C3—128no—
828C22×C3C24×D311yescharacteristic
829C22×C3C24×D311yescharacteristic
830C2×D3—21no—
831C2×D3—22no—
832C2×D3—21no—
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—22no—
837C2×D3—48no—
838C2×D3C2×#23514yes—
839C2×D3C2×#23712yes—
840C3×C4—22no—
841C3×C4—22no—
842C3×C4—21no—
843C3×C4—21no—
844C3×C4—22no—
845C3×C4—22no—
846C3×C4—32no—
847C3×C4—42no—
848C3×C4—41no—
849C3×C4—62no—
850C3×C4—62no—
851C3×C4—61no—
852C3×C4—64no—
853C3×C4—61no—
854C3×C4C2×#23512yes—
855C3×C4C2×#23712yes—
856C3×C4D3×#4112yes—
857C3×C4D3×#4112yes—
858Dic3—21no—
859Dic3—22no—
860Dic3—22no—
861Dic3—21no—
862Dic3—24no—
863Dic3—64no—
864Dic3—62no—
865Dic3—62no—
866Dic3—64no—
867Dic3—62no—
868Dic3—62no—
869Dic3—124no—
870Dic3—122no—
871Dic3—122no—
872Dic3C2×#23712yes—
873C32#347511yescharacteristic, complemented, Sylow
874C23—32no—
875C23—31no—
876C23—32no—
877C23—64no—
878C23—64no—
879C23—122no—
880C23C22×D3212yes—
881Q8—122no—
882Q8—184no—
883Q8—182no—
884D4—22no—
885D4—34no—
886D4—64no—
887D4—62no—
888D4—124no—
889D4—188no—
890D4—184no—
891C2×C4—24no—
892C2×C4—31no—
893C2×C4—34no—
894C2×C4—31no—
895C2×C4—32no—
896C2×C4—31no—
897C2×C4—34no—
898C2×C4—32no—
899C2×C4—64no—
900C2×C4—64no—
901C2×C4—64no—
902C2×C4—62no—
903C2×C4—64no—
904C2×C4—64no—
905C2×C4—92no—
906C2×C4—94no—
907C2×C4—92no—
908C2×C4—121no—
909C2×C4—184no—
910C2×C4—188no—
911C2×C4—362no—
912C2×C4—364no—
913C2×C4C22×D3212yes—
914C2×C4C22×D3211yescharacteristic
915C2×C4C22×D3211yescharacteristic
916C2×C4C22×D3211yescharacteristic
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—42no—
921C2×C3—42no—
922C2×C3—62no—
923C2×C3—64no—
924C2×C3—82no—
925C2×C3—122no—
926C2×C3C22×#23511yescharacteristic
927C2×C3C22×#23711yescharacteristic
928C2×C3C2×D3×#4111yescharacteristic
929C2×C3C2×D3×#4111yescharacteristic
930C2×C3#596411yescharacteristic
931C2×C3#596611yescharacteristic
932D3—22no—
933D3—24no—
934D3—42no—
935C22—22no—
936C22—22no—
937C22—22no—
938C22—34no—
939C22—32no—
940C22—61no—
941C22—62no—
942C22—61no—
943C22—62no—
944C22—62no—
945C22—62no—
946C22—62no—
947C22—128no—
948C22C23×D3211yescharacteristic
949C4—22no—
950C4—21no—
951C4—32no—
952C4—62no—
953C4—61no—
954C4—62no—
955C4—61no—
956C4—64no—
957C4—184no—
958C4—182no—
959C4—182no—
960C4D3×#23512yes—
961C4D3×#23712yes—
962C3—21no—
963C3#8576411yescharacteristic, complemented
964C3#8695811yescharacteristic, complemented
965C2—42no—
966C2—62no—
967C2—64no—
968C2—122no—
969C2C2×D3×#23511yescharacteristic
970C2C2×D3×#23711yescharacteristic
971C2#1059669611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
hypercenterC4×D4D32
hypocenterC32#3475
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×#5563C2semidirect
3. C3×C4×D3×D4C2semidirect
4. #10595228C2semidirect
5. #10595172C2semidirect
6. #10594945C2semidirect
7. #10594939C2semidirect
8. D3×#926C2semidirect
9. #10594892C2semidirect
10. #10594550C2semidirect
11. #10594358C2semidirect
12. #10594092C2semidirect
13. #10594087C2semidirect
14. #10593956C2semidirect
15. #10593895C2semidirect
16. C4×#3795C2semidirect
17. #10593859C2semidirect
26. #64135C22semidirect
27. #64133C22semidirect
28. #64096C22semidirect
29. #64088C22semidirect
30. #64078C22semidirect
31. C4×#634C22semidirect
34. C3×#930C22semidirect
36. C3×#926C22semidirect
38. C3×#892C22semidirect
40. C3×#885C22semidirect
44. C3×C4×D12C22semidirect
46. C3×#869C22semidirect
48. Dic3×#67C22semidirect
51. #63969C22semidirect
53. #63956C22semidirect
54. #63955C22semidirect
55. #63908C22semidirect
57. #63902C22semidirect
60. Dic3×D12C22semidirect
61. #63891C22semidirect
62. D3×C4⋊Dic3C22semidirect
63. D3×C4⋊Dic3C22semidirect
64. #63887C22semidirect
66. #63879C22semidirect
67. #63877C22semidirect
68. #63877C22semidirect
69. C4×D3×Dic3C22semidirect
70. C4×D3×Dic3C22semidirect
71. #63872C22semidirect
72. #63869C22semidirect
73. #63867C22semidirect
74. #63862C22semidirect
76. #63857C22semidirect
77. #63857C22semidirect
80. #63844C22semidirect
81. #63844C22semidirect
82. Dic3×Dic6C22semidirect
99. #5563D3semidirect
103. C4×D3×D4D3semidirect
236. #930C2×D3semidirect
251. #926C2×D3semidirect
271. #892C2×D3semidirect
285. #885C2×D3semidirect
309. C4×D12C2×D3semidirect
321. #869C2×D3semidirect
356. C3×D12#41semidirect
363. C3×C4×D3#41semidirect
713. D12#235semidirect
724. C4×D3#237semidirect
873. C32#3475semidirect
963. C3#85764semidirect
964. C3#86958semidirect

Maximal subgroups

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

subgroupindex
#105960132
C3×#55632
C3×C4×D3×D42
#105952282
#105951722
#105949452
#105949392
D3×#9262
#105948922
#105945502
#105943582
#105940922
#105940872
#105939562
#105938952
C4×#37952
#105938592
#869583
#857643