Finite Group Databasebeta

← #11909787

Subgroups — #11909787

Order 1152.

2322 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596014C211yesmaximal, characteristic, complemented
2C3×#5557C211yesmaximal, characteristic, complemented
3C3×#5553C211yesmaximal, characteristic, complemented
4#10595199C212yesmaximal, complemented
5#10595133C212yesmaximal, complemented
6#10594992C212yesmaximal, complemented
7#10594983C212yesmaximal, complemented
8#10594907C212yesmaximal, complemented
9#10594899C212yesmaximal, complemented
10#10594452C212yesmaximal, complemented
11#10594444C212yesmaximal, complemented
12#10594148C214yesmaximal, complemented
13#10594062C214yesmaximal, complemented
14#10593951C211yesmaximal, characteristic, complemented
15#10593897C211yesmaximal, characteristic, complemented
16C4×D3×Dic6C211yesmaximal, characteristic, complemented
17Dic62C211yesmaximal, characteristic, complemented
18#86776—31nomaximal
19#86128—31nomaximal
20C2×C3×#235C2212yes—
21C2×#3805C2214yes—
22C2×#3795C2212yes—
23C2×D3×Dic6C2211yescharacteristic
24C32×C4×D4C2211yescharacteristic
25D4×C3⋊Dic3C2212yes—
26C2×C4⋊(C3⋊Dic3)C2212yes—
27#64133C2212yes—
28#64099C2212yes—
29#64087C2214yes—
30#64078C2211yescharacteristic
31C4×#634C2211yescharacteristic
32C3×#940C2212yes—
33C3×#938C2211yescharacteristic
34C3×#936C2211yescharacteristic
35C3×#930C2212yes—
36C3×C4×#67C2212yes—
37C3×#926C2212yes—
38C3×#897C2211yescharacteristic
39C3×#893C2212yes—
40C3×#890C2211yescharacteristic
41C3×#884C2214yes—
42C3×#883C2212yes—
43C3×#879C2212yes—
44C3×#874C2211yescharacteristic
45C3×C42×D3C2211yescharacteristic
46C3×C4×Dic6C2211yescharacteristic
47C3×C4×Dic6C2211yescharacteristic
48#67⋊Dic3C2214yes—
49#67⋊Dic3C2214yes—
50#63970C2214yes—
51#63969C2214yes—
52#63962C2214yes—
53#63959C2214yes—
54#63959C2214yes—
55#63918C2212yes—
56#63918C2212yes—
57C4×#627C2212yes—
58#63908C2212yes—
59#63908C2212yes—
60#63899C2214yes—
61#63898C2212yes—
62#63893C2214yes—
63Dic3×D12C2212yes—
64Dic3×D12C2212yes—
65Dic3×D12C2212yes—
66#63891C2214yes—
67D3×C4⋊Dic3C2214yes—
68D3×C4⋊Dic3C2211yescharacteristic
69#63884C2214yes—
70#63879C2214yes—
71D3×Dic3⋊C4C2212yes—
72C4×D3×Dic3C2212yes—
73#63863C2212yes—
74#63860C2212yes—
75#63860C2212yes—
76#63858C2214yes—
77#63851C2214yes—
78#63844C2211yescharacteristic
79Dic3×Dic6C2212yes—
80Dic3×Dic6C2212yes—
81Dic3×Dic6C2211yescharacteristic
82#63841C2214yes—
83#63840C2214yes—
84#63837C2212yes—
85C3×#550—31no—
86C3×#529—31no—
87#5831—32no—
88#5827—32no—
89#5716—32no—
90#5716—31no—
91#5713—32no—
92#5713—31no—
93#5710—34no—
94#5690—32no—
95#5681—32no—
96#5655—34no—
97#5624—32no—
98#5611—32no—
99#5611—34no—
100#5603—32no—
101#5603—34no—
102#5596—32no—
103#5585—31no—
104C4×D3×Q8—31no—
105Q8×Dic6—31no—
106Q8×Dic6—31no—
107#5557—32no—
108#5557D311yescharacteristic, complemented
109#5555—32no—
110#5553D311yescharacteristic, complemented
111#5552—32no—
112#5543—31no—
113#5543—31no—
114#5543—32no—
115#5543—61no—
116#5534—32no—
117#5523—32no—
118#5477—31no—
119C2×C4×Dic6—31no—
120C2×C32×D4C2311yescharacteristic
121C22×C32×C4C2312yes—
122C22×C3⋊Dic3C2314yes—
123C2×#634C2311yescharacteristic
124C2×#634C2312yes—
125C2×C3×#67C2312yes—
126C2×C3×#67C2314yes—
127C2×C3×#67C2314yes—
128C3×#235—28no—
129C2×C3×D12C2312yes—
130C2×C3×D12C2312yes—
131C2×C3×D12C2312yes—
132C2×C3×C4×D3C2311yescharacteristic
133C2×C3×C4×D3C2314yes—
134C2×C3×C4×D3C2311yescharacteristic
135C2×C3×C4×D3C2311yescharacteristic
136C2×C3×Dic6C2311yescharacteristic
137C2×C3×Dic6C2311yescharacteristic
138C2×#627C2312yes—
139C2×#627C2314yes—
140C2×#625C2314yes—
141#3805—48no—
142C2×D3×Dic3C2312yes—
143C2×D3×Dic3C2312yes—
144C2×D3×Dic3C2314yes—
145C2×D3×Dic3C2314yes—
146#3795—44no—
147D3×Dic6—24no—
148C32×C4⋊C4C2311yescharacteristic
149C32×C22⋊C4C2312yes—
150C32×C42C2311yescharacteristic
151#3757C2314yes—
152C4⋊(C3⋊Dic3)C2311yescharacteristic
153C4⋊(C3⋊Dic3)C2312yes—
154C4⋊(C3⋊Dic3)C2312yes—
155C4⋊(C3⋊Dic3)C2314yes—
156#3750C2312yes—
157#3750C2314yes—
158C4×C3⋊Dic3C2312yes—
159C3×#217C2312yes—
160C3×#217C2312yes—
161C3×#217C2312yes—
162C3×(C2×D3)⋊C4C2312yes—
163C3×(C2×D3)⋊C4C2314yes—
164C3×C4⋊Dic3C2312yes—
165C3×C4⋊Dic3C2312yes—
166C3×C4⋊Dic3C2311yescharacteristic
167C3×C4⋊Dic3C2311yescharacteristic
168C3×Dic3⋊C4C2312yes—
169C3×Dic3⋊C4C2312yes—
170C3×Dic3⋊C4C2312yes—
171C3×C4×Dic3C2311yescharacteristic
172C3×C4×Dic3C2311yescharacteristic
173C3×C4×Dic3C2312yes—
174C3×C4×Dic3C2311yescharacteristic
175C3×C4×Dic3C2312yes—
176#3724C2312yes—
177Dic3⋊Dic3C2312yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2312yes—
181(C2×D3)⋊Dic3C2314yes—
182(C2×D3)⋊Dic3C2314yes—
183(C2×D3)⋊Dic3C2314yes—
184(C2×D3)⋊Dic3C2314yes—
185(C2×D3)⋊Dic3C2314yes—
186Dic32C2312yes—
187Dic32C2312yes—
188Dic32C2314yes—
189#3522—91noSylow
190C2×C3×#41—32no—
191C2×D3×Q8—31no—
192C2×#237—34no—
193C2×#237—34no—
194C2×#237—32no—
195C2×#235—32no—
196C2×#235C2×D312yes—
197C22×Dic6—31no—
198C3×#127—32no—
199C3×#127—31no—
200C3×#126—32no—
201C3×#125—31no—
202C3×#124—31no—
203C3×#123—32no—
204C3×C22⋊Q8—31no—
205C3×#121—31no—
206C3×#121—32no—
207C3×#121—34no—
208C3×C4×Q8—31no—
209C3×C4×Q8—31no—
210C3×C4×D4—21no—
211C3×C4×D4—32no—
212C3×C4×D4—32no—
213C3×C4×D4C2×D311yescharacteristic
214C3×C4×D4C2×D311yescharacteristic
215C3×#117—32no—
216C2×C3×C42—31no—
217#947—32no—
218Q8×Dic3—32no—
219Q8×Dic3—32no—
220Q8×Dic3—31no—
221#940C2×D312yes—
222#939—34no—
223#938—34no—
224#938—32no—
225#938—32no—
226#938C2×D311yescharacteristic
227#936—32no—
228#936—34no—
229#936—34no—
230#936—32no—
231#936—32no—
232#936C2×D311yescharacteristic
233#935—34no—
234#935—34no—
235#935—34no—
236D4×Dic3—32no—
237D4×Dic3—32no—
238D4×Dic3—34no—
239D4×Dic3—34no—
240D4×Dic3—32no—
241D4×Dic3—32no—
242D4×Dic3—32no—
243D4×Dic3—32no—
244D4×Dic3—62no—
245#930—32no—
246#930—32no—
247#930C2×D312yes—
248C4×#67—34no—
249C4×#67C2×D312yes—
250#926—34no—
251#926C2×D312yes—
252C2×C4⋊Dic3—32no—
253C2×C4⋊Dic3—32no—
254C2×C4⋊Dic3—31no—
255C2×C4⋊Dic3—34no—
256C2×C4⋊Dic3—62no—
257#924—32no—
258#924—32no—
259#924—34no—
260#924—62no—
261C2×Dic3⋊C4—32no—
262C2×C4×Dic3—32no—
263#898—34no—
264#897—34no—
265#897C2×D311yescharacteristic
266#896—34no—
267#896—34no—
268#894—34no—
269#893—32no—
270#893C2×D312yes—
271#892—34no—
272D3×C4⋊C4—34no—
273D3×C4⋊C4—32no—
274D3×C4⋊C4—31no—
275#890—32no—
276#890—32no—
277#890—62no—
278#890C2×D311yescharacteristic
279#888—34no—
280#888—34no—
281#888—32no—
282#888—32no—
283#887—32no—
284#887—31no—
285#886—34no—
286#886—34no—
287#885—34no—
288#885—34no—
289#884C2×D314yes—
290#883—34no—
291#883—34no—
292#883C2×D312yes—
293#67⋊C4—34no—
294#67⋊C4—34no—
295#67⋊C4—34no—
296#879—34no—
297#879C2×D312yes—
298#878—34no—
299#878—34no—
300#878—34no—
301#878—34no—
302#878—64no—
303#875—32no—
304#875—32no—
305#874C2×D311yescharacteristic
306C4×D12—32no—
307C4×D12—32no—
308C4×D12—32no—
309C42×D3—32no—
310C42×D3C2×D311yescharacteristic
311#869—31no—
312#869—31no—
313#869—32no—
314#869—32no—
315#869—61no—
316C4×Dic6—32no—
317C4×Dic6—31no—
318C4×Dic6—32no—
319C4×Dic6—31no—
320C4×Dic6—31no—
321C4×Dic6—31no—
322C4×Dic6—32no—
323C4×Dic6—32no—
324C4×Dic6—32no—
325C4×Dic6—61no—
326C4×Dic6C2×D311yescharacteristic
327C4×Dic6C2×D311yescharacteristic
328C23×C32C2412yes—
329C22×C3×D3C2414yes—
330C22×C3×D3C2411yescharacteristic
331C32×D4—22no—
332C2×C32×C4—24no—
333C2×C32×C4C2411yescharacteristic
334C2×C32×C4C2412yes—
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2411yescharacteristic
337C2×C3⋊Dic3—44no—
338C2×C3⋊Dic3C2412yes—
339C2×C3⋊Dic3C2412yes—
340C2×C3⋊Dic3C2414yes—
341#634—22no—
342#634—42no—
343C3×#67—24no—
344C3×#67—28no—
345C3×#67—44no—
346C2×C3×Dic3C2411yescharacteristic
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2411yescharacteristic
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2411yescharacteristic
352C2×C3×Dic3C2412yes—
353C3×D12—24no—
354C3×D12—24no—
355C3×D12—42no—
356C3×C4×D3—22no—
357C3×C4×D3—22no—
358C3×C4×D3—22no—
359C3×C4×D3—28no—
360C3×Dic6—22no—
361C3×Dic6#4114yescomplemented
362#627—24no—
363#627—44no—
364#625—28no—
365D3×Dic3—24no—
366D3×Dic3—24no—
367D3×Dic3—44no—
368D3×Dic3—44no—
369#559—91no—
370#559—92no—
371Q82—91no—
372#554—92no—
373#554—91no—
374#550—31no—
375#548—92no—
376#547—92no—
377#547—94no—
378#542—92no—
379#542—94no—
380#532—91no—
381#532—92no—
382#529—31no—
383#529—92no—
384#520—92no—
385C2×C4×Q8—91no—
386C3×#41—68no—
387C2×C3×Q8—31no—
388C2×C3×Q8—31no—
389C2×C3×D4—21no—
390C2×C3×D4—34no—
391C2×C3×D4—32no—
392C2×C3×D4—34no—
393C2×C3×D4—32no—
394C2×C3×D4—32no—
395C2×C3×D4—32no—
396C2×C3×D4C22×D311yescharacteristic
397C2×C3×D4C22×D311yescharacteristic
398C22×C3×C4—22no—
399C22×C3×C4—31no—
400C22×C3×C4—31no—
401C22×C3×C4—34no—
402C22×C3×C4—31no—
403C22×C3×C4C22×D312yes—
404C22×C3×C4C22×D312yes—
405C2×#67—34no—
406C2×#67—34no—
407C2×#67C22×D314yes—
408C2×#67C22×D312yes—
409C2×#67C22×D314yes—
410C22×Dic3—34no—
411C22×Dic3—34no—
412C22×Dic3—32no—
413C22×Dic3—32no—
414C22×Dic3—34no—
415C22×Dic3—34no—
416C22×Dic3—64no—
417D3×Q8—64no—
418#237—124no—
419#237—128no—
420#237—128no—
421#235—28no—
422#235—124no—
423C2×D12C22×D312yes—
424C2×D12C22×D312yes—
425C2×D12C22×D312yes—
426C2×C4×D3—32no—
427C2×C4×D3—32no—
428C2×C4×D3—34no—
429C2×C4×D3—34no—
430C2×C4×D3C22×D311yescharacteristic
431C2×C4×D3C22×D311yescharacteristic
432C2×C4×D3C22×D311yescharacteristic
433C2×C4×D3C22×D314yes—
434C2×Dic6—31no—
435C2×Dic6—31no—
436C2×Dic6—32no—
437C2×Dic6—32no—
438C2×Dic6—32no—
439C2×Dic6—32no—
440C2×Dic6—34no—
441C2×Dic6—34no—
442C2×Dic6—61no—
443C2×Dic6—62no—
444C2×Dic6—64no—
445C2×Dic6C22×D311yescharacteristic
446C2×Dic6C22×D311yescharacteristic
447C3×C4⋊C4—21no—
448C3×C4⋊C4—32no—
449C3×C4⋊C4—31no—
450C3×C4⋊C4—31no—
451C3×C4⋊C4—32no—
452C3×C4⋊C4—32no—
453C3×C4⋊C4—32no—
454C3×C4⋊C4—32no—
455C3×C4⋊C4C22×D311yescharacteristic
456C3×C4⋊C4C22×D311yescharacteristic
457C3×C22⋊C4—22no—
458C3×C22⋊C4—32no—
459C3×C22⋊C4—32no—
460C3×C22⋊C4—32no—
461C3×C22⋊C4—34no—
462C3×C22⋊C4—32no—
463C3×C22⋊C4C22×D312yes—
464C3×C22⋊C4C22×D312yes—
465C3×C42—21no—
466C3×C42—32no—
467C3×C42—31no—
468C3×C42—31no—
469C3×C42—31no—
470C3×C42—32no—
471C3×C42C22×D311yescharacteristic
472C3×C42C22×D311yescharacteristic
473#217—34no—
474#217—34no—
475#217—34no—
476#217—34no—
477#217—34no—
478#217—34no—
479#217—34no—
480#217—64no—
481#217C22×D312yes—
482#217C22×D312yes—
483#217C22×D312yes—
484(C2×D3)⋊C4—34no—
485(C2×D3)⋊C4—34no—
486(C2×D3)⋊C4—34no—
487(C2×D3)⋊C4—34no—
488(C2×D3)⋊C4—34no—
489(C2×D3)⋊C4C22×D312yes—
490(C2×D3)⋊C4C22×D314yes—
491C4⋊Dic3—31no—
492C4⋊Dic3—32no—
493C4⋊Dic3—32no—
494C4⋊Dic3—31no—
495C4⋊Dic3—32no—
496C4⋊Dic3—32no—
497C4⋊Dic3—34no—
498C4⋊Dic3—34no—
499C4⋊Dic3—32no—
500C4⋊Dic3—32no—
501C4⋊Dic3—34no—
502C4⋊Dic3—34no—
503C4⋊Dic3—61no—
504C4⋊Dic3—62no—
505C4⋊Dic3—62no—
506C4⋊Dic3—64no—
507C4⋊Dic3C22×D311yescharacteristic
508C4⋊Dic3C22×D311yescharacteristic
509C4⋊Dic3C22×D312yes—
510C4⋊Dic3C22×D312yes—
511Dic3⋊C4—32no—
512Dic3⋊C4—32no—
513Dic3⋊C4—34no—
514Dic3⋊C4—34no—
515Dic3⋊C4—32no—
516Dic3⋊C4—32no—
517Dic3⋊C4—32no—
518Dic3⋊C4—32no—
519Dic3⋊C4—34no—
520Dic3⋊C4—34no—
521Dic3⋊C4—62no—
522Dic3⋊C4—64no—
523Dic3⋊C4C22×D312yes—
524Dic3⋊C4C22×D312yes—
525Dic3⋊C4C22×D312yes—
526C4×Dic3—32no—
527C4×Dic3—32no—
528C4×Dic3—32no—
529C4×Dic3—32no—
530C4×Dic3—34no—
531C4×Dic3—34no—
532C4×Dic3—32no—
533C4×Dic3—32no—
534C4×Dic3—62no—
535C4×Dic3C22×D311yescharacteristic
536C4×Dic3C22×D312yes—
537C4×Dic3C22×D312yes—
538C4×Dic3C22×D311yescharacteristic
539C4×Dic3C22×D311yescharacteristic
540C22×C32—22no—
541C22×C32—22no—
542C22×C32—22no—
543C22×C32C2511yescharacteristic
544C2×C3×D3—21no—
545C2×C3×D3—21no—
546C2×C3×D3—24no—
547C2×C3×D3—24no—
548C2×C3×D3—24no—
549C2×C3×D3H(5,𝔽2)12yes—
550C32×C4—22no—
551C32×C4—21no—
552C32×C4C2×#4112yes—
553C32×C42−1+412yes—
554C3⋊Dic3—22no—
555C3⋊Dic3—22no—
556C3⋊Dic3—24no—
557C3×Dic3—21no—
558C3×Dic3—22no—
559C3×Dic3—21no—
560C3×Dic3—22no—
561C3×Dic3—22no—
562C3×Dic3—21no—
563C3×Dic3C2×#4114yes—
564C2×#41—32no—
565C2×#41—92no—
566C2×#41—94no—
567C22×Q8—91no—
568C4⋊Q8—92no—
569C4⋊Q8—92no—
570C4⋊Q8—94no—
571C4⋊Q8—91no—
572#127—32no—
573#127—31no—
574#126—32no—
575#126—94no—
576#125—31no—
577#125—92no—
578#124—31no—
579#124—92no—
580#124—92no—
581#124—94no—
582#124—94no—
583#124—92no—
584#123—32no—
585#123—94no—
586#123—94no—
587#123—94no—
588#123—94no—
589C22⋊Q8—31no—
590C22⋊Q8—94no—
591C22⋊Q8—94no—
592C22⋊Q8—94no—
593C22⋊Q8—92no—
594C22⋊Q8—94no—
595#121—31no—
596#121—32no—
597#121—34no—
598#121—92no—
599#121—92no—
600#121—94no—
601C4×Q8—31no—
602C4×Q8—31no—
603C4×Q8—92no—
604C4×Q8—91no—
605C4×Q8—92no—
606C4×Q8—91no—
607C4×Q8—92no—
608C4×Q8—92no—
609C4×Q8—91no—
610C4×D4—32no—
611C4×D4—32no—
612C4×D4—92no—
613C4×D4—92no—
614C4×D4—92no—
615C4×D4—94no—
616C4×D4—94no—
617C4×D4—94no—
618C4×D4—92no—
619C4×D4—92no—
620C4×D4D3211yescharacteristic
621#117—32no—
622#117—94no—
623C2×C4⋊C4—92no—
624C2×C4⋊C4—91no—
625C2×C4⋊C4—94no—
626C2×C4⋊C4—92no—
627C2×C42—31no—
628C2×C42—92no—
629C23×C3—22no—
630C23×C3—31no—
631C23×C3—34no—
632C23×C3C23×D312yes—
633C23×C3C23×D312yes—
634C22×D3C23×D314yes—
635C22×D3C23×D311yescharacteristic
636C3×Q8—34no—
637C3×Q8—62no—
638C3×D4—24no—
639C3×D4—22no—
640C3×D4—22no—
641C3×D4—68no—
642C3×D4—64no—
643C3×D4—64no—
644C3×D4—64no—
645C3×D4—122no—
646C3×D4—124no—
647C2×C3×C4—24no—
648C2×C3×C4—24no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—22no—
652C2×C3×C4—21no—
653C2×C3×C4—32no—
654C2×C3×C4—31no—
655C2×C3×C4—32no—
656C2×C3×C4—32no—
657C2×C3×C4—31no—
658C2×C3×C4—32no—
659C2×C3×C4—31no—
660C2×C3×C4—44no—
661C2×C3×C4—68no—
662C2×C3×C4—62no—
663C2×C3×C4—62no—
664C2×C3×C4—62no—
665C2×C3×C4C23×D311yescharacteristic
666C2×C3×C4C23×D311yescharacteristic
667C2×C3×C4C23×D312yes—
668C2×C3×C4C23×D312yes—
669C2×C3×C4C23×D311yescharacteristic
670C2×C3×C4C23×D311yescharacteristic
671C2×C3×C4C23×D311yescharacteristic
672C2×C3×C4C23×D311yescharacteristic
673#67—24no—
674#67—28no—
675#67—44no—
676#67—68no—
677#67—68no—
678C2×Dic3—32no—
679C2×Dic3—32no—
680C2×Dic3—32no—
681C2×Dic3—32no—
682C2×Dic3—34no—
683C2×Dic3—34no—
684C2×Dic3—62no—
685C2×Dic3—62no—
686C2×Dic3—64no—
687C2×Dic3—64no—
688C2×Dic3—64no—
689C2×Dic3—124no—
690C2×Dic3—124no—
691C2×Dic3—124no—
692C2×Dic3—124no—
693C2×Dic3—244no—
694C2×Dic3C23×D311yescharacteristic
695C2×Dic3C23×D312yes—
696C2×Dic3C23×D312yes—
697C2×Dic3C23×D311yescharacteristic
698C2×Dic3C23×D311yescharacteristic
699C2×Dic3C23×D312yes—
700C2×Dic3C23×D312yes—
701D12—24no—
702D12—24no—
703D12—42no—
704C4×D3—22no—
705C4×D3—22no—
706C4×D3—22no—
707C4×D3—28no—
708C4×D3—64no—
709C4×D3—64no—
710C4×D3—124no—
711C4×D3—124no—
712Dic6—22no—
713Dic6—64no—
714Dic6—62no—
715Dic6—62no—
716Dic6—64no—
717Dic6—122no—
718Dic6—124no—
719Dic6—124no—
720Dic6—122no—
721Dic6—122no—
722Dic6—242no—
723Dic6#23714yescomplemented
724C2×C32—42no—
725C2×C32C22×#4111yescharacteristic
726C2×C32C2×H(5,𝔽2)11yescharacteristic
727C2×C32C2×2−1+411yescharacteristic
728C3×D3—22no—
729C3×D3—44no—
730#41—68no—
731#41—364no—
732#41—368no—
733C2×Q8—31no—
734C2×Q8—31no—
735C2×Q8—92no—
736C2×Q8—94no—
737C2×Q8—91no—
738C2×Q8—92no—
739C2×Q8—184no—
740C2×D4—32no—
741C2×D4—34no—
742C2×D4—34no—
743C2×D4—32no—
744C2×D4—32no—
745C2×D4—32no—
746C2×D4—94no—
747C2×D4C2×D3211yescharacteristic
748C22×C4—31no—
749C22×C4—31no—
750C22×C4—31no—
751C22×C4—34no—
752C22×C4—92no—
753C22×C4—92no—
754C22×C4—94no—
755C22×C4—94no—
756C22×C4—94no—
757C22×C4C2×D3212yes—
758C4⋊C4—32no—
759C4⋊C4—32no—
760C4⋊C4—31no—
761C4⋊C4—32no—
762C4⋊C4—32no—
763C4⋊C4—31no—
764C4⋊C4—32no—
765C4⋊C4—92no—
766C4⋊C4—94no—
767C4⋊C4—92no—
768C4⋊C4—92no—
769C4⋊C4—94no—
770C4⋊C4—91no—
771C4⋊C4—94no—
772C4⋊C4—92no—
773C4⋊C4—92no—
774C4⋊C4—92no—
775C4⋊C4—94no—
776C4⋊C4C2×D3211yescharacteristic
777C22⋊C4—32no—
778C22⋊C4—32no—
779C22⋊C4—32no—
780C22⋊C4—32no—
781C22⋊C4—34no—
782C22⋊C4—94no—
783C22⋊C4—94no—
784C22⋊C4—94no—
785C22⋊C4—94no—
786C22⋊C4—94no—
787C22⋊C4—94no—
788C22⋊C4C2×D3212yes—
789C42—31no—
790C42—31no—
791C42—31no—
792C42—32no—
793C42—32no—
794C42—92no—
795C42—92no—
796C42—94no—
797C42—92no—
798C42C2×D3211yescharacteristic
799C22×C3—24no—
800C22×C3—22no—
801C22×C3—22no—
802C22×C3—22no—
803C22×C3—22no—
804C22×C3—22no—
805C22×C3—22no—
806C22×C3—21no—
807C22×C3—32no—
808C22×C3—42no—
809C22×C3—42no—
810C22×C3—61no—
811C22×C3—61no—
812C22×C3—64no—
813C22×C3—64no—
814C22×C3—64no—
815C22×C3C24×D311yescharacteristic
816C22×C3C24×D311yescharacteristic
817C2×D3—21no—
818C2×D3—21no—
819C2×D3—24no—
820C2×D3—24no—
821C2×D3—24no—
822C2×D3#100912yes—
823C3×C4—22no—
824C3×C4—22no—
825C3×C4—21no—
826C3×C4—21no—
827C3×C4—22no—
828C3×C4—22no—
829C3×C4—34no—
830C3×C4—41no—
831C3×C4—42no—
832C3×C4—61no—
833C3×C4—62no—
834C3×C4—61no—
835C3×C4—62no—
836C3×C4—62no—
837C3×C4—61no—
838C3×C4C2×#23712yes—
839C3×C4D3×#4112yes—
840C3×C4#101012yes—
841C3×C4#101012yes—
842Dic3—21no—
843Dic3—22no—
844Dic3—21no—
845Dic3—22no—
846Dic3—21no—
847Dic3—22no—
848Dic3—62no—
849Dic3—62no—
850Dic3—64no—
851Dic3—62no—
852Dic3—64no—
853Dic3—62no—
854Dic3—122no—
855Dic3—124no—
856Dic3—122no—
857Dic3C2×#23714yes—
858C32#352211yescharacteristic, complemented, Sylow
859C23—31no—
860C23—34no—
861C23C22×D3212yes—
862Q8—34no—
863Q8—62no—
864Q8—184no—
865Q8—182no—
866Q8—362no—
867Q8—364no—
868D4—22no—
869D4—68no—
870D4—64no—
871D4—64no—
872D4—64no—
873D4—122no—
874D4—124no—
875D4—188no—
876C2×C4—24no—
877C2×C4—32no—
878C2×C4—31no—
879C2×C4—31no—
880C2×C4—31no—
881C2×C4—32no—
882C2×C4—32no—
883C2×C4—32no—
884C2×C4—68no—
885C2×C4—62no—
886C2×C4—62no—
887C2×C4—62no—
888C2×C4—92no—
889C2×C4—92no—
890C2×C4—94no—
891C2×C4—184no—
892C2×C4—184no—
893C2×C4—364no—
894C2×C4—364no—
895C2×C4—364no—
896C2×C4C22×D3211yescharacteristic
897C2×C4C22×D3212yes—
898C2×C4C22×D3211yescharacteristic
899C2×C4C22×D3211yescharacteristic
900C2×C3—21no—
901C2×C3—21no—
902C2×C3—21no—
903C2×C3—44no—
904C2×C3—42no—
905C2×C3—42no—
906C2×C3—62no—
907C2×C3—124no—
908C2×C3C22×#23711yescharacteristic
909C2×C3C2×D3×#4111yescharacteristic
910C2×C3C2×#100911yescharacteristic
911C2×C3C2×#101011yescharacteristic
912C2×C3C2×#101011yescharacteristic
913C2×C3D3×H(5,𝔽2)11yescharacteristic
914D3—22no—
915D3—44no—
916C22—22no—
917C22—22no—
918C22—22no—
919C22—32no—
920C22—61no—
921C22—61no—
922C22—64no—
923C22—64no—
924C22—64no—
925C22C23×D3211yescharacteristic
926C4—22no—
927C4—21no—
928C4—34no—
929C4—61no—
930C4—62no—
931C4—61no—
932C4—61no—
933C4—62no—
934C4—62no—
935C4—182no—
936C4—182no—
937C4—184no—
938C4#6429812yes—
939C4D3×#23712yes—
940C3—21no—
941C3#8612811yescharacteristic, complemented
942C3#8677611yescharacteristic, complemented
943C2—42no—
944C2—62no—
945C2—124no—
946C2C2×#6429811yescharacteristic
947C2C2×D3×#23711yescharacteristic
948C2D3×#100911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
hypercenterC4×D4D32
hypocenterC32#3522
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596014C2semidirect
2. C3×#5557C2semidirect
3. C3×#5553C2semidirect
4. #10595199C2semidirect
5. #10595133C2semidirect
6. #10594992C2semidirect
7. #10594983C2semidirect
8. #10594907C2semidirect
9. #10594899C2semidirect
10. #10594452C2semidirect
11. #10594444C2semidirect
12. #10594148C2semidirect
13. #10594062C2semidirect
14. #10593951C2semidirect
15. #10593897C2semidirect
16. C4×D3×Dic6C2semidirect
17. Dic62C2semidirect
108. #5557D3semidirect
110. #5553D3semidirect
361. C3×Dic6#41semidirect
723. Dic6#237semidirect
858. C32#3522semidirect
941. C3#86128semidirect
942. C3#86776semidirect

Maximal subgroups

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

subgroupindex
#105960142
C3×#55572
C3×#55532
#105951992
#105951332
#105949922
#105949832
#105949072
#105948992
#105944522
#105944442
#105941482
#105940622
#105939512
#105938972
C4×D3×Dic62
Dic622
#867763
#861283