Finite Group Databasebeta

← #11905919

Subgroups — #11905919

Order 1152.

3381 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64367C211yesmaximal, characteristic, complemented
2C2×#64298C211yesmaximal, characteristic, complemented
3C3×#5833C211yesmaximal, characteristic, complemented
4C3×#5832C211yesmaximal, characteristic, complemented
5#10595362C212yesmaximal, complemented
6#10595361C212yesmaximal, complemented
7#10595166C214yesmaximal, complemented
8#10595165C214yesmaximal, complemented
9#10595164C212yesmaximal, complemented
10#10595161C212yesmaximal, complemented
11#10595043C211yesmaximal, characteristic, complemented
12#10595029C211yesmaximal, characteristic, complemented
13#10594919C212yesmaximal, complemented
14#10594918C212yesmaximal, complemented
15#10594916C212yesmaximal, complemented
16#10594915C212yesmaximal, complemented
17C2×#63844C211yesmaximal, characteristic, complemented
18#86367—31nomaximal
19#86222—31nomaximal
20C2×C32×#41C2211yescharacteristic
21#64367—28no—
22C2×Q8×C3⋊D3C2212yes—
23C2×#3830C2212yes—
24C2×#3830C2214yes—
25C2×#3828C2212yes—
26C2×#3828C2211yescharacteristic
27C22×#634C2212yes—
28C22×#634C2211yescharacteristic
29C2×C3×#235C2211yescharacteristic
30C2×C3×#235C2211yescharacteristic
31C2×#3805C2214yes—
32#64298—28no—
33C2×#3795C2212yes—
34C2×#3795C2212yes—
35C2×D3×Dic6C2212yes—
36C2×D3×Dic6C2212yes—
37C3×#947C2211yescharacteristic
38C3×#946C2212yes—
39C3×#944C2211yescharacteristic
40C3×#940C2211yescharacteristic
41C3×#939C2212yes—
42C3×#939C2212yes—
43C3×#939C2214yes—
44C3×#938C2212yes—
45C3×#936C2211yescharacteristic
46C3×#930C2212yes—
47C3×C4×#67C2212yes—
48C3×C4×#67C2212yes—
49C2×C3×C4⋊Dic3C2211yescharacteristic
50C3×#924C2212yes—
51C2×C3×C4×Dic3C2211yescharacteristic
52#63982C2214yes—
53#63980C2214yes—
54#63979C2214yes—
55#63978C2212yes—
56#63978C2214yes—
57#63978C2212yes—
58#67⋊Dic3C2214yes—
59#67⋊Dic3C2214yes—
60#63971C2214yes—
61#63971C2214yes—
62C2×#3724C2212yes—
63C2×Dic32C2212yes—
64#63953C2214yes—
65#63916C2212yes—
66#63913C2214yes—
67#63912C2214yes—
68#63911C2211yescharacteristic
69#63909C2212yes—
70C4×#626C2212yes—
71C4×#626C2212yes—
72#63896C2214yes—
73#63896C2214yes—
74#63881C2214yes—
75#63881C2214yes—
76#63871C2212yes—
77#63866C2211yescharacteristic
78#63865C2214yes—
79#63864C2211yescharacteristic
80#63860C2211yescharacteristic
81#63857C2212yes—
82#63844C2212yes—
83#63844C2212yes—
84#63844C2212yes—
85#63844C2212yes—
86#63840C2214yes—
87C2×#1010—31no—
88C2×#1010—31no—
89C2×#1010—31no—
90C2×#1010—31no—
91C2×#1010—61no—
92C3×#537—31no—
93C3×#532—31no—
94#5833—31no—
95#5833D311yescharacteristic, complemented
96#5832—31no—
97#5832D311yescharacteristic, complemented
98#5727—32no—
99#5718—32no—
100#5677—32no—
101#5677—32no—
102#5633—32no—
103#5633—32no—
104#5632—32no—
105#5632—32no—
106#5599—32no—
107#5599—32no—
108#5598—32no—
109#5598—32no—
110#5597—34no—
111#5597—34no—
112#5596—34no—
113#5596—34no—
114#5553—32no—
115#5552—32no—
116#5552—32no—
117D4×Dic6—32no—
118#5510—31no—
119C2×#887—31no—
120#5477—31no—
121C2×C4×Dic6—31no—
122C32×#41—24no—
123C2×C32×Q8C2311yescharacteristic
124C2×C32×D4C2311yescharacteristic
125C2×C32×D4C2312yes—
126C22×C32×C4C2312yes—
127C22×C32×C4C2311yescharacteristic
128C2×#638C2314yes—
129C2×#638C2312yes—
130C22×C3⋊Dic3C2314yes—
131C22×C3⋊Dic3C2312yes—
132Q8×C3⋊D3—28no—
133#3830—216no—
134#3830—28no—
135#3828—24no—
136#3828—28no—
137C2×C4⋊(C3⋊D3)C2311yescharacteristic
138C2×C4×C3⋊D3C2314yes—
139C2×C4×C3⋊D3C2312yes—
140C2×#634—28no—
141C2×#634D418yescomplemented
142C2×#634C2314yes—
143C2×#634C2311yescharacteristic
144C2×#634C2312yes—
145C2×#634C2312yes—
146C2×C3×#67C2312yes—
147C2×C3×#67C2312yes—
148C2×C3×#67C2312yes—
149C2×C3×#67C2312yes—
150C2×C3×#67C2314yes—
151C22×C3×Dic3C2311yescharacteristic
152C22×C3×Dic3C2311yescharacteristic
153C22×C3×Dic3C2312yes—
154C3×#235—24no—
155C3×#235—24no—
156C2×C3×D12C2311yescharacteristic
157C2×C3×D12C2311yescharacteristic
158C2×C3×C4×D3C2312yes—
159C2×C3×C4×D3C2312yes—
160C2×C3×Dic6C2311yescharacteristic
161C2×C3×Dic6C2311yescharacteristic
162C2×#627C2314yes—
163C2×#626C2312yes—
164C2×#626C2314yes—
165C2×#626C2312yes—
166C2×#625C2314yes—
167#3805—216no—
168C2×D3×Dic3C2314yes—
169C2×D3×Dic3C2314yes—
170#3795—28no—
171#3795—28no—
172D3×Dic6—28no—
173D3×Dic6—28no—
174C3×#217C2314yes—
175C3×#217C2312yes—
176C3×#217C2312yes—
177C3×(C2×D3)⋊C4C2312yes—
178C3×(C2×D3)⋊C4C2312yes—
179C3×(C2×D3)⋊C4C2314yes—
180C3×C4⋊Dic3C2312yes—
181C3×C4⋊Dic3C2312yes—
182C3×Dic3⋊C4C2314yes—
183C3×Dic3⋊C4C2312yes—
184C3×Dic3⋊C4C2312yes—
185C3×C4×Dic3C2311yescharacteristic
186C3×C4×Dic3C2311yescharacteristic
187C3×C4×Dic3C2311yescharacteristic
188C3×C4×Dic3C2311yescharacteristic
189#3724C2314yes—
190#3724C2314yes—
191Dic3⋊Dic3C2312yes—
192Dic3⋊Dic3C2314yes—
193Dic3⋊Dic3C2312yes—
194#3722C2312yes—
195#3722C2312yes—
196#3722C2314yes—
197(C2×D3)⋊Dic3C2314yes—
198(C2×D3)⋊Dic3C2312yes—
199(C2×D3)⋊Dic3C2312yes—
200Dic32C2314yes—
201Dic32C2314yes—
202#3497—91noSylow
203C2×C3×#41—21no—
204C2×C3×#41—31no—
205C2×C3×#41—31no—
206C2×C3×#41C2×D311yescharacteristic
207C2×C3×#41C2×D311yescharacteristic
208#1010—68no—
209#1010—68no—
210#1010—68no—
211#1010—68no—
212#1010—616no—
213C2×D3×Q8—32no—
214C2×D3×Q8—32no—
215C2×D3×Q8—32no—
216C2×D3×Q8—32no—
217C2×D3×Q8—62no—
218C2×#237—32no—
219C2×#237—34no—
220C2×#237—34no—
221C2×#237—32no—
222C2×#237—34no—
223C2×#237—34no—
224C2×#237—32no—
225C2×#237—32no—
226C2×#237—64no—
227C2×#237—62no—
228C2×#235—32no—
229C2×#235—31no—
230C2×#235—31no—
231C2×#235—32no—
232C2×#235—32no—
233C2×#235—32no—
234C2×#235—61no—
235C2×#235—62no—
236C2×#235C2×D311yescharacteristic
237C2×#235C2×D311yescharacteristic
238C22×Dic6—31no—
239C22×Dic6—31no—
240C22×Dic6—32no—
241C22×Dic6—32no—
242C22×Dic6—32no—
243C22×Dic6—32no—
244C22×Dic6—61no—
245C22×Dic6—62no—
246C3×C4⋊Q8—31no—
247C3×#127—31no—
248C3×#124—31no—
249C3×#124—31no—
250C3×C22⋊Q8—32no—
251C3×C22⋊Q8—32no—
252C3×#121—32no—
253C3×#121—32no—
254C3×#121—34no—
255C3×#121—32no—
256C3×#121—32no—
257C3×C4×D4—32no—
258C3×C4×D4—32no—
259C2×C3×C4⋊C4—31no—
260C2×C3×C42—31no—
261#947—31no—
262#947C2×D311yescharacteristic
263#946—32no—
264#946C2×D312yes—
265#944—31no—
266#944C2×D311yescharacteristic
267#940—34no—
268#940—34no—
269#940—31no—
270#940C2×D311yescharacteristic
271#939—34no—
272#939—34no—
273#939—32no—
274#939—32no—
275#939—34no—
276#939—34no—
277#939—34no—
278#939C2×D312yes—
279#939C2×D312yes—
280#939C2×D314yes—
281#938—32no—
282#938C2×D312yes—
283#936—31no—
284#936C2×D311yescharacteristic
285D4×Dic3—34no—
286D4×Dic3—34no—
287#930—32no—
288#930—32no—
289#930—34no—
290#930—32no—
291#930C2×D312yes—
292C4×#67—32no—
293C4×#67—32no—
294C4×#67C2×D312yes—
295C4×#67C2×D312yes—
296C2×C4⋊Dic3C2×D311yescharacteristic
297#924—32no—
298#924C2×D312yes—
299C2×Dic3⋊C4—32no—
300C2×Dic3⋊C4—32no—
301C2×C4×Dic3—32no—
302C2×C4×Dic3—32no—
303C2×C4×Dic3C2×D311yescharacteristic
304#897—32no—
305#897—32no—
306#896—34no—
307#896—34no—
308#896—34no—
309#896—34no—
310#895—32no—
311#895—32no—
312#893—34no—
313#893—34no—
314#888—34no—
315#888—34no—
316#887—32no—
317#887—32no—
318#887—32no—
319#887—32no—
320#885—34no—
321#885—34no—
322#885—34no—
323#885—34no—
324#884—34no—
325#884—34no—
326#884—34no—
327#884—34no—
328#67⋊C4—34no—
329#67⋊C4—34no—
330#67⋊C4—34no—
331#67⋊C4—34no—
332#878—34no—
333#878—34no—
334#878—34no—
335#878—34no—
336#875—31no—
337#875—31no—
338#874—31no—
339C4×D12—32no—
340C4×D12—32no—
341#869—31no—
342C4×Dic6—32no—
343C4×Dic6—32no—
344C4×Dic6—32no—
345C4×Dic6—32no—
346C23×C32C2412yes—
347C23×C32C2411yescharacteristic
348C22×C3⋊D3C2412yes—
349C22×C3×D3C2412yes—
350C22×C3×D3C2412yes—
351C32×Q8—22no—
352C32×D4—24no—
353C32×D4—22no—
354C2×C32×C4—24no—
355C2×C32×C4C2×D414yes—
356C2×C32×C4C2412yes—
357C2×C32×C4C2411yescharacteristic
358C2×C32×C4C2411yescharacteristic
359#638—24no—
360#638—28no—
361C2×C3⋊Dic3—28no—
362C2×C3⋊Dic3C2×D418yes—
363C2×C3⋊Dic3C2412yes—
364C2×C3⋊Dic3C2414yes—
365C4⋊(C3⋊D3)—22no—
366C4×C3⋊D3—24no—
367C4×C3⋊D3—28no—
368#634—22no—
369#634—28no—
370#634C2×D418yes—
371#634C2×D418yes—
372C3×#67—24no—
373C3×#67—24no—
374C3×#67—24no—
375C3×#67—44no—
376C3×#67—42no—
377C2×C3×Dic3—22no—
378C2×C3×Dic3—41no—
379C2×C3×Dic3—42no—
380C2×C3×Dic3C2411yescharacteristic
381C2×C3×Dic3C2414yes—
382C2×C3×Dic3C2411yescharacteristic
383C2×C3×Dic3C2412yes—
384C2×C3×Dic3C2412yes—
385C2×C3×Dic3C2411yescharacteristic
386C2×C3×Dic3C2411yescharacteristic
387C3×D12—22no—
388C3×D12—22no—
389C3×C4×D3—24no—
390C3×C4×D3—24no—
391C3×Dic6—22no—
392C3×Dic6—22no—
393#627—28no—
394#626—24no—
395#626—42no—
396#626—44no—
397#625—28no—
398D3×Dic3—28no—
399D3×Dic3—28no—
400C2×2−1+4—91no—
401C2×2−1+4—91no—
402#550—92no—
403#550—92no—
404D4×Q8—92no—
405D4×Q8—92no—
406#548—92no—
407#548—92no—
408#548—92no—
409#548—92no—
410#537—31no—
411#537—91no—
412#537—94no—
413#532—31no—
414#532—91no—
415#532—94no—
416C2×C4×Q8—91no—
417C3×#41—28no—
418C3×#41—24no—
419C3×#41—24no—
420C3×#41—64no—
421C3×#41—64no—
422C2×C3×Q8—21no—
423C2×C3×Q8—31no—
424C2×C3×Q8—31no—
425C2×C3×Q8C22×D311yescharacteristic
426C2×C3×Q8C22×D311yescharacteristic
427C2×C3×D4—22no—
428C2×C3×D4—21no—
429C2×C3×D4—32no—
430C2×C3×D4—32no—
431C2×C3×D4—32no—
432C2×C3×D4—34no—
433C2×C3×D4—32no—
434C2×C3×D4—31no—
435C2×C3×D4—31no—
436C2×C3×D4C22×D311yescharacteristic
437C2×C3×D4C22×D311yescharacteristic
438C2×C3×D4C22×D312yes—
439C2×C3×D4C22×D312yes—
440C22×C3×C4—22no—
441C22×C3×C4—21no—
442C22×C3×C4—31no—
443C22×C3×C4—32no—
444C22×C3×C4—31no—
445C22×C3×C4—32no—
446C22×C3×C4—32no—
447C22×C3×C4C22×D312yes—
448C22×C3×C4C22×D312yes—
449C22×C3×C4C22×D311yescharacteristic
450C22×C3×C4C22×D311yescharacteristic
451C2×#67—34no—
452C2×#67—34no—
453C2×#67—32no—
454C2×#67—32no—
455C2×#67—34no—
456C2×#67—34no—
457C2×#67—32no—
458C2×#67—34no—
459C2×#67—32no—
460C2×#67—62no—
461C2×#67—64no—
462C2×#67C22×D312yes—
463C2×#67C22×D312yes—
464C2×#67C22×D312yes—
465C2×#67C22×D314yes—
466C2×#67C22×D312yes—
467C22×Dic3—32no—
468C22×Dic3—32no—
469C22×Dic3—34no—
470C22×Dic3—34no—
471C22×Dic3—34no—
472C22×Dic3—34no—
473C22×Dic3—62no—
474C22×Dic3—64no—
475C22×Dic3C22×D311yescharacteristic
476C22×Dic3C22×D312yes—
477C22×Dic3C22×D311yescharacteristic
478D3×Q8—68no—
479D3×Q8—68no—
480D3×Q8—68no—
481D3×Q8—68no—
482D3×Q8—616no—
483#237—68no—
484#237—68no—
485#237—68no—
486#237—68no—
487#237—616no—
488#237—616no—
489#237—616no—
490#237—616no—
491#237—632no—
492#237—616no—
493#235—24no—
494#235—24no—
495#235—68no—
496#235—68no—
497#235—68no—
498#235—68no—
499#235—616no—
500#235—68no—
501#235—64no—
502#235—64no—
503C2×D12—32no—
504C2×D12—31no—
505C2×D12—31no—
506C2×D12—32no—
507C2×D12—34no—
508C2×D12—61no—
509C2×D12C22×D311yescharacteristic
510C2×D12C22×D311yescharacteristic
511C2×C4×D3—34no—
512C2×C4×D3—34no—
513C2×C4×D3—32no—
514C2×C4×D3—34no—
515C2×C4×D3—34no—
516C2×C4×D3—32no—
517C2×C4×D3—64no—
518C2×C4×D3—62no—
519C2×C4×D3C22×D312yes—
520C2×C4×D3C22×D312yes—
521C2×Dic6—38no—
522C2×Dic6—38no—
523C2×Dic6—32no—
524C2×Dic6—32no—
525C2×Dic6—32no—
526C2×Dic6—32no—
527C2×Dic6—31no—
528C2×Dic6—34no—
529C2×Dic6—34no—
530C2×Dic6—31no—
531C2×Dic6—34no—
532C2×Dic6—34no—
533C2×Dic6—62no—
534C2×Dic6—61no—
535C2×Dic6—62no—
536C2×Dic6—64no—
537C2×Dic6—68no—
538C2×Dic6—68no—
539C2×Dic6—68no—
540C2×Dic6—68no—
541C2×Dic6—68no—
542C2×Dic6—616no—
543C2×Dic6C22×D311yescharacteristic
544C2×Dic6C22×D311yescharacteristic
545C3×C4⋊C4—32no—
546C3×C4⋊C4—32no—
547C3×C4⋊C4—32no—
548C3×C4⋊C4—34no—
549C3×C4⋊C4—32no—
550C3×C22⋊C4—32no—
551C3×C22⋊C4—34no—
552C3×C22⋊C4—32no—
553C3×C22⋊C4—32no—
554C3×C22⋊C4—34no—
555C3×C22⋊C4—32no—
556C3×C42—31no—
557C3×C42—31no—
558C3×C42—31no—
559C3×C42—31no—
560#217—32no—
561#217—34no—
562#217—32no—
563#217C22×D312yes—
564#217C22×D314yes—
565#217C22×D312yes—
566(C2×D3)⋊C4—32no—
567(C2×D3)⋊C4—32no—
568(C2×D3)⋊C4—34no—
569(C2×D3)⋊C4—32no—
570(C2×D3)⋊C4—32no—
571(C2×D3)⋊C4—34no—
572(C2×D3)⋊C4—32no—
573(C2×D3)⋊C4—34no—
574(C2×D3)⋊C4—32no—
575(C2×D3)⋊C4C22×D312yes—
576(C2×D3)⋊C4C22×D314yes—
577(C2×D3)⋊C4C22×D312yes—
578C4⋊Dic3—32no—
579C4⋊Dic3—32no—
580C4⋊Dic3—34no—
581C4⋊Dic3C22×D312yes—
582C4⋊Dic3C22×D312yes—
583Dic3⋊C4—34no—
584Dic3⋊C4—34no—
585Dic3⋊C4—32no—
586Dic3⋊C4—34no—
587Dic3⋊C4—34no—
588Dic3⋊C4—34no—
589Dic3⋊C4—32no—
590Dic3⋊C4C22×D312yes—
591Dic3⋊C4C22×D314yes—
592Dic3⋊C4C22×D312yes—
593C4×Dic3—34no—
594C4×Dic3—34no—
595C4×Dic3—34no—
596C4×Dic3—34no—
597C4×Dic3C22×D311yescharacteristic
598C4×Dic3C22×D311yescharacteristic
599C4×Dic3C22×D311yescharacteristic
600C4×Dic3C22×D311yescharacteristic
601C22×C32—22no—
602C22×C32—21no—
603C22×C32—21no—
604C22×C32—22no—
605C22×C32—22no—
606C22×C32C22×D412yes—
607C22×C32C2511yescharacteristic
608C2×C3⋊D3—22no—
609C2×C3⋊D3—22no—
610C2×C3⋊D3—22no—
611C2×C3×D3—22no—
612C2×C3×D3—22no—
613C2×C3×D3—22no—
614C2×C3×D3—22no—
615C2×C3×D3—22no—
616C2×C3×D3—22no—
617C32×C4—22no—
618C32×C4C22×D412yes—
619C32×C4C22×D412yes—
620C3⋊Dic3—22no—
621C3⋊Dic3C22×D418yes—
622C3×Dic3—22no—
623C3×Dic3—22no—
624C3×Dic3—21no—
625C3×Dic3—21no—
626C3×Dic3—24no—
627C3×Dic3—21no—
628C3×Dic32−1+412yescomplemented
6292−1+4—188no—
6302−1+4—188no—
631C2×#41—31no—
632C2×#41—31no—
633C2×#41—92no—
634C2×#41—92no—
635C2×#41—94no—
636C2×#41—94no—
637C2×#41—92no—
638C2×#41—91no—
639C2×#41—92no—
640C2×#41D3211yescharacteristic
641C22×Q8—92no—
642C22×Q8—92no—
643C22×Q8—92no—
644C22×Q8—91no—
645C22×Q8—92no—
646C4⋊Q8—31no—
647C4⋊Q8—91no—
648C4⋊Q8—94no—
649#127—31no—
650#127—91no—
651#127—94no—
652#124—31no—
653#124—31no—
654#124—91no—
655#124—91no—
656#124—94no—
657#124—94no—
658C22⋊Q8—32no—
659C22⋊Q8—32no—
660C22⋊Q8—94no—
661C22⋊Q8—94no—
662C22⋊Q8—94no—
663C22⋊Q8—94no—
664C22⋊Q8—92no—
665C22⋊Q8—92no—
666#121—32no—
667#121—32no—
668#121—34no—
669#121—32no—
670#121—32no—
671#121—94no—
672#121—94no—
673#121—94no—
674#121—92no—
675#121—92no—
676#121—92no—
677#121—92no—
678#121—94no—
679#121—94no—
680C4×Q8—92no—
681C4×Q8—92no—
682C4×Q8—92no—
683C4×Q8—92no—
684C4×D4—32no—
685C4×D4—32no—
686C4×D4—92no—
687C4×D4—92no—
688C4×D4—94no—
689C4×D4—94no—
690C4×D4—94no—
691C4×D4—94no—
692C2×C4⋊C4—31no—
693C2×C4⋊C4—92no—
694C2×C42—31no—
695C2×C42—92no—
696C23×C3—22no—
697C23×C3—21no—
698C23×C3—32no—
699C23×C3—32no—
700C23×C3C23×D312yes—
701C23×C3C23×D312yes—
702C23×C3C23×D311yescharacteristic
703C23×C3C23×D311yescharacteristic
704C22×D3—32no—
705C22×D3—32no—
706C22×D3—62no—
707C22×D3C23×D312yes—
708C22×D3C23×D312yes—
709C3×Q8—24no—
710C3×Q8—22no—
711C3×Q8—22no—
712C3×Q8—62no—
713C3×Q8—62no—
714C3×D4—28no—
715C3×D4—24no—
716C3×D4—24no—
717C3×D4—24no—
718C3×D4—22no—
719C3×D4—22no—
720C3×D4—64no—
721C3×D4—64no—
722C3×D4—64no—
723C3×D4—62no—
724C3×D4—62no—
725C3×D4—124no—
726C3×D4—122no—
727C2×C3×C4—28no—
728C2×C3×C4—24no—
729C2×C3×C4—24no—
730C2×C3×C4—21no—
731C2×C3×C4—22no—
732C2×C3×C4—21no—
733C2×C3×C4—24no—
734C2×C3×C4—31no—
735C2×C3×C4—31no—
736C2×C3×C4—34no—
737C2×C3×C4—31no—
738C2×C3×C4—31no—
739C2×C3×C4—32no—
740C2×C3×C4—32no—
741C2×C3×C4—62no—
742C2×C3×C4—64no—
743C2×C3×C4—64no—
744C2×C3×C4—122no—
745C2×C3×C4—121no—
746C2×C3×C4D3×D414yes—
747C2×C3×C4D3×D414yes—
748C2×C3×C4C23×D312yes—
749C2×C3×C4C23×D312yes—
750C2×C3×C4C23×D311yescharacteristic
751C2×C3×C4C23×D311yescharacteristic
752C2×C3×C4C23×D311yescharacteristic
753C2×C3×C4C23×D311yescharacteristic
754#67—24no—
755#67—24no—
756#67—24no—
757#67—42no—
758#67—44no—
759#67—68no—
760#67—68no—
761#67—68no—
762#67—68no—
763#67—616no—
764#67—68no—
765#67—64no—
766#67—64no—
767#67—64no—
768#67—122no—
769#67—124no—
770C2×Dic3—22no—
771C2×Dic3—38no—
772C2×Dic3—38no—
773C2×Dic3—34no—
774C2×Dic3—34no—
775C2×Dic3—32no—
776C2×Dic3—32no—
777C2×Dic3—41no—
778C2×Dic3—42no—
779C2×Dic3—68no—
780C2×Dic3—64no—
781C2×Dic3—62no—
782C2×Dic3—68no—
783C2×Dic3—68no—
784C2×Dic3—68no—
785C2×Dic3—68no—
786C2×Dic3—616no—
787C2×Dic3C23×D311yescharacteristic
788C2×Dic3C23×D314yes—
789C2×Dic3C23×D311yescharacteristic
790C2×Dic3C23×D311yescharacteristic
791C2×Dic3C23×D312yes—
792C2×Dic3C23×D312yes—
793C2×Dic3C23×D311yescharacteristic
794D12—22no—
795D12—22no—
796D12—64no—
797D12—64no—
798D12—62no—
799D12—62no—
800D12—124no—
801D12—122no—
802C4×D3—24no—
803C4×D3—24no—
804C4×D3—68no—
805C4×D3—68no—
806C4×D3—68no—
807C4×D3—68no—
808C4×D3—616no—
809C4×D3—68no—
810C4×D3—64no—
811C4×D3—64no—
812Dic6—22no—
813Dic6—22no—
814Dic6—38no—
815Dic6—38no—
816Dic6—38no—
817Dic6—38no—
818Dic6—68no—
819Dic6—68no—
820Dic6—68no—
821Dic6—68no—
822Dic6—68no—
823Dic6—68no—
824Dic6—64no—
825Dic6—616no—
826Dic6—62no—
827Dic6—62no—
828C2×C32—22no—
829C2×C32—42no—
830C2×C32C23×D411yescharacteristic
831C2×C32C2×2−1+411yescharacteristic
832C2×C32#58511yescharacteristic
833C3⋊D3—42no—
834C3×D3—42no—
835C3×D3—42no—
836#41—24no—
837#41—64no—
838#41—64no—
839#41—188no—
840#41—188no—
841#41—188no—
842#41—1816no—
843#41—1816no—
844#41—188no—
845#41—184no—
846C2×Q8—31no—
847C2×Q8—31no—
848C2×Q8—94no—
849C2×Q8—92no—
850C2×Q8—92no—
851C2×Q8—94no—
852C2×Q8—91no—
853C2×Q8—98no—
854C2×Q8—188no—
855C2×Q8—188no—
856C2×Q8—188no—
857C2×Q8—188no—
858C2×Q8C2×D3211yescharacteristic
859C2×D4—32no—
860C2×D4—32no—
861C2×D4—32no—
862C2×D4—32no—
863C2×D4—34no—
864C2×D4—31no—
865C2×D4—31no—
866C2×D4—92no—
867C2×D4—92no—
868C2×D4—94no—
869C2×D4—94no—
870C2×D4—92no—
871C2×D4—94no—
872C2×D4—91no—
873C2×D4C2×D3212yes—
874C2×D4C2×D3211yescharacteristic
875C22×C4—31no—
876C22×C4—31no—
877C22×C4—32no—
878C22×C4—32no—
879C22×C4—32no—
880C22×C4—94no—
881C22×C4—94no—
882C22×C4—92no—
883C22×C4—94no—
884C22×C4—94no—
885C22×C4—92no—
886C22×C4C2×D3212yes—
887C22×C4C2×D3211yescharacteristic
888C4⋊C4—32no—
889C4⋊C4—32no—
890C4⋊C4—32no—
891C4⋊C4—32no—
892C4⋊C4—34no—
893C4⋊C4—94no—
894C4⋊C4—94no—
895C4⋊C4—92no—
896C4⋊C4—92no—
897C4⋊C4—94no—
898C22⋊C4—32no—
899C22⋊C4—32no—
900C22⋊C4—34no—
901C22⋊C4—32no—
902C22⋊C4—32no—
903C22⋊C4—34no—
904C22⋊C4—92no—
905C22⋊C4—92no—
906C22⋊C4—94no—
907C22⋊C4—92no—
908C22⋊C4—92no—
909C22⋊C4—94no—
910C42—31no—
911C42—31no—
912C42—31no—
913C42—31no—
914C42—94no—
915C42—94no—
916C22×C3—21no—
917C22×C3—21no—
918C22×C3—21no—
919C22×C3—21no—
920C22×C3—24no—
921C22×C3—22no—
922C22×C3—22no—
923C22×C3—22no—
924C22×C3—22no—
925C22×C3—22no—
926C22×C3—22no—
927C22×C3—22no—
928C22×C3—21no—
929C22×C3—41no—
930C22×C3—41no—
931C22×C3—42no—
932C22×C3—42no—
933C22×C3—62no—
934C22×C3—62no—
935C22×C3—62no—
936C22×C3—62no—
937C22×C3—62no—
938C22×C3—62no—
939C22×C3C2×D3×D412yes—
940C22×C3C2×D3×D412yes—
941C22×C3C24×D311yescharacteristic
942C22×C3C24×D311yescharacteristic
943C2×D3—22no—
944C2×D3—22no—
945C2×D3—22no—
946C2×D3—22no—
947C2×D3—22no—
948C2×D3—22no—
949C2×D3—64no—
950C2×D3—62no—
951C2×D3—62no—
952C2×D3—62no—
953C2×D3—62no—
954C2×D3—62no—
955C2×D3—62no—
956C2×D3—122no—
957C2×D3—122no—
958C3×C4—24no—
959C3×C4—22no—
960C3×C4—22no—
961C3×C4—22no—
962C3×C4—22no—
963C3×C4—32no—
964C3×C4—62no—
965C3×C4—62no—
966C3×C4—64no—
967C3×C4—61no—
968C3×C4—61no—
969C3×C4—61no—
970C3×C4C2×D3×D412yes—
971C3×C4C2×D3×D412yes—
972C3×C4C2×D3×D412yes—
973C3×C4C2×D3×D412yes—
974Dic3—22no—
975Dic3—22no—
976Dic3—21no—
977Dic3—21no—
978Dic3—21no—
979Dic3—24no—
980Dic3—38no—
981Dic3—38no—
982Dic3—68no—
983Dic3—64no—
984Dic3—62no—
985Dic3—62no—
986Dic3#101012yescomplemented
987C32#349711yescharacteristic, complemented, Sylow
988C23—32no—
989C23—32no—
990C23—92no—
991C23C22×D3212yes—
992C23C22×D3211yescharacteristic
993Q8—22no—
994Q8—62no—
995Q8—62no—
996Q8—98no—
997Q8—98no—
998Q8—188no—
999Q8—188no—
1000Q8—182no—
1001D4—24no—
1002D4—22no—
1003D4—64no—
1004D4—64no—
1005D4—64no—
1006D4—62no—
1007D4—62no—
1008D4—122no—
1009D4—124no—
1010D4—184no—
1011D4—188no—
1012D4—188no—
1013D4—184no—
1014D4—182no—
1015D4—364no—
1016D4—362no—
1017C2×C4—24no—
1018C2×C4—31no—
1019C2×C4—31no—
1020C2×C4—31no—
1021C2×C4—31no—
1022C2×C4—34no—
1023C2×C4—32no—
1024C2×C4—32no—
1025C2×C4—62no—
1026C2×C4—64no—
1027C2×C4—64no—
1028C2×C4—98no—
1029C2×C4—94no—
1030C2×C4—92no—
1031C2×C4—121no—
1032C2×C4—122no—
1033C2×C4—188no—
1034C2×C4—188no—
1035C2×C4—188no—
1036C2×C4—188no—
1037C2×C4—184no—
1038C2×C4#381114yes—
1039C2×C4C22×D3212yes—
1040C2×C4C22×D3211yescharacteristic
1041C2×C4C22×D3211yescharacteristic
1042C2×C3—22no—
1043C2×C3—22no—
1044C2×C3—21no—
1045C2×C3—21no—
1046C2×C3—21no—
1047C2×C3—42no—
1048C2×C3—44no—
1049C2×C3—42no—
1050C2×C3—42no—
1051C2×C3—122no—
1052C2×C3—122no—
1053C2×C3C22×D3×D411yescharacteristic
1054C2×C3C22×D3×D411yescharacteristic
1055C2×C3C2×#101011yescharacteristic
1056C2×C3#596411yescharacteristic
1057C2×C3#596611yescharacteristic
1058C2×C3D3×2−1+411yescharacteristic
1059D3—42no—
1060D3—42no—
1061D3—124no—
1062D3—122no—
1063D3—122no—
1064C22—21no—
1065C22—21no—
1066C22—22no—
1067C22—22no—
1068C22—22no—
1069C22—62no—
1070C22—62no—
1071C22—62no—
1072C22—62no—
1073C22—62no—
1074C22—62no—
1075C22—182no—
1076C22—182no—
1077C22—182no—
1078C22C2×#381112yes—
1079C22C23×D3211yescharacteristic
1080C4—22no—
1081C4—32no—
1082C4—61no—
1083C4—61no—
1084C4—64no—
1085C4—61no—
1086C4—62no—
1087C4—62no—
1088C4—98no—
1089C4—182no—
1090C4C2×#381112yes—
1091C4C2×#381112yes—
1092C3—21no—
1093C3#8622211yescharacteristic, complemented
1094C3#8636711yescharacteristic, complemented
1095C2—22no—
1096C2—42no—
1097C2—122no—
1098C2—122no—
1099C2—362no—
1100C2D3×#101011yescharacteristic
1101C2#1059669611yescharacteristic
1102C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3497
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64367C2semidirect
2. C2×#64298C2semidirect
3. C3×#5833C2semidirect
4. C3×#5832C2semidirect
5. #10595362C2semidirect
6. #10595361C2semidirect
7. #10595166C2semidirect
8. #10595165C2semidirect
9. #10595164C2semidirect
10. #10595161C2semidirect
11. #10595043C2semidirect
12. #10595029C2semidirect
13. #10594919C2semidirect
14. #10594918C2semidirect
15. #10594916C2semidirect
16. #10594915C2semidirect
17. C2×#63844C2semidirect
95. #5833D3semidirect
97. #5832D3semidirect
141. C2×#634D4semidirect
628. C3×Dic32−1+4semidirect
986. Dic3#1010semidirect
987. C32#3497semidirect
1093. C3#86222semidirect
1094. C3#86367semidirect

Maximal subgroups

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

subgroupindex
C2×#643672
C2×#642982
C3×#58332
C3×#58322
#105953622
#105953612
#105951662
#105951652
#105951642
#105951612
#105950432
#105950292
#105949192
#105949182
#105949162
#105949152
C2×#638442
#863673
#862223