Finite Group Databasebeta

← #11864583

Subgroups — #11864583

Order 1152.

1627 conjugacy classes of subgroups.

The subgroup lattice has 1051 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64314C211yesmaximal, characteristic, complemented
2C2×#63935C211yesmaximal, characteristic, complemented
3C2×#63794C211yesmaximal, characteristic, complemented
4#10594523C211yesmaximal, characteristic, complemented
5#10592472C211yesmaximal, characteristic, complemented
6C3×#4776C211yesmaximal, characteristic, complemented
7C3×#4771C211yesmaximal, characteristic, complemented
8#10591467C211yesmaximal, characteristic, complemented
9#10591448C211yesmaximal, characteristic, complemented
10#10590967C211yesmaximal, characteristic, complemented
11#10590961C211yesmaximal, characteristic, complemented
12#10590955C211yesmaximal, characteristic, complemented
13#10590617C211yesmaximal, characteristic, complemented
14#10590616C211yesmaximal, characteristic, complemented
15D3×#809C211yesmaximal, characteristic, complemented
16#80149—31nomaximal
17#78886—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C2×#3811—21no—
22C2×D3×#67—21no—
23C22×#626—21no—
24C2×#3804—21no—
25#64314—24no—
26#64314—24no—
27C2×D3×D12C2211yescharacteristic
28C2×#3799C2211yescharacteristic
29C2×#3799C2211yescharacteristic, complemented
30C2×#3798C2211yescharacteristic
31C2×#3796C2211yescharacteristic
32C2×#3753C2211yescharacteristic, complemented
33C2×#3745C2211yescharacteristic, complemented
34#64104C2211yescharacteristic, complemented
35C2×C3×#214C2211yescharacteristic, complemented
36C2×C3×#204C2211yescharacteristic, complemented
37C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
38C3×#897C2211yescharacteristic, complemented
39C3×D3×C4⋊C4C2211yescharacteristic, complemented
40#63935—24no—
41#63910—21no—
42#63909—21no—
43#63909C2211yescharacteristic, complemented
44#63906—21no—
45#63895—21no—
46#63871C2211yescharacteristic, complemented
47C2×#3718C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic, complemented
49C2×#3717C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63794—24no—
53C32×#102C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55#63636C2211yescharacteristic, complemented
56C3×#832C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×#1009—31no—
66C2×#1004—31no—
67C2×#950—31no—
68C2×#916—31no—
69C2×#914—31no—
70C2×#908—31no—
71#5629—31no—
72#5510—31no—
73C3×#450—31no—
74C3×#417—31no—
75#5217—31no—
76#5173—31no—
77#5169—31no—
78#5129—31no—
79#5047—31no—
80C2×#809—31no—
81#4810—31no—
82#4810—31no—
83#4808—31no—
84#4808—31no—
85#4781—31no—
86#4776—31no—
87#4776D311yescharacteristic, complemented
88#4773—31no—
89#4773—31no—
90#4773—31no—
91#4773—61no—
92#4771D311yescharacteristic, complemented
93D3×#102—31no—
94#4734—31no—
95#4727—31no—
96C23×C3⋊D3—21no—
97C23×C3×D3—21no—
98C22×D32—21no—
99C2×C32×D4C2311yescharacteristic
100C2×#638—21no—
101D4×C3⋊D3—22no—
102D4×C3⋊D3—22no—
103C2×C4⋊(C3⋊D3)—21no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3C2311yescharacteristic
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C22×C3×Dic3—21no—
110C3×#237—22no—
111C3×#237D414yescomplemented
112C3×D3×D4—22no—
113C3×D3×D4—22no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119C2×C3×Dic6C2311yescharacteristic
120#3811—28no—
121D3×#67—28no—
122C2×#627D411yescharacteristic
123C2×#626—28no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#626—21no—
127C2×#626—21no—
128C2×#626—21no—
129C2×#626D411yescharacteristic
130C2×#626D411yescharacteristic
131C2×#625D411yescharacteristic
132C2×#624—21no—
133C2×#624—21no—
134#3804—28no—
135C2×D3×Dic3—21no—
136D3×D12—22no—
137D3×D12D414yescomplemented
138#3799—22no—
139#3799—22no—
140#3799—22no—
141#3799—22no—
142#3798—22no—
143#3798—22no—
144#3796—22no—
145#3796—22no—
146C2×C32×C8C2311yescharacteristic
147C32×C4⋊C4C2311yescharacteristic
148#3753—22no—
149#3752—21no—
150C2×C3⋊(C3⋊C8)C2311yescharacteristic
151#3745—22no—
152C3×#214—22no—
153C3×(C2×D3)⋊C4—21no—
154C3×C4⋊Dic3—21no—
155C3×C4⋊Dic3C2311yescharacteristic
156C3×Dic3⋊C4—21no—
157C2×C3×C3⋊C8C2311yescharacteristic
158C2×C3×C3⋊C8C2311yescharacteristic
159C3×#204—22no—
160C3×ΓL(1,𝔽25)—22no—
161Dic3⋊Dic3—21no—
162#3722—21no—
163#3722—21no—
164#3718—22no—
165#3717—22no—
166#3717—22no—
167#3714—22no—
168D3×C3⋊C8—22no—
169#3012—91noSylow
170C2×C3×#41—31no—
171C22×C3×D4—31no—
172C22×#67—61no—
173C22×#67—61no—
174#1009—64no—
175#1009—64no—
176C2×#239—31no—
177C2×#239—31no—
178C2×#239—31no—
179#1004—64no—
180#1004—64no—
181C2×#237—31no—
182C2×#237—61no—
183C2×#237C2×D311yescharacteristic
184C2×D3×D4—31no—
185C2×D3×D4—31no—
186C2×D3×D4—31no—
187C2×D3×D4—61no—
188C2×D3×D4—61no—
189C2×D3×D4—61no—
190C2×D3×D4—61no—
191C2×D3×D4C2×D311yescharacteristic
192C2×#235—31no—
193C2×#235—31no—
194C2×#235—31no—
195C2×#235—31no—
196C2×#235—61no—
197C22×D12—31no—
198C22×D12—61no—
199C2×C3×SD16—31no—
200C2×C3×SD16—31no—
201C2×C3×M16—31no—
202C3×C22⋊Q8—31no—
203C2×C3×C4⋊C4—31no—
204#950—64no—
205#946—31no—
206C2×#216—31no—
207C2×#216—31no—
208C2×#215—31no—
209C2×#215—31no—
210C2×#214C2×D311yescharacteristic, complemented
211C2×#213—31no—
212C2×#213—31no—
213C2×#213—31no—
214C2×#213—61no—
215#930—31no—
216#930—61no—
217#930—61no—
218C22×C3⋊C8—31no—
219#916—64no—
220#914—64no—
221#908—64no—
222C2×D24—31no—
223C2×D24—31no—
224C2×D24—31no—
225C2×D24—61no—
226C2×#204—31no—
227C2×#204—31no—
228C2×#204C2×D311yescharacteristic, complemented
229C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
230C2×D3×C8—31no—
231#897—31no—
232#897—61no—
233#897C2×D311yescharacteristic, complemented
234#896—61no—
235#895—31no—
236#895—31no—
237#895—31no—
238#895—61no—
239#895—61no—
240#895—61no—
241D3×C4⋊C4C2×D311yescharacteristic, complemented
242#884—61no—
243#884—61no—
244C3×#103—31no—
245C3×#103—31no—
246C3×#102—21no—
247C3×#102—31no—
248C3×#102—31no—
249C3×#102C2×D311yescharacteristic, complemented
250C3×#102C2×D311yescharacteristic, complemented
251C3×C22⋊C8—31no—
252#832—31no—
253#832C2×D311yescharacteristic, complemented
254#830—31no—
255#821—31no—
256(C2×D3)⋊C8—31no—
257(C2×D3)⋊C8—31no—
258(C2×D3)⋊C8—31no—
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—61no—
262(C2×D3)⋊C8C2×D311yescharacteristic, complemented
263#816C2×D311yescharacteristic, complemented
264#810C2×D311yescharacteristic, complemented
265#809—31no—
266#809—31no—
267#809—31no—
268#809—31no—
269#809—61no—
270#809C2×D311yescharacteristic, complemented
271C23×C32—21no—
272C22×C3⋊D3—21no—
273C22×C3⋊D3—24no—
274C22×C3⋊D3—21no—
275C22×C3⋊D3—81no—
276C22×C3⋊D3—81no—
277C22×C3⋊D3C2×D411yescharacteristic
278C22×C3×D3—21no—
279C22×C3×D3—24no—
280C22×C3×D3—81no—
281C22×C3×D3—81no—
282C22×C3×D3C2×D411yescharacteristic
283C22×C3×D3C2×D411yescharacteristic
284C2×D32—24no—
285C2×D32—81no—
286C2×D32—81no—
287C32×D4—21no—
288C32×D4C2×D412yes—
289C2×C32×C4—21no—
290C2×C32×C4C2411yescharacteristic
291#638—24no—
292C2×C3⋊Dic3C2×D411yescharacteristic
293C4⋊(C3⋊D3)—21no—
294C4⋊(C3⋊D3)—21no—
295C4⋊(C3⋊D3)—21no—
296C4⋊(C3⋊D3)—81no—
297C4⋊(C3⋊D3)C2×D412yes—
298C4×C3⋊D3—21no—
299C4×C3⋊D3—21no—
300C3×#67—24no—
301C3×#67—24no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—24no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3C2×D411yescharacteristic
307C2×C3×Dic3C2×D411yescharacteristic
308C3×D12—21no—
309C3×D12C2×D412yes—
310C3×C4×D3—21no—
311C3×C4×D3—21no—
312C3×C4×D3—81no—
313C3×C4×D3C2×D412yes—
314C3×C4×D3C2×D412yes—
315C3×Dic6—21no—
316C3×Dic6—21no—
317C3×Dic6—21no—
318C3×Dic6C2×D412yes—
319#627—22no—
320#626—24no—
321#626—24no—
322#626—22no—
323#626—22no—
324#626—24no—
325#626—42no—
326#626—81no—
327#625—22no—
328#624—24no—
329#624—42no—
330D3×Dic3—24no—
331C32×C8—21no—
332C3⋊(C3⋊C8)—21no—
333C3×C3⋊C8—21no—
334C3×C3⋊C8—21no—
335C2×H(5,𝔽2)—91no—
336C2×AGL(1,ℤ/8)—91no—
337C2×#135—91no—
338#537—91no—
339#452—91no—
340#452—91no—
341#450—31no—
342#450—91no—
343#449—91no—
344#449—91no—
345#447—91no—
346#447—91no—
347#417—31no—
348C2×#102—91no—
349#408—91no—
350C24×C3—61no—
351C23×D3—21no—
352C23×D3—61no—
353C23×D3—61no—
354C23×D3—61no—
355C23×D3—61no—
356C23×D3—121no—
357C3×#41—34no—
358C3×#41—62no—
359C2×C3×Q8—31no—
360C2×C3×Q8—31no—
361C2×C3×D4—21no—
362C2×C3×D4—31no—
363C2×C3×D4—61no—
364C2×C3×D4—62no—
365C2×C3×D4—61no—
366C2×C3×D4—62no—
367C2×C3×D4C22×D311yescharacteristic
368C2×C3×D4C22×D311yescharacteristic
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4—61no—
372C22×C3×C4—61no—
373C2×#67—21no—
374C2×#67—21no—
375C2×#67—31no—
376C2×#67—31no—
377C2×#67—31no—
378C2×#67—31no—
379C2×#67—61no—
380C2×#67—61no—
381C2×#67—68no—
382C2×#67—61no—
383C2×#67—61no—
384C2×#67—61no—
385C2×#67—61no—
386C2×#67—68no—
387C2×#67—61no—
388C2×#67—121no—
389C22×Dic3—21no—
390C22×Dic3—61no—
391#239—62no—
392#239—62no—
393#239—62no—
394#239—62no—
395#239—62no—
396#239—62no—
397#237—22no—
398#237—62no—
399#237—68no—
400#237—62no—
401#237D1214yescomplemented
402D3×D4—22no—
403D3×D4—22no—
404D3×D4—34no—
405D3×D4—62no—
406D3×D4—62no—
407D3×D4—68no—
408D3×D4—68no—
409D3×D4—68no—
410D3×D4—62no—
411D3×D4—62no—
412D3×D4—62no—
413D3×D4—122no—
414D3×D4—122no—
415#235—62no—
416#235—62no—
417#235—62no—
418#235—62no—
419#235—62no—
420#235—68no—
421#235—62no—
422#235—62no—
423#235—62no—
424C2×D12—31no—
425C2×D12—31no—
426C2×D12—34no—
427C2×D12—31no—
428C2×D12—31no—
429C2×D12—31no—
430C2×D12—31no—
431C2×D12—61no—
432C2×D12—61no—
433C2×D12—62no—
434C2×D12—61no—
435C2×D12—61no—
436C2×D12—68no—
437C2×D12—61no—
438C2×D12—61no—
439C2×D12—61no—
440C2×D12—61no—
441C2×D12—61no—
442C2×D12—121no—
443C2×D12C22×D311yescharacteristic
444C2×C4×D3—21no—
445C2×C4×D3—31no—
446C2×C4×D3—31no—
447C2×C4×D3—61no—
448C2×C4×D3—61no—
449C2×C4×D3—61no—
450C2×C4×D3—61no—
451C2×C4×D3—61no—
452C2×C4×D3—61no—
453C2×C4×D3C22×D311yescharacteristic
454C2×C4×D3C22×D311yescharacteristic
455C2×Dic6—31no—
456C2×Dic6—31no—
457C2×Dic6C22×D311yescharacteristic
458C2×Dic6C22×D311yescharacteristic
459C3×SD16—62no—
460C3×SD16—62no—
461C3×M16—62no—
462C2×C3×C8—21no—
463C2×C3×C8—31no—
464C2×C3×C8—31no—
465C2×C3×C8C22×D311yescharacteristic
466C2×C3×C8C22×D311yescharacteristic
467C3×C4⋊C4—21no—
468C3×C4⋊C4—31no—
469C3×C4⋊C4—61no—
470C3×C4⋊C4—61no—
471C3×C4⋊C4C22×D311yescharacteristic
472C3×C4⋊C4C22×D311yescharacteristic
473C3×C22⋊C4—61no—
474#216—62no—
475#216—62no—
476#215—62no—
477#215—62no—
478#214—22no—
479#213—62no—
480#213—62no—
481#213—62no—
482#213—122no—
483(C2×D3)⋊C4—21no—
484(C2×D3)⋊C4—61no—
485(C2×D3)⋊C4—61no—
486(C2×D3)⋊C4—61no—
487(C2×D3)⋊C4—61no—
488(C2×D3)⋊C4—61no—
489(C2×D3)⋊C4—61no—
490(C2×D3)⋊C4—121no—
491C4⋊Dic3—21no—
492C4⋊Dic3—61no—
493C4⋊Dic3C22×D311yescharacteristic
494Dic3⋊C4—21no—
495Dic3⋊C4—61no—
496C2×C3⋊C8—31no—
497C2×C3⋊C8—31no—
498C2×C3⋊C8—61no—
499C2×C3⋊C8—62no—
500C2×C3⋊C8C22×D311yescharacteristic
501C2×C3⋊C8C22×D311yescharacteristic
502D24—62no—
503D24—62no—
504D24—62no—
505D24—122no—
506#204—22no—
507#204—62no—
508#204—62no—
509ΓL(1,𝔽25)—22no—
510D3×C8—62no—
511C22×C32—22no—
512C22×C32—41no—
513C22×C32—41no—
514C22×C32C22×D411yescharacteristic
515C2×C3⋊D3—21no—
516C2×C3⋊D3—22no—
517C2×C3⋊D3—21no—
518C2×C3⋊D3—21no—
519C2×C3⋊D3—41no—
520C2×C3⋊D3—41no—
521C2×C3⋊D3—41no—
522C2×C3⋊D3—41no—
523C2×C3⋊D3—41no—
524C2×C3⋊D3—84no—
525C2×C3×D3—21no—
526C2×C3×D3—21no—
527C2×C3×D3—22no—
528C2×C3×D3—21no—
529C2×C3×D3—21no—
530C2×C3×D3—21no—
531C2×C3×D3—41no—
532C2×C3×D3—41no—
533C2×C3×D3—84no—
534C2×C3×D3#12012yes—
535D32—84no—
536C32×C4—41no—
537C32×C4C22×D411yescharacteristic
538C32×C4C22×D411yescharacteristic
539C3⋊Dic3—21no—
540C3×Dic3—22no—
541C3×Dic3—21no—
542C3×Dic3—41no—
543C3×Dic3—41no—
544C3×Dic3#12012yes—
545H(5,𝔽2)—184no—
546H(5,𝔽2)—184no—
547C2×#41—31no—
548C2×#41—91no—
549C2×#41—91no—
550C2×#41—91no—
551C2×#41—91no—
552C2×#41—181no—
553C22×D4—31no—
554C22×D4—91no—
555C22×D4—91no—
556C22×D4—181no—
557C22×D4—181no—
558C22×D4—181no—
559AGL(1,ℤ/8)—184no—
560#135—184no—
561C2×Q16—91no—
562C2×SD16—31no—
563C2×SD16—31no—
564C2×SD16—91no—
565C2×SD16—91no—
566C2×D8—91no—
567C2×D8—91no—
568C2×D8—91no—
569C2×M16—31no—
570C22×C8—91no—
571C22⋊Q8—31no—
572C22⋊Q8—91no—
573C22⋊Q8—181no—
574#121—91no—
575#121—91no—
576#121—181no—
577#121—181no—
578#121—181no—
579C2×C4⋊C4—31no—
580#103—31no—
581#103—31no—
582#102—31no—
583#102—31no—
584#102—91no—
585#102—91no—
586#102—91no—
587#102D3211yescharacteristic, complemented
588C22⋊C8—31no—
589C22⋊C8—91no—
590C22⋊C8—91no—
591C22⋊C8—91no—
592C23×C3—21no—
593C23×C3—21no—
594C23×C3—31no—
595C23×C3—31no—
596C23×C3—41no—
597C23×C3—64no—
598C23×C3—61no—
599C23×C3—241no—
600C23×C3—241no—
601C22×D3—21no—
602C22×D3—24no—
603C22×D3—31no—
604C22×D3—31no—
605C22×D3—61no—
606C22×D3—64no—
607C22×D3—61no—
608C22×D3—61no—
609C22×D3—64no—
610C22×D3—64no—
611C22×D3—64no—
612C22×D3—61no—
613C22×D3—61no—
614C22×D3—81no—
615C22×D3—81no—
616C22×D3—121no—
617C22×D3—124no—
618C22×D3—121no—
619C22×D3—241no—
620C22×D3—241no—
621C22×D3—241no—
622C22×D3—241no—
623C22×D3—241no—
624C22×D3—241no—
625C22×D3—241no—
626C22×D3—241no—
627C22×D3—242no—
628C22×D3—242no—
629C22×D3D3×D411yescharacteristic
630C22×D3D3×D411yescharacteristic
631C3×Q8—32no—
632C3×Q8—61no—
633C3×Q8—61no—
634C3×Q8—61no—
635C3×D4—21no—
636C3×D4—21no—
637C3×D4—22no—
638C3×D4—32no—
639C3×D4—41no—
640C3×D4—64no—
641C3×D4—64no—
642C3×D4—61no—
643C3×D4C2×D1212yes—
644C3×D4D3×D412yes—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—31no—
649C2×C3×C4—32no—
650C2×C3×C4—32no—
651C2×C3×C4—31no—
652C2×C3×C4—41no—
653C2×C3×C4—64no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—241no—
660C2×C3×C4C23×D311yescharacteristic
661C2×C3×C4C23×D311yescharacteristic
662#67—24no—
663#67—24no—
664#67—62no—
665#67—64no—
666#67—64no—
667#67—62no—
668#67—64no—
669#67—64no—
670#67—62no—
671#67—62no—
672#67—64no—
673#67—124no—
674#67—122no—
675#67—241no—
676C2×Dic3—21no—
677C2×Dic3—24no—
678C2×Dic3—21no—
679C2×Dic3—21no—
680C2×Dic3—31no—
681C2×Dic3—31no—
682C2×Dic3—61no—
683C2×Dic3—64no—
684C2×Dic3D3×D411yescharacteristic
685C2×Dic3D3×D411yescharacteristic
686D12—21no—
687D12—32no—
688D12—32no—
689D12—62no—
690D12—62no—
691D12—64no—
692D12—64no—
693D12—64no—
694D12—62no—
695D12—61no—
696D12—61no—
697D12—61no—
698D12—61no—
699D12—61no—
700D12—61no—
701D12—121no—
702D12—121no—
703D12—121no—
704D12—122no—
705D12—241no—
706D12—241no—
707D12—242no—
708D12—241no—
709D12D3×D412yes—
710C4×D3—21no—
711C4×D3—21no—
712C4×D3—64no—
713C4×D3—64no—
714C4×D3—64no—
715C4×D3—61no—
716C4×D3—61no—
717C4×D3—61no—
718C4×D3—61no—
719C4×D3—81no—
720C4×D3—121no—
721C4×D3—121no—
722C4×D3—122no—
723C4×D3—122no—
724C4×D3C2×D1212yes—
725C4×D3D3×D412yes—
726Dic6—21no—
727Dic6—21no—
728Dic6—21no—
729Dic6—62no—
730Dic6—62no—
731Dic6C2×D1212yes—
732C3×C8—21no—
733C3×C8—21no—
734C3×C8—41no—
735C3×C8—61no—
736C3×C8—61no—
737C3⋊C8—21no—
738C3⋊C8—21no—
739C3⋊C8—61no—
740C3⋊C8—61no—
741C3⋊C8—121no—
742C2×C32—42no—
743C2×C32C2×#12011yescharacteristic
744C2×C32#57611yescharacteristic
745C2×C32#57711yescharacteristic
746C3⋊D3—41no—
747C3⋊D3—42no—
748C3⋊D3—81no—
749C3×D3—22no—
750C3×D3—42no—
751C3×D3—41no—
752C24—61no—
753C24—181no—
754C24—181no—
755#41—34no—
756#41—62no—
757#41—182no—
758#41—182no—
759#41—182no—
760#41—182no—
761#41—188no—
762#41—182no—
763#41—182no—
764#41—182no—
765#41—182no—
766C2×Q8—31no—
767C2×Q8—31no—
768C2×Q8—91no—
769C2×D4—31no—
770C2×D4—61no—
771C2×D4—62no—
772C2×D4—61no—
773C2×D4—62no—
774C2×D4—94no—
775C2×D4—91no—
776C2×D4—91no—
777C2×D4—91no—
778C2×D4—91no—
779C2×D4—91no—
780C2×D4—181no—
781C2×D4—182no—
782C2×D4—181no—
783C2×D4—181no—
784C2×D4—181no—
785C2×D4—188no—
786C2×D4—181no—
787C2×D4—181no—
788C2×D4—181no—
789C2×D4—182no—
790C2×D4—188no—
791C2×D4—188no—
792C2×D4—182no—
793C2×D4C2×D3211yescharacteristic
794C22×C4—31no—
795C22×C4—31no—
796C22×C4—61no—
797C22×C4—61no—
798C22×C4—91no—
799C22×C4—181no—
800C22×C4—181no—
801C22×C4—181no—
802Q16—182no—
803SD16—62no—
804SD16—62no—
805SD16—182no—
806SD16—182no—
807D8—182no—
808D8—182no—
809D8—182no—
810M16—62no—
811C2×C8—31no—
812C2×C8—31no—
813C2×C8—91no—
814C2×C8—182no—
815C2×C8C2×D3211yescharacteristic
816C4⋊C4—31no—
817C4⋊C4—61no—
818C4⋊C4—61no—
819C4⋊C4—181no—
820C4⋊C4C2×D3211yescharacteristic
821C22⋊C4—61no—
822C22⋊C4—181no—
823C22⋊C4—181no—
824C22⋊C4—181no—
825C22×C3—22no—
826C22×C3—22no—
827C22×C3—21no—
828C22×C3—32no—
829C22×C3—42no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—41no—
833C22×C3—41no—
834C22×C3—61no—
835C22×C3—61no—
836C22×C3—62no—
837C22×C3—61no—
838C22×C3—61no—
839C22×C3—61no—
840C22×C3—81no—
841C22×C3—81no—
842C22×C3—121no—
843C22×C3—121no—
844C22×C3—244no—
845C22×C3C2×D3×D411yescharacteristic
846C22×C3C2×D3×D411yescharacteristic
847C2×D3—21no—
848C2×D3—21no—
849C2×D3—21no—
850C2×D3—21no—
851C2×D3—21no—
852C2×D3—22no—
853C2×D3—41no—
854C2×D3—41no—
855C2×D3—62no—
856C2×D3—62no—
857C2×D3—61no—
858C2×D3—61no—
859C2×D3—61no—
860C2×D3—61no—
861C2×D3—61no—
862C2×D3—62no—
863C2×D3—61no—
864C2×D3—84no—
865C2×D3—121no—
866C2×D3—121no—
867C2×D3—122no—
868C2×D3—121no—
869C2×D3—121no—
870C2×D3—121no—
871C2×D3—121no—
872C2×D3—121no—
873C2×D3—121no—
874C2×D3—121no—
875C2×D3—121no—
876C2×D3—121no—
877C2×D3—121no—
878C2×D3—241no—
879C2×D3—241no—
880C2×D3—241no—
881C2×D3—241no—
882C2×D3—241no—
883C2×D3—244no—
884C2×D3—244no—
885C2×D3—244no—
886C2×D3—244no—
887C2×D3—248no—
888C2×D3#88212yes—
889C3×C4—21no—
890C3×C4—21no—
891C3×C4—32no—
892C3×C4—41no—
893C3×C4—41no—
894C3×C4—61no—
895C3×C4—62no—
896C3×C4—81no—
897C3×C4—121no—
898C3×C4—121no—
899C3×C4C22×D1211yescharacteristic
900C3×C4C2×D3×D411yescharacteristic
901C3×C4C2×D3×D411yescharacteristic
902C3×C4C2×D3×D411yescharacteristic
903Dic3—22no—
904Dic3—21no—
905Dic3—41no—
906Dic3—41no—
907Dic3—61no—
908Dic3—61no—
909Dic3—121no—
910Dic3#88212yes—
911C32#301211yescharacteristic, complemented, Sylow
912C23—21no—
913C23—31no—
914C23—31no—
915C23—64no—
916C23—61no—
917C23—91no—
918C23—184no—
919C23—184no—
920C23—181no—
921C23—181no—
922C23—241no—
923C23—241no—
924C23—721no—
925C23—721no—
926C23—721no—
927C23—721no—
928Q8—32no—
929Q8—61no—
930Q8—61no—
931Q8—61no—
932Q8—182no—
933D4—21no—
934D4—32no—
935D4—64no—
936D4—64no—
937D4—61no—
938D4—92no—
939D4—182no—
940D4—184no—
941D4—182no—
942D4—184no—
943D4—184no—
944D4—184no—
945D4—182no—
946D4—181no—
947D4—181no—
948D4—181no—
949D4—362no—
950D4—721no—
951D4—721no—
952D4D3×D1212yes—
953C2×C4—21no—
954C2×C4—31no—
955C2×C4—32no—
956C2×C4—32no—
957C2×C4—31no—
958C2×C4—64no—
959C2×C4—61no—
960C2×C4—61no—
961C2×C4—61no—
962C2×C4—61no—
963C2×C4—61no—
964C2×C4—91no—
965C2×C4—184no—
966C2×C4—184no—
967C2×C4—181no—
968C2×C4—181no—
969C2×C4—241no—
970C2×C4—362no—
971C2×C4C22×D3211yescharacteristic
972C8—21no—
973C8—61no—
974C8—61no—
975C8—181no—
976C2×C3—21no—
977C2×C3—21no—
978C2×C3—21no—
979C2×C3—42no—
980C2×C3—42no—
981C2×C3—62no—
982C2×C3—82no—
983C2×C3—122no—
984C2×C3—121no—
985C2×C3C2×#88211yescharacteristic
986C2×C3D3×#12011yescharacteristic
987C2×C3#576211yescharacteristic
988C2×C3#577411yescharacteristic
989C2×C3#577411yescharacteristic
990C2×C3#577811yescharacteristic
991D3—22no—
992D3—41no—
993D3—42no—
994D3—122no—
995D3—121no—
996D3—122no—
997D3—121no—
998D3—122no—
999D3—242no—
1000D3—241no—
1001D3—241no—
1002D3—481no—
1003C22—22no—
1004C22—32no—
1005C22—41no—
1006C22—41no—
1007C22—61no—
1008C22—61no—
1009C22—61no—
1010C22—61no—
1011C22—61no—
1012C22—62no—
1013C22—121no—
1014C22—121no—
1015C22—181no—
1016C22—181no—
1017C22—182no—
1018C22—181no—
1019C22—244no—
1020C22—361no—
1021C22—361no—
1022C22—361no—
1023C22—361no—
1024C22—361no—
1025C22—724no—
1026C22—724no—
1027C22D32×D411yescharacteristic
1028C4—32no—
1029C4—41no—
1030C4—61no—
1031C4—62no—
1032C4—121no—
1033C4—121no—
1034C4—181no—
1035C4C2×D3×D1211yescharacteristic
1036C4D32×D411yescharacteristic
1037C3—21no—
1038C3#7888611yescharacteristic, complemented
1039C3#8014911yescharacteristic, complemented
1040C2—42no—
1041C2—62no—
1042C2—121no—
1043C2—122no—
1044C2—361no—
1045C2—362no—
1046C2—721no—
1047C2D3×#88211yescharacteristic
1048C2#1059473511yescharacteristic
1049C2#1059475111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3012
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. C2×#64314C2semidirect
2. C2×#63935C2semidirect
3. C2×#63794C2semidirect
4. #10594523C2semidirect
5. #10592472C2semidirect
6. C3×#4776C2semidirect
7. C3×#4771C2semidirect
8. #10591467C2semidirect
9. #10591448C2semidirect
10. #10590967C2semidirect
11. #10590961C2semidirect
12. #10590955C2semidirect
13. #10590617C2semidirect
14. #10590616C2semidirect
15. D3×#809C2semidirect
29. C2×#3799C22semidirect
32. C2×#3753C22semidirect
33. C2×#3745C22semidirect
34. #64104C22semidirect
35. C2×C3×#214C22semidirect
36. C2×C3×#204C22semidirect
37. C2×C3×ΓL(1,𝔽25)C22semidirect
38. C3×#897C22semidirect
39. C3×D3×C4⋊C4C22semidirect
43. #63909C22semidirect
46. #63871C22semidirect
47. C2×#3718C22semidirect
48. C2×#3717C22semidirect
49. C2×#3717C22semidirect
50. C2×#3714C22semidirect
51. C2×D3×C3⋊C8C22semidirect
53. C32×#102C22semidirect
54. #63647C22semidirect
55. #63636C22semidirect
56. C3×#832C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#816C22semidirect
59. C3×#810C22semidirect
60. C3×#809C22semidirect
61. #63564C22semidirect
62. #63562C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
87. #4776D3semidirect
92. #4771D3semidirect
111. C3×#237D4semidirect
137. D3×D12D4semidirect
210. C2×#214C2×D3semidirect
228. C2×#204C2×D3semidirect
229. C2×ΓL(1,𝔽25)C2×D3semidirect
233. #897C2×D3semidirect
241. D3×C4⋊C4C2×D3semidirect
249. C3×#102C2×D3semidirect
250. C3×#102C2×D3semidirect
253. #832C2×D3semidirect
262. (C2×D3)⋊C8C2×D3semidirect
263. #816C2×D3semidirect
264. #810C2×D3semidirect
270. #809C2×D3semidirect
401. #237D12semidirect
587. #102D32semidirect
911. C32#3012semidirect
1038. C3#78886semidirect
1039. C3#80149semidirect

Maximal subgroups

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

subgroupindex
C2×#643142
C2×#639352
C2×#637942
#105945232
#105924722
C3×#47762
C3×#47712
#105914672
#105914482
#105909672
#105909612
#105909552
#105906172
#105906162
D3×#8092
#801493
#788863