Finite Group Databasebeta

← #11864585

Subgroups — #11864585

Order 1152.

1622 conjugacy classes of subgroups.

The subgroup lattice has 1047 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64314C211yesmaximal, characteristic, complemented
2C2×#63933C211yesmaximal, characteristic, complemented
3C2×#63795C211yesmaximal, characteristic, complemented
4#10594522C211yesmaximal, characteristic, complemented
5#10592475C211yesmaximal, characteristic, complemented
6C3×#4773C211yesmaximal, characteristic, complemented
7C3×#4771C211yesmaximal, characteristic, complemented
8#10591459C211yesmaximal, characteristic, complemented
9#10591456C211yesmaximal, characteristic, complemented
10#10590970C211yesmaximal, characteristic, complemented
11#10590963C211yesmaximal, characteristic, complemented
12#10590955C211yesmaximal, characteristic, complemented
13#10590618C211yesmaximal, characteristic, complemented
14#10590615C211yesmaximal, characteristic, complemented
15D3×#809C211yesmaximal, characteristic, complemented
16#80005—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×#3798C2211yescharacteristic
30C2×#3796C2211yescharacteristic
31C2×#3795C2211yescharacteristic, complemented
32C2×#3754C2211yescharacteristic, complemented
33C2×#3744C2211yescharacteristic, complemented
34#64106C2211yescharacteristic, complemented
35C2×C3×#213C2211yescharacteristic, complemented
36C2×C3×D24C2211yescharacteristic, complemented
37C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
38C3×#895C2211yescharacteristic, complemented
39C3×D3×C4⋊C4C2211yescharacteristic, complemented
40#63933—24no—
41#63916C2211yescharacteristic, complemented
42#63908—21no—
43#63906—21no—
44#63893—21no—
45#63886—21no—
46#63857C2211yescharacteristic, complemented
47C2×#3719C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63795—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×#912—31no—
69C2×#911—31no—
70C2×#908—31no—
71#5608—31no—
72#5510—31no—
73C3×#447—31no—
74C3×#417—31no—
75#5218—31no—
76#5158—31no—
77#5156—31no—
78#5129—31no—
79#5037—31no—
80C2×#809—31no—
81#4810—31no—
82#4810—31no—
83#4808—31no—
84#4808—31no—
85#4783—31no—
86#4776—31no—
87#4776—31no—
88#4776—31no—
89#4776—61no—
90#4773—31no—
91#4773D311yescharacteristic, complemented
92#4771D311yescharacteristic, complemented
93D3×#102—31no—
94#4733—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)C2311yescharacteristic
104C2×C4×C3⋊D3C2311yescharacteristic
105C2×#634C2311yescharacteristic
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C22×C3×Dic3—21no—
109C3×#237—22no—
110C3×#237D414yescomplemented
111C3×D3×D4—22no—
112C3×D3×D4—22no—
113C2×C3×D12—21no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×C4×D3C2311yescharacteristic
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×#626D411yescharacteristic
129C2×#626D411yescharacteristic
130C2×#625—21no—
131C2×#625D411yescharacteristic
132C2×#624—21no—
133#3804—28no—
134C2×D3×Dic3—21no—
135C2×D3×Dic3—21no—
136D3×D12—22no—
137D3×D12D414yescomplemented
138#3799—22no—
139#3799—22no—
140#3798—22no—
141#3798—22no—
142#3796—22no—
143#3796—22no—
144#3795—22no—
145#3795—22no—
146C2×C32×C8C2311yescharacteristic
147C32×C4⋊C4C2311yescharacteristic
148#3754—22no—
149#3752—21no—
150C4⋊(C3⋊Dic3)—21no—
151C2×C3⋊(C3⋊C8)C2311yescharacteristic
152#3744—22no—
153C3×#213—22no—
154C3×(C2×D3)⋊C4—21no—
155C3×C4⋊Dic3C2311yescharacteristic
156C3×Dic3⋊C4—21no—
157C2×C3×C3⋊C8C2311yescharacteristic
158C2×C3×C3⋊C8C2311yescharacteristic
159C3×D24—22no—
160C3×ΓL(1,𝔽25)—22no—
161Dic3⋊Dic3—21no—
162(C2×D3)⋊Dic3—21no—
163(C2×D3)⋊Dic3—21no—
164#3719—22no—
165#3716—22no—
166#3715—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—
178#1004—64no—
179#1004—64no—
180C2×#237—31no—
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×D8—31no—
200C2×C3×D8—31no—
201C2×C3×M16—31no—
202C3×#121—31no—
203C2×C3×C4⋊C4—31no—
204#950—64no—
205C2×#216—31no—
206C2×#215—31no—
207#939—61no—
208#938—31no—
209#938—61no—
210C2×#214—31no—
211C2×#214—31no—
212C2×#214—31no—
213C2×#214—31no—
214C2×#214—61no—
215C2×#213—31no—
216C2×#213C2×D311yescharacteristic, complemented
217#930—61no—
218#930—61no—
219#924—31no—
220C22×C3⋊C8—31no—
221#912—64no—
222#911—64no—
223#908—64no—
224C2×Dic12—31no—
225C2×D24—31no—
226C2×D24C2×D311yescharacteristic, complemented
227C2×#204—31no—
228C2×#204—31no—
229C2×#204—31no—
230C2×#204—61no—
231C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
232C2×D3×C8—31no—
233#897—31no—
234#897—31no—
235#897—31no—
236#897—61no—
237#897—61no—
238#895—31no—
239#895—61no—
240#895C2×D311yescharacteristic, complemented
241D3×C4⋊C4C2×D311yescharacteristic, complemented
242#884—61no—
243#878—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—81no—
275C22×C3⋊D3—81no—
276C22×C3⋊D3C2×D411yescharacteristic
277C22×C3×D3—21no—
278C22×C3×D3—24no—
279C22×C3×D3—21no—
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⋊Dic3—21no—
293C2×C3⋊Dic3C2×D411yescharacteristic
294C4⋊(C3⋊D3)—21no—
295C4⋊(C3⋊D3)C2×D412yes—
296C4×C3⋊D3—21no—
297C4×C3⋊D3—21no—
298#634—21no—
299#634—21no—
300C3×#67—24no—
301C3×#67—24no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—24no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3C2×D411yescharacteristic
306C2×C3×Dic3C2×D411yescharacteristic
307C3×D12—21no—
308C3×D12—21no—
309C3×D12—21no—
310C3×D12—81no—
311C3×D12C2×D412yes—
312C3×C4×D3—21no—
313C3×C4×D3—21no—
314C3×C4×D3—81no—
315C3×C4×D3C2×D412yes—
316C3×C4×D3C2×D412yes—
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—81no—
326#625—22no—
327#625—42no—
328#624—24no—
329D3×Dic3—24no—
330D3×Dic3—42no—
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—91no—
342#450—91no—
343#449—91no—
344#449—91no—
345#447—31no—
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×D4—21no—
361C2×C3×D4—31no—
362C2×C3×D4—31no—
363C2×C3×D4—61no—
364C2×C3×D4—61no—
365C2×C3×D4—62no—
366C2×C3×D4—61no—
367C2×C3×D4—62no—
368C2×C3×D4C22×D311yescharacteristic
369C2×C3×D4C22×D311yescharacteristic
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—61no—
373C22×C3×C4—61no—
374C2×#67—21no—
375C2×#67—21no—
376C2×#67—31no—
377C2×#67—31no—
378C2×#67—31no—
379C2×#67—31no—
380C2×#67—61no—
381C2×#67—61no—
382C2×#67—68no—
383C2×#67—61no—
384C2×#67—61no—
385C2×#67—61no—
386C2×#67—68no—
387C2×#67—61no—
388C2×#67—61no—
389C2×#67—61no—
390C2×#67—121no—
391C22×Dic3—21no—
392C22×Dic3—61no—
393C22×Dic3—61no—
394#239—62no—
395#239—62no—
396#239—62no—
397#239—62no—
398#237—22no—
399#237—62no—
400#237—68no—
401#237—62no—
402#237—62no—
403#237—62no—
404#237D1214yescomplemented
405D3×D4—22no—
406D3×D4—22no—
407D3×D4—34no—
408D3×D4—62no—
409D3×D4—62no—
410D3×D4—68no—
411D3×D4—68no—
412D3×D4—68no—
413D3×D4—62no—
414D3×D4—62no—
415D3×D4—62no—
416D3×D4—122no—
417D3×D4—122no—
418#235—62no—
419#235—62no—
420#235—62no—
421#235—68no—
422#235—62no—
423#235—62no—
424#235—62no—
425#235—62no—
426#235—62no—
427C2×D12—21no—
428C2×D12—31no—
429C2×D12—31no—
430C2×D12—34no—
431C2×D12—31no—
432C2×D12—31no—
433C2×D12—61no—
434C2×D12—62no—
435C2×D12—61no—
436C2×D12—61no—
437C2×D12—68no—
438C2×D12—61no—
439C2×D12—61no—
440C2×D12C22×D311yescharacteristic
441C2×D12C22×D311yescharacteristic
442C2×C4×D3—21no—
443C2×C4×D3—31no—
444C2×C4×D3—31no—
445C2×C4×D3—61no—
446C2×C4×D3—61no—
447C2×C4×D3—61no—
448C2×C4×D3—61no—
449C2×C4×D3—61no—
450C2×C4×D3C22×D311yescharacteristic
451C2×C4×D3C22×D311yescharacteristic
452C2×Dic6—31no—
453C2×Dic6—31no—
454C2×Dic6—31no—
455C2×Dic6—31no—
456C2×Dic6—61no—
457C2×Dic6C22×D311yescharacteristic
458C3×D8—62no—
459C3×D8—62no—
460C3×M16—62no—
461C2×C3×C8—21no—
462C2×C3×C8—31no—
463C2×C3×C8—31no—
464C2×C3×C8C22×D311yescharacteristic
465C2×C3×C8C22×D311yescharacteristic
466C3×C4⋊C4—21no—
467C3×C4⋊C4—31no—
468C3×C4⋊C4—61no—
469C3×C4⋊C4C22×D311yescharacteristic
470C3×C4⋊C4C22×D311yescharacteristic
471C3×C22⋊C4—61no—
472#217—61no—
473#217—61no—
474#216—62no—
475#215—62no—
476#214—62no—
477#214—62no—
478#214—62no—
479#214—62no—
480#214—122no—
481#213—22no—
482#213—62no—
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—121no—
489C4⋊Dic3—61no—
490C4⋊Dic3—61no—
491C4⋊Dic3—61no—
492C4⋊Dic3—121no—
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
502Dic12—62no—
503D24—22no—
504D24—62no—
505#204—62no—
506#204—62no—
507#204—62no—
508#204—122no—
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—84no—
522C2×C3×D3—21no—
523C2×C3×D3—21no—
524C2×C3×D3—22no—
525C2×C3×D3—21no—
526C2×C3×D3—21no—
527C2×C3×D3—21no—
528C2×C3×D3—41no—
529C2×C3×D3—41no—
530C2×C3×D3—41no—
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—41no—
541C3×Dic3—22no—
542C3×Dic3—21no—
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—91no—
563C2×SD16—91no—
564C2×SD16—91no—
565C2×SD16—91no—
566C2×D8—31no—
567C2×D8—31no—
568C2×D8—91no—
569C2×M16—31no—
570C22×C8—91no—
571C22⋊Q8—91no—
572C22⋊Q8—91no—
573C22⋊Q8—181no—
574#121—31no—
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—61no—
600C23×C3—241no—
601C23×C3—241no—
602C22×D3—21no—
603C22×D3—24no—
604C22×D3—21no—
605C22×D3—31no—
606C22×D3—31no—
607C22×D3—61no—
608C22×D3—64no—
609C22×D3—61no—
610C22×D3—61no—
611C22×D3—64no—
612C22×D3—64no—
613C22×D3—64no—
614C22×D3—81no—
615C22×D3—81no—
616C22×D3—121no—
617C22×D3—124no—
618C22×D3—241no—
619C22×D3—241no—
620C22×D3—241no—
621C22×D3—241no—
622C22×D3—241no—
623C22×D3—241no—
624C22×D3—241no—
625C22×D3—241no—
626C22×D3—242no—
627C22×D3—242no—
628C22×D3D3×D411yescharacteristic
629C22×D3D3×D411yescharacteristic
630C3×Q8—32no—
631C3×Q8—61no—
632C3×D4—21no—
633C3×D4—21no—
634C3×D4—22no—
635C3×D4—32no—
636C3×D4—41no—
637C3×D4—64no—
638C3×D4—64no—
639C3×D4—61no—
640C3×D4—61no—
641C3×D4—61no—
642C3×D4—241no—
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—241no—
659C2×C3×C4C23×D311yescharacteristic
660C2×C3×C4C23×D311yescharacteristic
661#67—24no—
662#67—24no—
663#67—62no—
664#67—64no—
665#67—64no—
666#67—62no—
667#67—64no—
668#67—64no—
669#67—62no—
670#67—62no—
671#67—64no—
672#67—124no—
673#67—122no—
674#67—122no—
675#67—241no—
676C2×Dic3—21no—
677C2×Dic3—24no—
678C2×Dic3—21no—
679C2×Dic3—31no—
680C2×Dic3—31no—
681C2×Dic3—61no—
682C2×Dic3—64no—
683C2×Dic3—61no—
684C2×Dic3—61no—
685C2×Dic3—121no—
686C2×Dic3—122no—
687C2×Dic3D3×D411yescharacteristic
688C2×Dic3D3×D411yescharacteristic
689D12—21no—
690D12—21no—
691D12—21no—
692D12—32no—
693D12—32no—
694D12—62no—
695D12—62no—
696D12—64no—
697D12—64no—
698D12—64no—
699D12—62no—
700D12—61no—
701D12—61no—
702D12—81no—
703D12—121no—
704D12—241no—
705D12D3×D412yes—
706C4×D3—21no—
707C4×D3—21no—
708C4×D3—64no—
709C4×D3—64no—
710C4×D3—64no—
711C4×D3—61no—
712C4×D3—61no—
713C4×D3—61no—
714C4×D3—61no—
715C4×D3—81no—
716C4×D3—121no—
717C4×D3—121no—
718C4×D3—122no—
719C4×D3C2×D1212yes—
720C4×D3D3×D412yes—
721Dic6—21no—
722Dic6—62no—
723Dic6—62no—
724Dic6—61no—
725Dic6—61no—
726Dic6—61no—
727Dic6—61no—
728Dic6—121no—
729Dic6—121no—
730Dic6C2×D1212yes—
731C3×C8—21no—
732C3×C8—21no—
733C3×C8—41no—
734C3×C8—61no—
735C3×C8—61no—
736C3⋊C8—21no—
737C3⋊C8—21no—
738C3⋊C8—61no—
739C3⋊C8—61no—
740C3⋊C8—121no—
741C2×C32—42no—
742C2×C32C2×#12011yescharacteristic
743C2×C32#57611yescharacteristic
744C2×C32#57711yescharacteristic
745C3⋊D3—41no—
746C3⋊D3—42no—
747C3×D3—22no—
748C3×D3—42no—
749C3×D3—41no—
750C3×D3—81no—
751C24—61no—
752C24—181no—
753C24—181no—
754#41—34no—
755#41—62no—
756#41—182no—
757#41—182no—
758#41—182no—
759#41—182no—
760#41—188no—
761#41—182no—
762#41—182no—
763#41—182no—
764#41—182no—
765C2×Q8—31no—
766C2×Q8—91no—
767C2×Q8—91no—
768C2×D4—31no—
769C2×D4—31no—
770C2×D4—61no—
771C2×D4—61no—
772C2×D4—62no—
773C2×D4—61no—
774C2×D4—62no—
775C2×D4—94no—
776C2×D4—91no—
777C2×D4—91no—
778C2×D4—91no—
779C2×D4—91no—
780C2×D4—182no—
781C2×D4—181no—
782C2×D4—181no—
783C2×D4—181no—
784C2×D4—188no—
785C2×D4—181no—
786C2×D4—181no—
787C2×D4—182no—
788C2×D4—188no—
789C2×D4—188no—
790C2×D4—182no—
791C2×D4—181no—
792C2×D4C2×D3211yescharacteristic
793C22×C4—31no—
794C22×C4—31no—
795C22×C4—61no—
796C22×C4—61no—
797C22×C4—91no—
798C22×C4—181no—
799C22×C4—181no—
800C22×C4—181no—
801Q16—182no—
802SD16—182no—
803SD16—182no—
804SD16—182no—
805SD16—182no—
806D8—62no—
807D8—62no—
808D8—182no—
809M16—62no—
810C2×C8—31no—
811C2×C8—31no—
812C2×C8—91no—
813C2×C8—182no—
814C2×C8C2×D3211yescharacteristic
815C4⋊C4—31no—
816C4⋊C4—61no—
817C4⋊C4—181no—
818C4⋊C4—181no—
819C4⋊C4C2×D3211yescharacteristic
820C22⋊C4—61no—
821C22⋊C4—181no—
822C22⋊C4—181no—
823C22⋊C4—181no—
824C22×C3—22no—
825C22×C3—22no—
826C22×C3—21no—
827C22×C3—32no—
828C22×C3—42no—
829C22×C3—41no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—41no—
833C22×C3—61no—
834C22×C3—61no—
835C22×C3—62no—
836C22×C3—61no—
837C22×C3—61no—
838C22×C3—61no—
839C22×C3—81no—
840C22×C3—81no—
841C22×C3—121no—
842C22×C3—121no—
843C22×C3—121no—
844C22×C3—121no—
845C22×C3—121no—
846C22×C3—244no—
847C22×C3C2×D3×D411yescharacteristic
848C22×C3C2×D3×D411yescharacteristic
849C2×D3—21no—
850C2×D3—21no—
851C2×D3—21no—
852C2×D3—21no—
853C2×D3—21no—
854C2×D3—22no—
855C2×D3—41no—
856C2×D3—41no—
857C2×D3—41no—
858C2×D3—41no—
859C2×D3—41no—
860C2×D3—62no—
861C2×D3—62no—
862C2×D3—61no—
863C2×D3—61no—
864C2×D3—61no—
865C2×D3—61no—
866C2×D3—61no—
867C2×D3—62no—
868C2×D3—61no—
869C2×D3—84no—
870C2×D3—121no—
871C2×D3—121no—
872C2×D3—122no—
873C2×D3—121no—
874C2×D3—121no—
875C2×D3—121no—
876C2×D3—121no—
877C2×D3—241no—
878C2×D3—241no—
879C2×D3—244no—
880C2×D3—244no—
881C2×D3—244no—
882C2×D3—244no—
883C2×D3—248no—
884C2×D3#88212yes—
885C3×C4—21no—
886C3×C4—21no—
887C3×C4—32no—
888C3×C4—41no—
889C3×C4—41no—
890C3×C4—61no—
891C3×C4—62no—
892C3×C4—81no—
893C3×C4—121no—
894C3×C4C22×D1211yescharacteristic
895C3×C4C2×D3×D411yescharacteristic
896C3×C4C2×D3×D411yescharacteristic
897C3×C4C2×D3×D411yescharacteristic
898Dic3—22no—
899Dic3—21no—
900Dic3—41no—
901Dic3—61no—
902Dic3—61no—
903Dic3—121no—
904Dic3—121no—
905Dic3—121no—
906Dic3—241no—
907Dic3#88212yes—
908C32#301211yescharacteristic, complemented, Sylow
909C23—21no—
910C23—31no—
911C23—31no—
912C23—64no—
913C23—61no—
914C23—61no—
915C23—91no—
916C23—184no—
917C23—184no—
918C23—181no—
919C23—241no—
920C23—241no—
921C23—721no—
922C23—721no—
923C23—721no—
924C23—721no—
925Q8—32no—
926Q8—61no—
927Q8—182no—
928Q8—181no—
929Q8—181no—
930D4—21no—
931D4—32no—
932D4—64no—
933D4—64no—
934D4—61no—
935D4—61no—
936D4—61no—
937D4—92no—
938D4—182no—
939D4—184no—
940D4—182no—
941D4—184no—
942D4—184no—
943D4—184no—
944D4—182no—
945D4—181no—
946D4—241no—
947D4—362no—
948D4—721no—
949D4D3×D1212yes—
950C2×C4—21no—
951C2×C4—31no—
952C2×C4—32no—
953C2×C4—32no—
954C2×C4—31no—
955C2×C4—64no—
956C2×C4—61no—
957C2×C4—61no—
958C2×C4—61no—
959C2×C4—61no—
960C2×C4—91no—
961C2×C4—184no—
962C2×C4—184no—
963C2×C4—181no—
964C2×C4—181no—
965C2×C4—181no—
966C2×C4—241no—
967C2×C4—362no—
968C2×C4C22×D3211yescharacteristic
969C8—21no—
970C8—61no—
971C8—61no—
972C8—181no—
973C2×C3—21no—
974C2×C3—21no—
975C2×C3—21no—
976C2×C3—42no—
977C2×C3—42no—
978C2×C3—62no—
979C2×C3—82no—
980C2×C3—122no—
981C2×C3—121no—
982C2×C3—241no—
983C2×C3C2×#88211yescharacteristic
984C2×C3D3×#12011yescharacteristic
985C2×C3#575711yescharacteristic
986C2×C3#577411yescharacteristic
987C2×C3#577511yescharacteristic
988C2×C3#577811yescharacteristic
989D3—22no—
990D3—41no—
991D3—42no—
992D3—81no—
993D3—122no—
994D3—121no—
995D3—122no—
996D3—121no—
997D3—122no—
998D3—242no—
999C22—22no—
1000C22—32no—
1001C22—41no—
1002C22—41no—
1003C22—61no—
1004C22—61no—
1005C22—61no—
1006C22—61no—
1007C22—61no—
1008C22—62no—
1009C22—121no—
1010C22—121no—
1011C22—121no—
1012C22—121no—
1013C22—121no—
1014C22—181no—
1015C22—181no—
1016C22—182no—
1017C22—181no—
1018C22—244no—
1019C22—361no—
1020C22—361no—
1021C22—724no—
1022C22—724no—
1023C22D32×D411yescharacteristic
1024C4—32no—
1025C4—41no—
1026C4—61no—
1027C4—62no—
1028C4—121no—
1029C4—181no—
1030C4—361no—
1031C4C2×D3×D1211yescharacteristic
1032C4D32×D411yescharacteristic
1033C3—21no—
1034C3#7888611yescharacteristic, complemented
1035C3#8000511yescharacteristic, complemented
1036C2—42no—
1037C2—62no—
1038C2—121no—
1039C2—122no—
1040C2—241no—
1041C2—361no—
1042C2—362no—
1043C2D3×#88211yescharacteristic
1044C2#1059473211yescharacteristic
1045C2#1059475411yescharacteristic
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×#63933C2semidirect
3. C2×#63795C2semidirect
4. #10594522C2semidirect
5. #10592475C2semidirect
6. C3×#4773C2semidirect
7. C3×#4771C2semidirect
8. #10591459C2semidirect
9. #10591456C2semidirect
10. #10590970C2semidirect
11. #10590963C2semidirect
12. #10590955C2semidirect
13. #10590618C2semidirect
14. #10590615C2semidirect
15. D3×#809C2semidirect
31. C2×#3795C22semidirect
32. C2×#3754C22semidirect
33. C2×#3744C22semidirect
34. #64106C22semidirect
35. C2×C3×#213C22semidirect
36. C2×C3×D24C22semidirect
37. C2×C3×ΓL(1,𝔽25)C22semidirect
38. C3×#895C22semidirect
39. C3×D3×C4⋊C4C22semidirect
41. #63916C22semidirect
46. #63857C22semidirect
47. C2×#3719C22semidirect
48. C2×#3716C22semidirect
49. C2×#3715C22semidirect
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
91. #4773D3semidirect
92. #4771D3semidirect
110. C3×#237D4semidirect
137. D3×D12D4semidirect
216. C2×#213C2×D3semidirect
226. C2×D24C2×D3semidirect
231. C2×ΓL(1,𝔽25)C2×D3semidirect
240. #895C2×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
404. #237D12semidirect
587. #102D32semidirect
908. C32#3012semidirect
1034. C3#78886semidirect
1035. C3#80005semidirect

Maximal subgroups

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

subgroupindex
C2×#643142
C2×#639332
C2×#637952
#105945222
#105924752
C3×#47732
C3×#47712
#105914592
#105914562
#105909702
#105909632
#105909552
#105906182
#105906152
D3×#8092
#800053
#788863