Finite Group Databasebeta

← #11889164

Subgroups — #11889164

Order 1152.

960 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595379C211yesmaximal, characteristic, complemented
2#10594621C211yesmaximal, characteristic
3#10592511C211yesmaximal, characteristic, complemented
4C3×#4817C211yesmaximal, characteristic, complemented
5C3×#4807C211yesmaximal, characteristic, complemented
6#10591652C211yesmaximal, characteristic, complemented
7#10591651C211yesmaximal, characteristic, complemented
8#10591617C211yesmaximal, characteristic, complemented
9#10590941C211yesmaximal, characteristic, complemented
10D3×#821C211yesmaximal, characteristic, complemented
11#10590882C211yesmaximal, characteristic, complemented
12#10590726C211yesmaximal, characteristic, complemented
13#10590545C211yesmaximal, characteristic, complemented
14#10590451C211yesmaximal, characteristic, complemented
15#10590438C211yesmaximal, characteristic, complemented
16#80685—31nomaximal
17#79800—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×D3×D12—21no—
20C2×D3×D12C2211yescharacteristic
21#64155C2211yescharacteristic, complemented
22C2×#3755C2211yescharacteristic, complemented
23C2×#3743C2211yescharacteristic, complemented
24#64104C2211yescharacteristic
25C3×#946C2211yescharacteristic, complemented
26C3×Q8×Dic3C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic, complemented
29C2×C3×D3×C8C2211yescharacteristic, complemented
30C3×#895C2211yescharacteristic
31C3×#893C2211yescharacteristic
32#63923—21no—
33#63922—21no—
34#63911C2211yescharacteristic
35#63906—21no—
36C4×#626C2211yescharacteristic
37#63890—21no—
38D3×C4⋊Dic3C2211yescharacteristic, complemented
39#63877—21no—
40#63869C2211yescharacteristic, complemented
41#63868—21no—
42#63849C2211yescharacteristic, complemented
43#63846—21no—
44C32×#103C2211yescharacteristic, complemented
45#63648C2211yescharacteristic, complemented
46#63634C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic
48C3×#821C2211yescharacteristic, complemented
49C3×#815C2211yescharacteristic, complemented
50C3×#808C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63564C2211yescharacteristic, complemented
54#63564C2211yescharacteristic, complemented
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61#5642—31no—
62#5609—31no—
63#5581—31no—
64D4×D12—31no—
65C3×#465—31no—
66C3×#440—31no—
67#5169—31no—
68#5169—31no—
69#5169—31no—
70#5163—31no—
71C2×#821—31no—
72#5111—31no—
73#5046—31no—
74#5033—31no—
75#5027—31no—
76#5009—31no—
77#4885—31no—
78#4882—31no—
79#4871—31no—
80#4866—31no—
81#4817D311yescharacteristic, complemented
82#4812—31no—
83#4812—31no—
84#4812—61no—
85#4807D311yescharacteristic, complemented
86#4770—31no—
87#4770—31no—
88D3×#102—31no—
89#4764—31no—
90#4713—31no—
91#4706—31no—
92C22×D32—21no—
93C22×D32—21no—
94C2×C32×Q8C2311yescharacteristic
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×#626—21no—
104C2×#626—21no—
105C2×#626—21no—
106C2×#626D411yescharacteristic
107C2×#625—21no—
108C2×D3×Dic3—21no—
109#3802—22no—
110#3802—41no—
111D3×D12—22no—
112D3×D12—44no—
113D3×D12—41no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116#3755—41no—
117#3752—21no—
118#3752—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122#3743—41no—
123C3×#215—22no—
124C3×#215—41no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×D3×C8—41no—
137#3724—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3D411yescharacteristic
141#3722—21no—
142#3722D411yescharacteristic
143(C2×D3)⋊Dic3D411yescharacteristic
144Dic32—21no—
145#3310—91noSylow
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×D3×D4—61no—
150C22×D12—31no—
151C22×D12—61no—
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C22×C3×C8—31no—
155C3×C22⋊Q8—31no—
156C3×#121—31no—
157C3×C4×Q8—31no—
158C3×C4×D4—31no—
159#946—31no—
160#946—31no—
161#946—61no—
162#946C2×D311yescharacteristic, complemented
163Q8×Dic3C2×D311yescharacteristic, complemented
164C2×#215—31no—
165C2×#215—31no—
166C2×#215—61no—
167C2×#215C2×D311yescharacteristic
168C2×#215C2×D311yescharacteristic, complemented
169#940—31no—
170#937—61no—
171#930—61no—
172C4×#67—31no—
173C2×C4⋊Dic3—31no—
174C2×ΓL(1,𝔽25)—31no—
175C2×ΓL(1,𝔽25)—31no—
176C2×ΓL(1,𝔽25)—61no—
177C2×D3×C8C2×D311yescharacteristic, complemented
178#898—61no—
179#895—31no—
180#895—31no—
181#895—61no—
182#895C2×D311yescharacteristic
183#894—61no—
184#893C2×D311yescharacteristic
185#892—31no—
186#892—31no—
187D3×C4⋊C4—31no—
188#890—31no—
189#890—61no—
190#889—61no—
191#886—61no—
192#884—61no—
193#882—61no—
194#882—61no—
195#882—61no—
196#877—61no—
197#876—61no—
198#874—31no—
199C4×D12—31no—
200#872—61no—
201#870—31no—
202C3×#107—31no—
203C3×#106—31no—
204C3×#103—21no—
205C3×#103C2×D311yescharacteristic, complemented
206C3×#103C2×D311yescharacteristic, complemented
207C3×#102—31no—
208C3×#102—31no—
209C3×#97—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#830—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821—61no—
222#821C2×D311yescharacteristic
223#821C2×D311yescharacteristic, complemented
224(C2×D3)⋊C8—31no—
225(C2×D3)⋊C8—31no—
226(C2×D3)⋊C8—31no—
227#815C2×D311yescharacteristic, complemented
228Dic3⋊C8—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#808C2×D311yescharacteristic, complemented
234#807—31no—
235#807—31no—
236#807—61no—
237#807C2×D311yescharacteristic, complemented
238C4⋊(C3⋊C8)—31no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3C2×D411yescharacteristic
244C2×D32—42no—
245C2×D32—42no—
246C2×D32—42no—
247C2×D32—42no—
248C2×D32—81no—
249C2×D32—81no—
250C32×Q8—21no—
251C32×Q8—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4C2411yescharacteristic
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3C2×D411yescharacteristic
257C4⋊(C3⋊D3)—21no—
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)—42no—
260C4×C3⋊D3—21no—
261C4×C3⋊D3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—42no—
271C3×D12#4112yes—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—42no—
275#626—22no—
276#626—42no—
277#626—42no—
278#626—81no—
279#625—42no—
280D3×Dic3—42no—
281C32×C8—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#552—91no—
286D42—91no—
287#490—91no—
288#482—91no—
289#480—91no—
290#478—91no—
291#468—91no—
292#465—31no—
293#460—91no—
294#450—91no—
295#450—91no—
296#440—31no—
297#435—91no—
298#418—91no—
299C2×#102—91no—
300C23×D3—61no—
301C23×D3—61no—
302C23×D3—61no—
303C23×D3—61no—
304C2×C3×Q8—21no—
305C2×C3×Q8C22×D311yescharacteristic
306C2×C3×Q8C22×D311yescharacteristic
307C2×C3×D4—31no—
308C2×C3×D4—31no—
309C2×C3×D4—61no—
310C22×C3×C4—31no—
311C22×C3×C4—61no—
312C2×#67—31no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C22×Dic3—61no—
319D3×D4—62no—
320D3×D4—62no—
321D3×D4—62no—
322D3×D4—121no—
323D3×D4—124no—
324D3×D4—121no—
325D3×D4—121no—
326C2×D12—21no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—31no—
330C2×D12—61no—
331C2×D12—62no—
332C2×D12—61no—
333C2×D12—61no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12—61no—
337C2×D12—121no—
338C2×D12—121no—
339C2×D12—124no—
340C2×D12C22×D311yescharacteristic
341C2×D12C22×D311yescharacteristic
342C2×C4×D3—21no—
343C2×C4×D3—31no—
344C2×C4×D3—31no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3C22×D311yescharacteristic
348C3×SD16—62no—
349C3×SD16—121no—
350C2×C3×C8—21no—
351C2×C3×C8—31no—
352C2×C3×C8—31no—
353C2×C3×C8—121no—
354C2×C3×C8C22×D311yescharacteristic
355C2×C3×C8C22×D311yescharacteristic
356C3×C4⋊C4—21no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C42—31no—
367C3×C42—61no—
368#217—31no—
369#215—22no—
370#215—41no—
371#215—121no—
372#215—121no—
373#215—122no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—31no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—31no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—121no—
387(C2×D3)⋊C4—121no—
388C4⋊Dic3—21no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3C22×D311yescharacteristic
396C4⋊Dic3C22×D311yescharacteristic
397Dic3⋊C4—21no—
398Dic3⋊C4—31no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—121no—
406C4×Dic3—21no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C4×Dic3C22×D311yescharacteristic
410C2×C3⋊C8—31no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—61no—
413C2×C3⋊C8C22×D311yescharacteristic
414C2×C3⋊C8C22×D311yescharacteristic
415ΓL(1,𝔽25)—121no—
416ΓL(1,𝔽25)—121no—
417ΓL(1,𝔽25)—122no—
418D3×C8—41no—
419C22×C32C22×D411yescharacteristic
420C2×C3⋊D3—21no—
421C2×C3⋊D3—21no—
422C2×C3⋊D3—21no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—22no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3AGL(1,ℤ/8)12yes—
435D32—84no—
436D32—84no—
437C32×C4—41no—
438C32×C4—41no—
439C32×C4C2×#4111yescharacteristic
440C32×C4H(5,𝔽2)11yescharacteristic
441C3⋊Dic3—21no—
442C3⋊Dic3—41no—
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C22×D4—91no—
449C22×D4—91no—
450C22×D4—181no—
451C2×SD16—31no—
452C2×SD16—31no—
453C2×SD16—91no—
454C2×M16—91no—
455C22×C8—31no—
456#127—91no—
457#126—181no—
458#125—91no—
459#125—181no—
460#123—181no—
461C22⋊Q8—31no—
462C22⋊Q8—91no—
463#121—31no—
464#121—91no—
465#121—181no—
466#120—181no—
467#120—181no—
468C4×Q8—31no—
469C4×D4—31no—
470C4×D4—91no—
471#117—91no—
472#117—181no—
473C2×C4⋊C4—91no—
474#107—31no—
475#107—91no—
476#106—31no—
477C4⋊C8—91no—
478#103D3211yescharacteristic, complemented
479#102—31no—
480#102—31no—
481#102—91no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488C22⋊C8—91no—
489C22⋊C8—91no—
490#97—31no—
491C23×C3—31no—
492C23×C3—61no—
493C23×C3—61no—
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—31no—
497C22×D3—31no—
498C22×D3—61no—
499C22×D3—61no—
500C22×D3—61no—
501C22×D3—121no—
502C22×D3—122no—
503C22×D3—122no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—241no—
511C22×D3—241no—
512C22×D3—241no—
513C22×D3—241no—
514C22×D3D3×D411yescharacteristic
515C3×Q8—21no—
516C3×Q8—21no—
517C3×Q8—21no—
518C3×Q8—21no—
519C3×Q8—41no—
520C3×Q8—41no—
521C3×D4—32no—
522C3×D4—61no—
523C3×D4—61no—
524C3×D4—61no—
525C3×D4—122no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—31no—
532C2×C3×C4—31no—
533C2×C3×C4—31no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—122no—
541C2×C3×C4C23×D311yescharacteristic
542C2×C3×C4C23×D311yescharacteristic
543#67—62no—
544#67—122no—
545#67—122no—
546#67—122no—
547#67—122no—
548#67—241no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—31no—
552C2×Dic3—31no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—121no—
557C2×Dic3—122no—
558C2×Dic3D3×D411yescharacteristic
559C2×Dic3D3×D411yescharacteristic
560C2×Dic3D3×D411yescharacteristic
561D12—21no—
562D12—21no—
563D12—21no—
564D12—42no—
565D12—62no—
566D12—61no—
567D12—61no—
568D12—61no—
569D12—61no—
570D12—121no—
571D12—121no—
572D12—122no—
573D12—122no—
574D12—122no—
575D12—122no—
576D12—242no—
577D12—241no—
578D12#23512yes—
579C4×D3—21no—
580C4×D3—21no—
581C4×D3—42no—
582C4×D3—61no—
583C4×D3—61no—
584C4×D3—61no—
585C4×D3—61no—
586C4×D3—121no—
587C4×D3—121no—
588C4×D3—122no—
589C3×C8—21no—
590C3×C8—21no—
591C3×C8—41no—
592C3×C8—61no—
593C3×C8—61no—
594C3⋊C8—21no—
595C3⋊C8—21no—
596C3⋊C8—62no—
597C3⋊C8—61no—
598C3⋊C8—61no—
599C2×C32#54611yescharacteristic
600C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
601C2×C32#57711yescharacteristic
602C3⋊D3—41no—
603C3⋊D3—81no—
604C3×D3—22no—
605C3×D3—42no—
606C3×D3—81no—
607C24—181no—
608C24—181no—
609C2×Q8C2×D3211yescharacteristic
610C2×D4—31no—
611C2×D4—31no—
612C2×D4—61no—
613C2×D4—91no—
614C2×D4—91no—
615C2×D4—181no—
616C2×D4—181no—
617C2×D4—181no—
618C2×D4—181no—
619C2×D4—182no—
620C2×D4—181no—
621C2×D4—182no—
622C2×D4—361no—
623C2×D4—364no—
624C2×D4—361no—
625C22×C4—31no—
626C22×C4—61no—
627C22×C4—91no—
628C22×C4—181no—
629SD16—62no—
630SD16—121no—
631SD16—361no—
632M16—361no—
633C2×C8—31no—
634C2×C8—31no—
635C2×C8—91no—
636C2×C8—121no—
637C2×C8C2×D3211yescharacteristic
638C4⋊C4—31no—
639C4⋊C4—31no—
640C4⋊C4—61no—
641C4⋊C4—61no—
642C4⋊C4—91no—
643C4⋊C4—91no—
644C4⋊C4—181no—
645C4⋊C4—181no—
646C4⋊C4—181no—
647C4⋊C4—181no—
648C4⋊C4C2×D3211yescharacteristic
649C22⋊C4—61no—
650C22⋊C4—61no—
651C22⋊C4—61no—
652C22⋊C4—91no—
653C22⋊C4—91no—
654C22⋊C4—181no—
655C22⋊C4—181no—
656C22⋊C4—181no—
657C42—31no—
658C42—61no—
659C42—181no—
660C22×C3—21no—
661C22×C3—32no—
662C22×C3—61no—
663C22×C3—61no—
664C22×C3—62no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3C2×D3×D411yescharacteristic
671C22×C3C2×D3×D411yescharacteristic
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—22no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—61no—
681C2×D3—61no—
682C2×D3—61no—
683C2×D3—61no—
684C2×D3—61no—
685C2×D3—61no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—121no—
691C2×D3—121no—
692C2×D3—121no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—241no—
696C2×D3—241no—
697C2×D3—241no—
698C2×D3—244no—
699C2×D3—244no—
700C2×D3—244no—
701C2×D3—244no—
702C2×D3#91412yes—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—41no—
706C3×C4—41no—
707C3×C4—41no—
708C3×C4—41no—
709C3×C4—61no—
710C3×C4—61no—
711C3×C4—61no—
712C3×C4—81no—
713C3×C4—81no—
714C3×C4—121no—
715C3×C4—121no—
716C3×C4C2×#23511yescharacteristic
717C3×C4#100411yescharacteristic
718C3×C4D3×#4111yescharacteristic
719C3×C4#100911yescharacteristic
720Dic3—21no—
721Dic3—21no—
722Dic3—21no—
723Dic3—41no—
724Dic3—41no—
725Dic3—61no—
726Dic3—61no—
727Dic3—121no—
728Dic3—121no—
729Dic3—121no—
730Dic3—241no—
731C32#331011yescharacteristic, complemented, Sylow
732C23—31no—
733C23—61no—
734C23—61no—
735C23—91no—
736C23—181no—
737C23—362no—
738C23—362no—
739C23—362no—
740C23—362no—
741C23—721no—
742C23—721no—
743Q8—21no—
744Q8—21no—
745D4—32no—
746D4—61no—
747D4—61no—
748D4—61no—
749D4—122no—
750D4—182no—
751D4—181no—
752D4—181no—
753D4—362no—
754D4—362no—
755D4—362no—
756D4—362no—
757D4—721no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—31no—
761C2×C4—31no—
762C2×C4—31no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—91no—
768C2×C4—122no—
769C2×C4—181no—
770C2×C4—181no—
771C2×C4—181no—
772C2×C4—362no—
773C2×C4C22×D3211yescharacteristic
774C8—21no—
775C8—61no—
776C8—61no—
777C8—181no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—62no—
782C2×C3—122no—
783C2×C3—241no—
784C2×C3#555011yescharacteristic
785C2×C3#561011yescharacteristic
786C2×C3C2×#91411yescharacteristic
787C2×C3#577011yescharacteristic
788C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
789C2×C3#577811yescharacteristic
790D3—22no—
791D3—42no—
792D3—81no—
793D3—121no—
794D3—121no—
795D3—241no—
796D3—241no—
797D3—241no—
798D3—481no—
799C22—32no—
800C22—61no—
801C22—61no—
802C22—62no—
803C22—121no—
804C22—121no—
805C22—121no—
806C22—121no—
807C22—121no—
808C22—181no—
809C22—181no—
810C22—181no—
811C22—361no—
812C22—361no—
813C22—361no—
814C22—724no—
815C22—724no—
816C22D32×D411yescharacteristic
817C4—41no—
818C4—41no—
819C4—61no—
820C4—61no—
821C4—61no—
822C4—121no—
823C4—121no—
824C4—181no—
825C4—361no—
826C4D3×#23511yescharacteristic
827C4#6431411yescharacteristic
828C3—21no—
829C3#7980011yescharacteristic, complemented
830C3#8068511yescharacteristic, complemented
831C2—62no—
832C2—122no—
833C2—241no—
834C2—361no—
835C2—721no—
836C2#1059428311yescharacteristic
837C2D3×#91411yescharacteristic
838C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10594621C2
hypercenter#103D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595379C2semidirect
3. #10592511C2semidirect
4. C3×#4817C2semidirect
5. C3×#4807C2semidirect
6. #10591652C2semidirect
7. #10591651C2semidirect
8. #10591617C2semidirect
9. #10590941C2semidirect
10. D3×#821C2semidirect
11. #10590882C2semidirect
12. #10590726C2semidirect
13. #10590545C2semidirect
14. #10590451C2semidirect
15. #10590438C2semidirect
21. #64155C22semidirect
22. C2×#3755C22semidirect
23. C2×#3743C22semidirect
25. C3×#946C22semidirect
26. C3×Q8×Dic3C22semidirect
28. C2×C3×#215C22semidirect
29. C2×C3×D3×C8C22semidirect
38. D3×C4⋊Dic3C22semidirect
40. #63869C22semidirect
42. #63849C22semidirect
44. C32×#103C22semidirect
45. #63648C22semidirect
46. #63634C22semidirect
48. C3×#821C22semidirect
49. C3×#815C22semidirect
50. C3×#808C22semidirect
51. C3×#807C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
53. #63564C22semidirect
54. #63564C22semidirect
56. #63563C22semidirect
58. #63562C22semidirect
59. #63557C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
81. #4817D3semidirect
85. #4807D3semidirect
162. #946C2×D3semidirect
163. Q8×Dic3C2×D3semidirect
168. C2×#215C2×D3semidirect
177. C2×D3×C8C2×D3semidirect
205. C3×#103C2×D3semidirect
206. C3×#103C2×D3semidirect
223. #821C2×D3semidirect
227. #815C2×D3semidirect
233. #808C2×D3semidirect
237. #807C2×D3semidirect
478. #103D32semidirect
731. C32#3310semidirect
829. C3#79800semidirect
830. C3#80685semidirect

Maximal subgroups

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

subgroupindex
#105953792
#105946212
#105925112
C3×#48172
C3×#48072
#105916522
#105916512
#105916172
#105909412
D3×#8212
#105908822
#105907262
#105905452
#105904512
#105904382
#806853
#798003