Finite Group Databasebeta

← #11889092

Subgroups — #11889092

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 837 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5513C211yesmaximal, characteristic, complemented
2D12×#67C211yesmaximal, characteristic
3#10592666C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic, complemented
5#10591177C211yesmaximal, characteristic, complemented
6#10591169C211yesmaximal, characteristic, complemented
7#10591155C211yesmaximal, characteristic, complemented
8#10590596C211yesmaximal, characteristic, complemented
9#10590592C211yesmaximal, characteristic, complemented
10#10590550C211yesmaximal, characteristic, complemented
11#10590549C211yesmaximal, characteristic, complemented
12#10590503C211yesmaximal, characteristic, complemented
13#10590502C211yesmaximal, characteristic, complemented
14#10590467C211yesmaximal, characteristic, complemented
15#10590454C211yesmaximal, characteristic, complemented
16#83599—31nomaximal
17#78762—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×D12C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic, complemented
22#64139C2211yescharacteristic
23C3×#929—21no—
24C3×C4×#67C2211yescharacteristic
25C3×#926—21no—
26C3×#924C2211yescharacteristic, complemented
27C22×C3×C3⋊C8C2211yescharacteristic, complemented
28C3×#898—21no—
29C3×#897C2211yescharacteristic, complemented
30C3×#892C2211yescharacteristic, complemented
31C3×#890C2211yescharacteristic, complemented
32C3×#889—21no—
33C3×#887C2211yescharacteristic, complemented
34#63977—21no—
35#63922—21no—
36#63911C2211yescharacteristic
37#63908C2211yescharacteristic
38Dic3×D12C2211yescharacteristic
39#63886—21no—
40C2×#3717C2211yescharacteristic, complemented
41C2×#3715C2211yescharacteristic
42C2×#3715C2211yescharacteristic, complemented
43C2×#3711C2211yescharacteristic, complemented
44#63657C2211yescharacteristic, complemented
45#63636C2211yescharacteristic, complemented
46#63636C2211yescharacteristic, complemented
47#63634C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic
50C3×#809C2211yescharacteristic
51C3×#809C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61C3×#552—31no—
62D4×#67—31no—
63D4×D12—31no—
64#5513D311yescharacteristic, complemented
65C2×C3×#102—31no—
66#5218—31no—
67#5114—31no—
68#5111—31no—
69#5067—31no—
70#5066—31no—
71#5049—31no—
72#5048—31no—
73#5046—31no—
74#5046—31no—
75#5027—31no—
76#5026—31no—
77#5011—31no—
78#5003—31no—
79#5001—31no—
80#4967—31no—
81#4967—31no—
82#4967—61no—
83C2×#809D311yescharacteristic, complemented
84#4780—31no—
85#4779—31no—
86#4776—31no—
87#4770—31no—
88#4764—31no—
89#4763—31no—
90#4762—31no—
91#4757—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C22×C32×C4—21no—
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C3×#67D411yescharacteristic
99C2×C3×D12—22no—
100C2×C3×D12—21no—
101C2×C3×D12—41no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106D3×#67—44no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#625—21no—
111C2×D3×Dic3—21no—
112D3×D12—22no—
113D3×D12—41no—
114C32×C4⋊C4—21no—
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#217—21no—
122C3×#217D411yescharacteristic
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8—41no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141#3717—41no—
142#3715—22no—
143#3715—41no—
144#3711—41no—
145#3310—91noSylow
146C22×C3×D4—31no—
147C22×#67—61no—
148C2×D3×D4—31no—
149C2×D3×D4—61no—
150C22×D12—31no—
151C22×D12C2×D311yescharacteristic
152C22×C3×C8—31no—
153C3×#126—61no—
154C3×#125—31no—
155C3×#125—61no—
156C3×#123—61no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—31no—
159C3×C4×Q8—31no—
160C3×C4×D4—31no—
161C3×#117—31no—
162C3×#117—61no—
163C2×C3×C4⋊C4—21no—
164C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
165C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
166#953—61no—
167C2×#215—31no—
168C2×#215—31no—
169C2×#215—31no—
170#940—31no—
171#939—61no—
172#938—31no—
173#937—61no—
174D4×Dic3—31no—
175C2×#214—31no—
176C2×#214—31no—
177#930—31no—
178#930—31no—
179#930—31no—
180#930—61no—
181#929—21no—
182C4×#67C2×D311yescharacteristic
183#926—21no—
184#924C2×D311yescharacteristic, complemented
185C2×#208—31no—
186C22×C3⋊C8C2×D311yescharacteristic, complemented
187C2×#204—31no—
188C2×ΓL(1,𝔽25)—31no—
189#898—21no—
190#897C2×D311yescharacteristic, complemented
191#895—61no—
192#892C2×D311yescharacteristic, complemented
193#890C2×D311yescharacteristic, complemented
194#889—21no—
195#887C2×D311yescharacteristic, complemented
196#882—61no—
197#882—61no—
198#874—31no—
199C4×D12—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#102—31no—
204#835—31no—
205#832—31no—
206#832—31no—
207#830—31no—
208#830—31no—
209#830—31no—
210#830—61no—
211#821—31no—
212(C2×D3)⋊C8—31no—
213#817—31no—
214#816—31no—
215#815—31no—
216Dic3⋊C8—31no—
217#809—31no—
218#809—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—61no—
225#809—61no—
226#809C2×D311yescharacteristic
227#809C2×D311yescharacteristic
228#809C2×D311yescharacteristic, complemented
229#809C2×D311yescharacteristic, complemented
230#808—31no—
231#807—31no—
232#807—31no—
233#807—31no—
234#807—31no—
235#807—61no—
236#807—61no—
237C4⋊(C3⋊C8)—31no—
238#803—31no—
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—42no—
244C22×C3×D3—42no—
245C22×C3×D3—81no—
246C22×C3×D3C2×D411yescharacteristic
247C2×D32—42no—
248C2×D32—42no—
249C2×D32—81no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—42no—
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2411yescharacteristic
257#638—42no—
258C2×C3⋊Dic3—21no—
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)—21no—
261C3×#67—22no—
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×Dic6—21no—
275C3×Dic6—21no—
276#626—42no—
277#626—42no—
278#626—81no—
279#625—42no—
280D3×Dic3—42no—
281C3⋊(C3⋊C8)—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#552—31no—
286D42—91no—
287#490—91no—
288#482—91no—
289#480—91no—
290#478—91no—
291#468—91no—
292#465—91no—
293#460—91no—
294#450—91no—
295#450—91no—
296#440—91no—
297#435—91no—
298#418—91no—
299C2×#102—31no—
300C24×C3—61no—
301C23×D3—21no—
302C23×D3—61no—
303C23×D3—61no—
304C2×C3×Q8—31no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C2×C3×D4—62no—
309C2×C3×D4—61no—
310C2×C3×D4—121no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—31no—
315C22×C3×C4—41no—
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—121no—
326C2×#67—124no—
327C2×#67#6711yescharacteristic
328C22×Dic3—61no—
329D3×D4—62no—
330D3×D4—121no—
331D3×D4—124no—
332C2×D12—22no—
333C2×D12—21no—
334C2×D12—31no—
335C2×D12—31no—
336C2×D12—41no—
337C2×D12—61no—
338C2×D12—62no—
339C2×D12—61no—
340C2×D12—61no—
341C2×D12—61no—
342C2×D12—121no—
343C2×D12C22×D311yescharacteristic
344C2×D12C22×D311yescharacteristic
345C2×C4×D3—61no—
346C2×C4×D3C22×D311yescharacteristic
347C2×Dic6C22×D311yescharacteristic
348C2×C3×C8—31no—
349C2×C3×C8—31no—
350C2×C3×C8—121no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—41no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C4⋊C4C22×D311yescharacteristic
367C3×C22⋊C4—31no—
368C3×C22⋊C4—31no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C42—31no—
373C3×C42—61no—
374C3×C42—61no—
375#217—21no—
376#217—61no—
377#217—61no—
378#217#6711yescharacteristic
379#215—62no—
380#215—121no—
381#215—121no—
382#214—62no—
383#214—121no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—121no—
391(C2×D3)⋊C4#6711yescharacteristic
392C4⋊Dic3—21no—
393C4⋊Dic3—21no—
394C4⋊Dic3—31no—
395C4⋊Dic3—31no—
396C4⋊Dic3—61no—
397C4⋊Dic3C22×D311yescharacteristic
398Dic3⋊C4—21no—
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401Dic3⋊C4#6711yescharacteristic
402C4×Dic3—21no—
403C4×Dic3—21no—
404C4×Dic3C22×D311yescharacteristic
405#208—121no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—41no—
411C2×C3⋊C8—61no—
412C2×C3⋊C8—61no—
413C2×C3⋊C8C22×D311yescharacteristic
414C2×C3⋊C8C22×D311yescharacteristic
415#204—121no—
416ΓL(1,𝔽25)—121no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32AGL(1,ℤ/8)12yes—
420C22×C32C22×D411yescharacteristic
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3×D3—22no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—84no—
434D32—84no—
435C32×C4—21no—
436C32×C4—41no—
437C32×C4—41no—
438C32×C4C2×#4111yescharacteristic
439C32×C4H(5,𝔽2)11yescharacteristic
440C3⋊Dic3—41no—
441C3×Dic3—21no—
442C3×Dic3—21no—
443C3×Dic3—21no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C22×D4—31no—
447C22×D4—91no—
448C22×D4—181no—
449C2×SD16—91no—
450C2×SD16—91no—
451C2×SD16—91no—
452C2×M16—91no—
453C22×C8—31no—
454#127—91no—
455#126—61no—
456#125—31no—
457#125—61no—
458#123—61no—
459C22⋊Q8—31no—
460C22⋊Q8—31no—
461#121—91no—
462#121—91no—
463#121—181no—
464#120—181no—
465#120—181no—
466C4×Q8—31no—
467C4×D4—31no—
468C4×D4—91no—
469#117—31no—
470#117—61no—
471C2×C4⋊C4D3211yescharacteristic, complemented
472#107—91no—
473#107—91no—
474#106—91no—
475C4⋊C8—91no—
476#103—91no—
477#102—31no—
478#102—31no—
479#102—31no—
480#102—31no—
481#102—91no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102—91no—
486C22⋊C8—91no—
487C22⋊C8—91no—
488#97—91no—
489C23×C3—21no—
490C23×C3—31no—
491C23×C3—61no—
492C23×C3—61no—
493C23×C3—122no—
494C23×C3—122no—
495C23×C3—241no—
496C23×C3D3×D411yescharacteristic
497C23×C3C2×#6711yescharacteristic
498C22×D3—21no—
499C22×D3—21no—
500C22×D3—42no—
501C22×D3—42no—
502C22×D3—61no—
503C22×D3—61no—
504C22×D3—81no—
505C22×D3—121no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—241no—
511C22×D3—241no—
512C22×D3C2×#6711yescharacteristic
513C3×Q8—61no—
514C3×Q8—61no—
515C3×D4—32no—
516C3×D4—62no—
517C3×D4—61no—
518C3×D4—61no—
519C3×D4—61no—
520C3×D4—122no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
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—41no—
537C2×C3×C4—41no—
538C2×C3×C4—42no—
539C2×C3×C4—42no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—82no—
545C2×C3×C4D3×D411yescharacteristic
546C2×C3×C4C2×#6711yescharacteristic
547C2×C3×C4C23×D311yescharacteristic
548C2×C3×C4C23×D311yescharacteristic
549#67—22no—
550#67—122no—
551#67—122no—
552#67—122no—
553#67—122no—
554#67—122no—
555#67—122no—
556#67—242no—
557#67—241no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—121no—
563C2×Dic3—122no—
564C2×Dic3C2×#6711yescharacteristic
565C2×Dic3C2×#6711yescharacteristic
566C2×Dic3C2×#6711yescharacteristic
567D12—21no—
568D12—21no—
569D12—21no—
570D12—42no—
571D12—61no—
572D12—61no—
573D12—61no—
574D12—61no—
575D12—121no—
576D12—121no—
577D12—122no—
578D12—122no—
579D12—241no—
580D12#23512yes—
581C4×D3—21no—
582C4×D3—21no—
583C4×D3—122no—
584Dic6—21no—
585Dic6—21no—
586C3×C8—61no—
587C3×C8—61no—
588C3⋊C8—21no—
589C3⋊C8—21no—
590C3⋊C8—61no—
591C3⋊C8—61no—
592C3⋊C8—61no—
593C3⋊C8—61no—
594C3⋊C8—121no—
595C3⋊C8—121no—
596C2×C32—22no—
597C2×C32#54611yescharacteristic
598C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
599C2×C32#57711yescharacteristic
600C3⋊D3—81no—
601C3×D3—41no—
602C3×D3—42no—
603C3×D3—81no—
604C24—61no—
605C24—181no—
606C2×Q8—31no—
607C2×D4—31no—
608C2×D4—31no—
609C2×D4—31no—
610C2×D4—62no—
611C2×D4—61no—
612C2×D4—91no—
613C2×D4—121no—
614C2×D4—181no—
615C2×D4—181no—
616C2×D4—181no—
617C2×D4—182no—
618C2×D4—181no—
619C2×D4—181no—
620C2×D4—361no—
621C2×D4—364no—
622C22×C4—21no—
623C22×C4—31no—
624C22×C4—181no—
625C22×C4C2×D3211yescharacteristic
626SD16—182no—
627SD16—361no—
628SD16—361no—
629M16—361no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—91no—
633C2×C8—91no—
634C2×C8—121no—
635C4⋊C4—21no—
636C4⋊C4—31no—
637C4⋊C4—31no—
638C4⋊C4—61no—
639C4⋊C4—61no—
640C4⋊C4—61no—
641C4⋊C4—61no—
642C4⋊C4—61no—
643C4⋊C4—91no—
644C4⋊C4C2×D3211yescharacteristic
645C4⋊C4C2×D3211yescharacteristic
646C22⋊C4—31no—
647C22⋊C4—31no—
648C22⋊C4—61no—
649C22⋊C4—61no—
650C22⋊C4—61no—
651C22⋊C4—181no—
652C22⋊C4—181no—
653C22⋊C4—181no—
654C42—31no—
655C42—61no—
656C42—61no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—22no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—61no—
666C22×C3—61no—
667C22×C3—61no—
668C22×C3—62no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—244no—
675C22×C3#91112yes—
676C22×C3#94912yes—
677C22×C3C2×D3×D411yescharacteristic
678C22×C3C22×#6711yescharacteristic
679C2×D3—22no—
680C2×D3—21no—
681C2×D3—21no—
682C2×D3—21no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—84no—
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—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—21no—
704C3×C4—41no—
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—121no—
726Dic3—121no—
727Dic3—241no—
728C32#331011yescharacteristic, complemented, Sylow
729C23—31no—
730C23—61no—
731C23—61no—
732C23—122no—
733C23—122no—
734C23—181no—
735C23—241no—
736C23—362no—
737C23—362no—
738C23—721no—
739C23D3×#6711yescharacteristic
740Q8—61no—
741Q8—61no—
742D4—32no—
743D4—62no—
744D4—61no—
745D4—61no—
746D4—61no—
747D4—122no—
748D4—181no—
749D4—181no—
750D4—362no—
751D4—362no—
752D4—362no—
753D4—362no—
754D4—721no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—31no—
760C2×C4—31no—
761C2×C4—31no—
762C2×C4—42no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—181no—
768C2×C4—362no—
769C2×C4D3×#6711yescharacteristic
770C2×C4C22×D3211yescharacteristic
771C8—61no—
772C8—61no—
773C8—181no—
774C8—181no—
775C2×C3—22no—
776C2×C3—22no—
777C2×C3—21no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—42no—
781C2×C3—122no—
782C2×C3—121no—
783C2×C3—241no—
784C2×C3#549011yescharacteristic
785C2×C3C2×#91111yescharacteristic
786C2×C3#576211yescharacteristic
787C2×C3C2×#94911yescharacteristic
788C2×C3#582911yescharacteristic
789C2×C3#583711yescharacteristic
790D3—41no—
791D3—42no—
792D3—81no—
793D3—241no—
794D3—241no—
795D3—481no—
796C22—21no—
797C22—21no—
798C22—61no—
799C22—61no—
800C22—61no—
801C22—62no—
802C22—121no—
803C22—121no—
804C22—121no—
805C22—121no—
806C22—121no—
807C22—244no—
808C22—361no—
809C22—361no—
810C22—361no—
811C22—724no—
812C22#6392512yes—
813C22C2×D3×#6711yescharacteristic
814C4—21no—
815C4—41no—
816C4—41no—
817C4—61no—
818C4—61no—
819C4—61no—
820C4—121no—
821C4—121no—
822C4—361no—
823C4D3×#23511yescharacteristic
824C4#6430711yescharacteristic
825C3—21no—
826C3#7876211yescharacteristic, complemented
827C3#8359911yescharacteristic, complemented
828C2—22no—
829C2—121no—
830C2—122no—
831C2—241no—
832C2—721no—
833C2#1059506511yescharacteristic
834C2C2×#6392511yescharacteristic
835C2#1059531811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalD12×#67C2
hypercenterC2×C4⋊C4D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#5513C2semidirect
3. #10592666C2semidirect
4. C2×C3×#809C2semidirect
5. #10591177C2semidirect
6. #10591169C2semidirect
7. #10591155C2semidirect
8. #10590596C2semidirect
9. #10590592C2semidirect
10. #10590550C2semidirect
11. #10590549C2semidirect
12. #10590503C2semidirect
13. #10590502C2semidirect
14. #10590467C2semidirect
15. #10590454C2semidirect
21. C2×C32×C4⋊C4C22semidirect
26. C3×#924C22semidirect
27. C22×C3×C3⋊C8C22semidirect
29. C3×#897C22semidirect
30. C3×#892C22semidirect
31. C3×#890C22semidirect
33. C3×#887C22semidirect
40. C2×#3717C22semidirect
42. C2×#3715C22semidirect
43. C2×#3711C22semidirect
44. #63657C22semidirect
45. #63636C22semidirect
46. #63636C22semidirect
47. #63634C22semidirect
48. #63634C22semidirect
51. C3×#809C22semidirect
52. C3×#809C22semidirect
53. #63573C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63566C22semidirect
56. #63564C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63554C22semidirect
64. #5513D3semidirect
83. C2×#809D3semidirect
164. C2×C3×C4⋊C4C2×D3semidirect
165. C2×C3×C4⋊C4C2×D3semidirect
184. #924C2×D3semidirect
186. C22×C3⋊C8C2×D3semidirect
190. #897C2×D3semidirect
192. #892C2×D3semidirect
193. #890C2×D3semidirect
195. #887C2×D3semidirect
228. #809C2×D3semidirect
229. #809C2×D3semidirect
471. C2×C4⋊C4D32semidirect
728. C32#3310semidirect
826. C3#78762semidirect
827. C3#83599semidirect

Maximal subgroups

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

subgroupindex
C3×#55132
D12×#672
#105926662
C2×C3×#8092
#105911772
#105911692
#105911552
#105905962
#105905922
#105905502
#105905492
#105905032
#105905022
#105904672
#105904542
#835993
#787623