Finite Group Databasebeta

← #13175954

Subgroups — #13175954

Order 1728.

1804 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723926C211yesmaximal, characteristic, complemented
2C3×#64093C211yesmaximal, characteristic, complemented
3C32×#67⋊C4C211yesmaximal, characteristic, complemented
4#11723643C211yesmaximal, characteristic, complemented
5#11723632C211yesmaximal, characteristic, complemented
6#11723615C211yesmaximal, characteristic, complemented
7#11723605C211yesmaximal, characteristic, complemented
8#11723541C211yesmaximal, characteristic, complemented
9D3×#3752C211yesmaximal, characteristic, complemented
10C4×#6290C211yesmaximal, characteristic, complemented
11#11723496C211yesmaximal, characteristic, complemented
12#11723453C211yesmaximal, characteristic, complemented
13#11723439C211yesmaximal, characteristic, complemented
14#11723433C211yesmaximal, characteristic, complemented
15#11723417C211yesmaximal, characteristic, complemented
16#10596031—31nomaximal
17#10594297—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C2×#6312C2211yescharacteristic
20C2×#6308C2211yescharacteristic, complemented
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic, complemented
23C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
24C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic
26C22×C32×Dic3C2211yescharacteristic, complemented
27C2×C32×C4×D3C2211yescharacteristic
28C2×#6292C2211yescharacteristic
29C2×#6290C2211yescharacteristic
30C2×D3×C3⋊Dic3C2211yescharacteristic
31C33×C22⋊C4C2211yescharacteristic, complemented
32#88864C2211yescharacteristic, complemented
33#88859C2211yescharacteristic
34#88859C2211yescharacteristic
35C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
36C3×#3752C2211yescharacteristic
37C3×#3750C2211yescharacteristic, complemented
38C32×(C2×D3)⋊C4C2211yescharacteristic
39C32×Dic3⋊C4C2211yescharacteristic, complemented
40C32×C4×Dic3C2211yescharacteristic, complemented
41#88807C2211yescharacteristic, complemented
42#88806C2211yescharacteristic, complemented
43#88806C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45#88804C2211yescharacteristic
46#88804C2211yescharacteristic
47#88803C2211yescharacteristic
48#88803C2211yescharacteristic
49#88803C2211yescharacteristic
50#88803C2211yescharacteristic, complemented
51#88803C2211yescharacteristic, complemented
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
53C32×C4×D4—31no—
54#64148—31no—
55#64146—31no—
56#64139—31no—
57#64138—31no—
58C4×#638—31no—
59C2×#3752—31no—
60#64107—31no—
61#64103—31no—
62#64094—31no—
63#64094—34no—
64#64094—64no—
65#64093D311yescharacteristic, complemented
66#64091—31no—
67#64087—31no—
68#64085—31no—
69#64084—31no—
70C3×#884—34no—
71C3×#67⋊C4D314yescomplemented
72#63983—34no—
73#63978—34no—
74#63970—34no—
75#63961—34no—
76#63922—34no—
77D3×(C2×D3)⋊C4—34no—
78C4×#625—34no—
79#63896—34no—
80#63868—34no—
81#63862—34no—
82#63860—34no—
83#63850—34no—
84C23×C33C2311yescharacteristic
85C22×C3⋊(C3⋊D3)C2311yescharacteristic
86C22×C3×C3⋊D3C2311yescharacteristic
87C22×C3×C3⋊D3C2311yescharacteristic
88C22×C32×D3C2311yescharacteristic
89C2×D3×C3⋊D3—22no—
90C2×D3×C3⋊D3—41no—
91C2×D3×C3⋊D3—41no—
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94#6312—41no—
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98#6308—41no—
99C3×#638—41no—
100C3×#638—41no—
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C3×C4⋊(C3⋊D3)—41no—
104C3×C4×C3⋊D3—41no—
105C32×#67—22no—
106C2×C32×Dic3—41no—
107C2×C32×Dic3C2311yescharacteristic
108C2×C32×Dic3C2311yescharacteristic
109C2×C32×Dic3C2311yescharacteristic
110C32×C4×D3—41no—
111#6292—41no—
112#6290—22no—
113D3×C3⋊Dic3—41no—
114#5613—91no—
115#5560—94no—
116C23×C3⋊D3—31no—
117C22×D32—34no—
118C2×C32×D4—31no—
119C22×C32×C4—31no—
120C22×C32×C4—31no—
121C2×#638—31no—
122C2×#638—31no—
123C2×#638—34no—
124C2×#638—64no—
125C2×#638C2×D311yescharacteristic
126C2×#638C2×D311yescharacteristic, complemented
127C22×C3⋊Dic3—31no—
128C2×C4⋊(C3⋊D3)—31no—
129C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
130C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
131C2×#634—31no—
132C2×#634—34no—
133C2×#634—64no—
134C2×C3×#67—34no—
135C2×C3×#67—34no—
136C2×C3×#67C2×D314yes—
137C22×C3×Dic3C2×D314yescomplemented
138C2×C3×D12—34no—
139C2×C3×C4×D3—34no—
140C2×C3×C4×D3C2×D314yes—
141C2×#626—34no—
142C2×#625—34no—
143C2×D3×Dic3—34no—
144C32×C4⋊C4—31no—
145C32×C22⋊C4—24no—
146C32×C22⋊C4—31no—
147C32×C22⋊C4C2×D314yescomplemented
148C32×C22⋊C4C2×D311yescharacteristic, complemented
149C32×C42—31no—
150#3757—31no—
151#3757—34no—
152#3757—31no—
153#3757—64no—
154#3752—31no—
155#3752—31no—
156#3752—31no—
157#3752—31no—
158#3752—31no—
159#3752—31no—
160#3752—31no—
161#3752—34no—
162#3752—34no—
163#3752—31no—
164#3752—31no—
165#3752—64no—
166#3752—64no—
167#3752C2×D311yescharacteristic
168C4⋊(C3⋊Dic3)—31no—
169#3750—31no—
170#3750—31no—
171#3750—31no—
172#3750C2×D311yescharacteristic, complemented
173C4×C3⋊Dic3—31no—
174C4×C3⋊Dic3—34no—
175C4×C3⋊Dic3—64no—
176C3×(C2×D3)⋊C4—34no—
177C3×(C2×D3)⋊C4C2×D314yes—
178C3×Dic3⋊C4—34no—
179C3×Dic3⋊C4C2×D314yescomplemented
180C3×C4×Dic3C2×D314yescomplemented
181#3724—34no—
182#3724—34no—
183Dic3⋊Dic3—34no—
184Dic3⋊Dic3—34no—
185#3722—34no—
186#3722—34no—
187(C2×D3)⋊Dic3—34no—
188(C2×D3)⋊Dic3—34no—
189(C2×D3)⋊Dic3—34no—
190(C2×D3)⋊Dic3—34no—
191(C2×D3)⋊Dic3—34no—
192(C2×D3)⋊Dic3—34no—
193C22×C33—21no—
194C22×C33—21no—
195C22×C33—21no—
196C22×C33C2411yescharacteristic
197C2×C3⋊(C3⋊D3)—21no—
198C2×C3⋊(C3⋊D3)—21no—
199C2×C3⋊(C3⋊D3)—21no—
200C2×C3×C3⋊D3—21no—
201C2×C3×C3⋊D3—21no—
202C2×C3×C3⋊D3—21no—
203C2×C3×C3⋊D3—21no—
204C2×C3×C3⋊D3—21no—
205C2×C3×C3⋊D3—21no—
206C2×C32×D3—21no—
207C2×C32×D3—21no—
208C2×C32×D3#4112yes—
209D3×C3⋊D3—44no—
210C33×C4—21no—
211C33×C4—21no—
212C3⋊(C3⋊Dic3)—21no—
213C3⋊(C3⋊Dic3)—21no—
214C3⋊(C3⋊Dic3)—21no—
215C3×C3⋊Dic3—21no—
216C3×C3⋊Dic3—21no—
217C32×Dic3—21no—
218C32×Dic3—21no—
219C32×Dic3—21no—
220C3×#121—91no—
221C3×C4×D4—34no—
222#939—94no—
223#939—91no—
224#938—91no—
225#937—94no—
226#937—91no—
227#937—91no—
228#936—91no—
229#935—91no—
230#930—94no—
231#929—94no—
232#929—91no—
233C4×#67—94no—
234C4×#67—91no—
235C2×(C2×D3)⋊C4—94no—
236#898—94no—
237#898—91no—
238#896—91no—
239#894—94no—
240#885—94no—
241#885—91no—
242#885—184no—
243#884—34no—
244#882—94no—
245#67⋊C4C3⋊D311yescharacteristic, complemented
246D3×C22⋊C4—91no—
247#879—91no—
248#878—94no—
249#876—94no—
250#875—94no—
251C23×C32—24no—
252C23×C32—31no—
253C23×C32C22×D314yes—
254C23×C32C22×D311yescharacteristic
255C22×C3⋊D3—31no—
256C22×C3⋊D3—34no—
257C22×C3⋊D3—64no—
258C22×C3⋊D3—62no—
259C22×C3⋊D3—121no—
260C22×C3⋊D3—121no—
261C22×C3⋊D3C22×D311yescharacteristic
262C22×C3⋊D3C22×D311yescharacteristic
263C22×C3×D3—34no—
264C22×C3×D3—34no—
265C22×C3×D3C22×D314yes—
266C2×D32—68no—
267C2×D32—124no—
268C2×D32—124no—
269C32×D4—62no—
270C2×C32×C4—24no—
271C2×C32×C4—24no—
272C2×C32×C4—31no—
273C2×C32×C4—31no—
274C2×C32×C4—31no—
275C2×C32×C4—121no—
276C2×C32×C4—121no—
277C2×C32×C4C22×D314yes—
278C2×C32×C4C22×D314yes—
279C2×C32×C4C22×D311yescharacteristic
280C2×C32×C4C22×D311yescharacteristic
281#638—41no—
282#638—41no—
283#638—62no—
284#638—121no—
285#638—124no—
286#638—128no—
287C2×C3⋊Dic3—31no—
288C2×C3⋊Dic3—31no—
289C2×C3⋊Dic3—31no—
290C2×C3⋊Dic3—34no—
291C2×C3⋊Dic3—34no—
292C2×C3⋊Dic3—34no—
293C2×C3⋊Dic3—64no—
294C2×C3⋊Dic3—64no—
295C2×C3⋊Dic3—64no—
296C2×C3⋊Dic3—121no—
297C2×C3⋊Dic3C22×D311yescharacteristic
298C2×C3⋊Dic3C22×D311yescharacteristic
299C4⋊(C3⋊D3)—41no—
300C4⋊(C3⋊D3)—121no—
301C4×C3⋊D3—41no—
302#634—121no—
303#634—124no—
304#634—128no—
305C3×#67—28no—
306C3×#67—124no—
307C3×#67—124no—
308C2×C3×Dic3—34no—
309C2×C3×Dic3—34no—
310C2×C3×Dic3—44no—
311C2×C3×Dic3C22×D314yes—
312C2×C3×Dic3C22×D314yes—
313C2×C3×Dic3C22×D314yes—
314C3×D12—124no—
315C3×C4×D3—44no—
316C3×C4×D3—124no—
317#626—124no—
318#625—68no—
319D3×Dic3—124no—
320#538—271noSylow
321C2×C33—41no—
322C2×C33C2×#4111yescharacteristic
323C2×C33H(5,𝔽2)11yescharacteristic
324C2×C33H(5,𝔽2)11yescharacteristic
325C3⋊(C3⋊D3)—41no—
326C3×C3⋊D3—41no—
327C3×C3⋊D3—41no—
328C32×D3—22no—
329C23×D3—94no—
330C23×D3—91no—
331C2×C3×D4—34no—
332C2×C3×D4—91no—
333C2×C3×D4—91no—
334C2×C3×D4—91no—
335C22×C3×C4—34no—
336C22×C3×C4—34no—
337C22×C3×C4—91no—
338C2×#67—34no—
339C2×#67—34no—
340C2×#67—94no—
341C2×#67—91no—
342C2×#67—94no—
343C2×#67—91no—
344C2×#67—91no—
345C2×#67—184no—
346C2×#67C2×C3⋊D311yescharacteristic
347C22×Dic3—94no—
348C22×Dic3C2×C3⋊D311yescharacteristic, complemented
349C2×D12—34no—
350C2×D12—94no—
351C2×C4×D3—34no—
352C2×C4×D3—91no—
353C2×C4×D3C2×C3⋊D311yescharacteristic
354C2×Dic6—94no—
355C2×Dic6—91no—
356C2×Dic6—184no—
357C3×C4⋊C4—34no—
358C3×C4⋊C4—91no—
359C3×C22⋊C4—24no—
360C3×C22⋊C4—34no—
361C3×C22⋊C4—91no—
362C3×C22⋊C4D3214yescomplemented
363C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
364C3×C42—34no—
365#217—94no—
366#217—94no—
367#217—91no—
368#217—91no—
369#217—91no—
370#217—91no—
371#217—91no—
372#217—91no—
373#217—184no—
374(C2×D3)⋊C4—34no—
375(C2×D3)⋊C4—94no—
376(C2×D3)⋊C4—94no—
377(C2×D3)⋊C4—94no—
378(C2×D3)⋊C4—94no—
379(C2×D3)⋊C4—94no—
380(C2×D3)⋊C4—94no—
381(C2×D3)⋊C4—94no—
382(C2×D3)⋊C4—91no—
383(C2×D3)⋊C4—94no—
384(C2×D3)⋊C4—94no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—91no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—184no—
390(C2×D3)⋊C4—184no—
391(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
392C4⋊Dic3—94no—
393C4⋊Dic3—91no—
394Dic3⋊C4—34no—
395Dic3⋊C4—94no—
396Dic3⋊C4—94no—
397Dic3⋊C4—94no—
398Dic3⋊C4—91no—
399Dic3⋊C4—91no—
400Dic3⋊C4—91no—
401Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
402C4×Dic3—94no—
403C4×Dic3—91no—
404C4×Dic3—184no—
405C4×Dic3C2×C3⋊D311yescharacteristic, complemented
406C22×C32—21no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—24no—
410C22×C32—24no—
411C22×C32—24no—
412C22×C32—24no—
413C22×C32—32no—
414C22×C32—44no—
415C22×C32—44no—
416C22×C32—44no—
417C22×C32—61no—
418C22×C32—61no—
419C22×C32C23×D314yes—
420C22×C32C23×D311yescharacteristic
421C2×C3⋊D3—21no—
422C2×C3⋊D3—21no—
423C2×C3⋊D3—21no—
424C2×C3⋊D3—21no—
425C2×C3⋊D3—21no—
426C2×C3⋊D3—21no—
427C2×C3⋊D3—61no—
428C2×C3⋊D3—61no—
429C2×C3⋊D3—61no—
430C2×C3⋊D3—64no—
431C2×C3⋊D3—64no—
432C2×C3⋊D3—64no—
433C2×C3⋊D3—124no—
434C2×C3⋊D3—124no—
435C2×C3⋊D3—124no—
436C2×C3⋊D3—124no—
437C2×C3×D3—24no—
438C2×C3×D3—24no—
439C2×C3×D3—64no—
440C2×C3×D3—64no—
441C2×C3×D3—64no—
442C2×C3×D3—64no—
443C2×C3×D3—64no—
444C2×C3×D3—64no—
445C2×C3×D3#23518yes—
446D32—1216no—
447C32×C4—21no—
448C32×C4—21no—
449C32×C4—24no—
450C32×C4—24no—
451C32×C4—44no—
452C32×C4—44no—
453C32×C4—61no—
454C32×C4—61no—
455C32×C4—61no—
456C3⋊Dic3—21no—
457C3⋊Dic3—21no—
458C3⋊Dic3—68no—
459C3⋊Dic3—61no—
460C3⋊Dic3—61no—
461C3⋊Dic3—61no—
462C3⋊Dic3—64no—
463C3⋊Dic3—64no—
464C3⋊Dic3—64no—
465C3⋊Dic3—124no—
466C3⋊Dic3—124no—
467C3×Dic3—24no—
468C3×Dic3—24no—
469C3×Dic3—24no—
470C3×Dic3—64no—
471C3×Dic3—64no—
472#126—271no—
473#126—271no—
474#124—271no—
475#124—271no—
476#123—271no—
477#123—271no—
478C22⋊Q8—271no—
479#121—91no—
480#121—271no—
481#121—271no—
482#120—271no—
483#120—271no—
484C4×D4—31no—
485C4×D4—271no—
486C2×C22⋊C4—271no—
487C33#53811yescharacteristic, complemented, Sylow
488C23×C3—24no—
489C23×C3—34no—
490C23×C3—91no—
491C23×C3—91no—
492C23×C3C2×D3214yes—
493C23×C3C22×C3⋊D311yescharacteristic
494C22×D3—34no—
495C22×D3—34no—
496C22×D3—94no—
497C22×D3—91no—
498C22×D3—184no—
499C22×D3—188no—
500C22×D3—182no—
501C22×D3—361no—
502C22×D3—361no—
503C22×D3—364no—
504C22×D3—364no—
505C22×D3C22×C3⋊D311yescharacteristic
506C3×D4—68no—
507C3×D4—361no—
508C3×D4—361no—
509C3×D4—361no—
510C2×C3×C4—24no—
511C2×C3×C4—24no—
512C2×C3×C4—34no—
513C2×C3×C4—34no—
514C2×C3×C4—34no—
515C2×C3×C4—91no—
516C2×C3×C4—91no—
517C2×C3×C4—124no—
518C2×C3×C4—124no—
519C2×C3×C4—361no—
520C2×C3×C4C2×D3214yes—
521C2×C3×C4C2×D3214yes—
522C2×C3×C4C22×C3⋊D311yescharacteristic
523C2×C3×C4C22×C3⋊D311yescharacteristic
524#67—22no—
525#67—124no—
526#67—124no—
527#67—188no—
528#67—182no—
529#67—361no—
530#67—364no—
531#67—361no—
532#67—368no—
533C2×Dic3—34no—
534C2×Dic3—34no—
535C2×Dic3—41no—
536C2×Dic3—94no—
537C2×Dic3—94no—
538C2×Dic3—94no—
539C2×Dic3—91no—
540C2×Dic3—91no—
541C2×Dic3—91no—
542C2×Dic3—184no—
543C2×Dic3—184no—
544C2×Dic3—184no—
545C2×Dic3—364no—
546C2×Dic3C22×C3⋊D311yescharacteristic
547C2×Dic3C22×C3⋊D311yescharacteristic
548C2×Dic3C22×C3⋊D311yescharacteristic
549D12—124no—
550D12—364no—
551C4×D3—41no—
552C4×D3—124no—
553C4×D3—361no—
554Dic6—364no—
555Dic6—361no—
556Dic6—368no—
557C2×C32—24no—
558C2×C32—24no—
559C2×C32—24no—
560C2×C32—41no—
561C2×C32—44no—
562C2×C32—62no—
563C2×C32—84no—
564C2×C32C2×#23514yes—
565C2×C32#100414yes—
566C2×C32#100411yescharacteristic
567C2×C32#100411yescharacteristic
568C2×C32D3×#4111yescharacteristic
569C2×C32#100914yes—
570C3⋊D3—41no—
571C3⋊D3—41no—
572C3⋊D3—121no—
573C3⋊D3—124no—
574C3⋊D3—244no—
575C3×D3—28no—
576C3×D3—124no—
577C3×D3—124no—
578C24—271no—
579C2×Q8—271no—
580C2×D4—31no—
581C2×D4—91no—
582C2×D4—91no—
583C2×D4—91no—
584C2×D4—271no—
585C2×D4—271no—
586C2×D4—271no—
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—91no—
590C22×C4—271no—
591C4⋊C4—31no—
592C4⋊C4—91no—
593C4⋊C4—271no—
594C4⋊C4—271no—
595C4⋊C4—271no—
596C4⋊C4—271no—
597C22⋊C4—31no—
598C22⋊C4—91no—
599C22⋊C4—271no—
600C22⋊C4—271no—
601C22⋊C4—271no—
602C22⋊C4—271no—
603C22⋊C4—271no—
604C22⋊C4—271no—
605C22⋊C4—271no—
606C22⋊C4—271no—
607C22⋊C4—271no—
608C22⋊C4—271no—
609C22⋊C4—271no—
610C22⋊C4D3×C3⋊D311yescharacteristic, complemented
611C42—31no—
612C42—271no—
613C22×C3—24no—
614C22×C3—24no—
615C22×C3—24no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—24no—
620C22×C3—38no—
621C22×C3—44no—
622C22×C3—44no—
623C22×C3—44no—
624C22×C3—64no—
625C22×C3—64no—
626C22×C3—181no—
627C22×C3—181no—
628C22×C3—181no—
629C22×C3—181no—
630C22×C3—181no—
631C22×C3—181no—
632C22×C3C22×D3214yes—
633C22×C3C23×C3⋊D311yescharacteristic
634C2×D3—21no—
635C2×D3—21no—
636C2×D3—64no—
637C2×D3—64no—
638C2×D3—64no—
639C2×D3—64no—
640C2×D3—64no—
641C2×D3—64no—
642C2×D3—184no—
643C2×D3—184no—
644C2×D3—184no—
645C2×D3—181no—
646C2×D3—181no—
647C2×D3—181no—
648C2×D3—364no—
649C2×D3—364no—
650C2×D3—364no—
651C2×D3—364no—
652C2×D3—3616no—
653C2×D3#382812yes—
654C3×C4—24no—
655C3×C4—24no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—44no—
659C3×C4—44no—
660C3×C4—64no—
661C3×C4—64no—
662C3×C4—64no—
663C3×C4—181no—
664C3×C4—181no—
665Dic3—21no—
666Dic3—21no—
667Dic3—21no—
668Dic3—64no—
669Dic3—64no—
670Dic3—188no—
671Dic3—184no—
672Dic3—184no—
673Dic3—184no—
674Dic3—181no—
675Dic3—181no—
676Dic3—181no—
677Dic3—364no—
678Dic3—364no—
679C32—24no—
680C32#556014yescomplemented
681C32#561311yescharacteristic, complemented
682C23—31no—
683C23—91no—
684C23—91no—
685C23—271no—
686C23—542no—
687C23—1081no—
688C23—1081no—
689C23C2×D3×C3⋊D311yescharacteristic
690Q8—1081no—
691D4—62no—
692D4—361no—
693D4—361no—
694D4—361no—
695D4—542no—
696D4—1081no—
697D4—1081no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—91no—
702C2×C4—91no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4—271no—
706C2×C4—271no—
707C2×C4—271no—
708C2×C4—361no—
709C2×C4—1081no—
710C2×C4C2×D3×C3⋊D311yescharacteristic
711C2×C4C2×D3×C3⋊D311yescharacteristic
712C2×C3—24no—
713C2×C3—24no—
714C2×C3—24no—
715C2×C3—41no—
716C2×C3—44no—
717C2×C3—68no—
718C2×C3—84no—
719C2×C3—361no—
720C2×C3—361no—
721C2×C3D3×#23514yes—
722C2×C3#6431314yes—
723C2×C3#6431414yes—
724C2×C3C2×#382811yescharacteristic
725C2×C3#6436111yescharacteristic
726C2×C3#6436611yescharacteristic
727D3—22no—
728D3—124no—
729D3—124no—
730D3—361no—
731D3—364no—
732D3—724no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—32no—
737C22—61no—
738C22—61no—
739C22—181no—
740C22—181no—
741C22—181no—
742C22—181no—
743C22—181no—
744C22—181no—
745C22—541no—
746C22—541no—
747C22—541no—
748C22—1084no—
749C22C22×D3×C3⋊D311yescharacteristic
750C4—21no—
751C4—21no—
752C4—61no—
753C4—61no—
754C4—61no—
755C4—181no—
756C4—181no—
757C4—541no—
758C4—541no—
759C4—541no—
760C3—24no—
761C3#1059429714yescomplemented
762C3#1059603111yescharacteristic, complemented
763C2—41no—
764C2—62no—
765C2—361no—
766C2—361no—
767C2—1081no—
768C2D3×#382811yescharacteristic
769C2#1172458711yescharacteristic
770C2#1172458911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #11723926C2semidirect
2. C3×#64093C2semidirect
3. C32×#67⋊C4C2semidirect
4. #11723643C2semidirect
5. #11723632C2semidirect
6. #11723615C2semidirect
7. #11723605C2semidirect
8. #11723541C2semidirect
9. D3×#3752C2semidirect
10. C4×#6290C2semidirect
11. #11723496C2semidirect
12. #11723453C2semidirect
13. #11723439C2semidirect
14. #11723433C2semidirect
15. #11723417C2semidirect
20. C2×#6308C22semidirect
22. C2×C3×#638C22semidirect
24. C2×C3×C4×C3⋊D3C22semidirect
26. C22×C32×Dic3C22semidirect
31. C33×C22⋊C4C22semidirect
32. #88864C22semidirect
35. C4×C3⋊(C3⋊Dic3)C22semidirect
37. C3×#3750C22semidirect
39. C32×Dic3⋊C4C22semidirect
40. C32×C4×Dic3C22semidirect
41. #88807C22semidirect
42. #88806C22semidirect
43. #88806C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
50. #88803C22semidirect
51. #88803C22semidirect
65. #64093D3semidirect
71. C3×#67⋊C4D3semidirect
126. C2×#638C2×D3semidirect
130. C2×C4×C3⋊D3C2×D3semidirect
137. C22×C3×Dic3C2×D3semidirect
147. C32×C22⋊C4C2×D3semidirect
148. C32×C22⋊C4C2×D3semidirect
172. #3750C2×D3semidirect
179. C3×Dic3⋊C4C2×D3semidirect
180. C3×C4×Dic3C2×D3semidirect
245. #67⋊C4C3⋊D3semidirect
348. C22×Dic3C2×C3⋊D3semidirect
362. C3×C22⋊C4D32semidirect
363. C3×C22⋊C4C2×C3⋊D3semidirect
401. Dic3⋊C4C2×C3⋊D3semidirect
405. C4×Dic3C2×C3⋊D3semidirect
487. C33#538semidirect
610. C22⋊C4D3×C3⋊D3semidirect
680. C32#5560semidirect
681. C32#5613semidirect
761. C3#10594297semidirect
762. C3#10596031semidirect

Maximal subgroups

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

subgroupindex
#117239262
C3×#640932
C32×#67⋊C42
#117236432
#117236322
#117236152
#117236052
#117235412
D3×#37522
C4×#62902
#117234962
#117234532
#117234392
#117234332
#117234172
#105960313
#105942973