Finite Group Databasebeta

← #13175492

Subgroups — #13175492

Order 1728.

2524 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89039C211yesmaximal, characteristic, complemented
2C2×#89022C211yesmaximal, characteristic, complemented
3#11723923C211yesmaximal, characteristic, complemented
4C3×#64094C211yesmaximal, characteristic, complemented
5C32×#884C211yesmaximal, characteristic, complemented
6#11723638C211yesmaximal, characteristic, complemented
7#11723633C211yesmaximal, characteristic, complemented
8#11723599C211yesmaximal, characteristic, complemented
9#11723542C211yesmaximal, characteristic, complemented
10#11723540C211yesmaximal, characteristic, complemented
11#11723524C211yesmaximal, characteristic, complemented
12#11723521C211yesmaximal, characteristic, complemented
13#11723514C211yesmaximal, characteristic, complemented
14#11723486C211yesmaximal, characteristic, complemented
15#11723469C211yesmaximal, characteristic, complemented
16#10596078—31nomaximal
17#10594287—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×#6312C2211yescharacteristic, complemented
21C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
22C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
23C2×C3×#638C2211yescharacteristic
24C2×C3×#634C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic
26C2×C32×#67C2211yescharacteristic, complemented
27C2×C32×D12C2211yescharacteristic, complemented
28C2×C32×C4×D3C2211yescharacteristic, complemented
29#89039—24no—
30C2×#6292C2211yescharacteristic
31C2×#6292C2211yescharacteristic, complemented
32C2×#6291C2211yescharacteristic
33C2×#6291C2211yescharacteristic
34C2×#6291C2211yescharacteristic, complemented
35C2×#6291C2211yescharacteristic, complemented
36C2×#6291C2211yescharacteristic, complemented
37C2×#6290C2211yescharacteristic, complemented
38C2×#6289C2211yescharacteristic
39C2×#6289C2211yescharacteristic, complemented
40#89022—24no—
41C33×C22⋊C4C2211yescharacteristic, complemented
42#88859C2211yescharacteristic
43#88859C2211yescharacteristic, complemented
44C3×#3757C2211yescharacteristic, complemented
45C3×#3752C2211yescharacteristic, complemented
46C3×#3752C2211yescharacteristic, complemented
47C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
48C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C32×Dic3⋊C4C2211yescharacteristic, complemented
50Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
51#88804C2211yescharacteristic
52#88804C2211yescharacteristic, complemented
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55C2×D4×C3⋊D3—31no—
56C2×#3828—31no—
57C2×#3811—34no—
58C2×#3799—34no—
59C32×#121—31no—
60#64149—31no—
61#64149—31no—
62#64147—31no—
63#64146—31no—
64#64146—31no—
65#64139—31no—
66#64104—31no—
67#64101—31no—
68#64094—31no—
69#64094D311yescharacteristic, complemented
70#64091—31no—
71#64091—31no—
72#64091—34no—
73#64091—64no—
74C3×#885—34no—
75C3×#884D314yescomplemented
76#63981—34no—
77#63979—34no—
78#63958—34no—
79#63923—34no—
80#63922—34no—
81#63911—34no—
82#63910—34no—
83#63907—34no—
84#63906—34no—
85#63836—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)—22no—
88C22×C3⋊(C3⋊D3)—41no—
89C22×C3⋊(C3⋊D3)—41no—
90C22×C3⋊(C3⋊D3)C2311yescharacteristic
91C22×C3⋊(C3⋊D3)C2311yescharacteristic
92C22×C3⋊(C3⋊D3)C2311yescharacteristic
93C22×C3×C3⋊D3C2311yescharacteristic
94C22×C32×D3C2311yescharacteristic
95C22×C32×D3C2311yescharacteristic
96C2×D3×C3⋊D3—22no—
97C2×D3×C3⋊D3—41no—
98C2×D3×C3⋊D3—41no—
99C2×C33×C4C2311yescharacteristic
100C2×C33×C4C2311yescharacteristic
101#6312—41no—
102C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
103C4⋊(C3⋊(C3⋊D3))—22no—
104C4⋊(C3⋊(C3⋊D3))—41no—
105C3×#638—22no—
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C3×#634—22no—
110C32×#67—22no—
111C32×#67—41no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C32×D12—41no—
115C32×C4×D3—22no—
116#6292—22no—
117#6292—41no—
118#6291—22no—
119#6291—22no—
120#6291—22no—
121#6291—41no—
122#6291—41no—
123#6290—41no—
124#6289—22no—
125#6289D414yescomplemented
126#5674—91no—
127#5607—94no—
128C23×C3⋊D3—31no—
129C23×C3⋊D3—34no—
130C23×C3⋊D3—31no—
131C23×C3⋊D3—64no—
132C22×D32—34no—
133C2×C32×D4—31no—
134C2×C32×D4—31no—
135C2×C32×D4—31no—
136C22×C32×C4—31no—
137C2×#638—31no—
138C2×#638—34no—
139C2×#638—31no—
140C2×#638—31no—
141C2×#638—31no—
142C2×#638—31no—
143C2×#638—31no—
144C2×#638—31no—
145C2×#638—64no—
146C2×#638C2×D311yescharacteristic
147D4×C3⋊D3—64no—
148#3828—64no—
149C2×C4⋊(C3⋊D3)—31no—
150C2×C4⋊(C3⋊D3)—31no—
151C2×C4⋊(C3⋊D3)—34no—
152C2×C4⋊(C3⋊D3)—31no—
153C2×C4⋊(C3⋊D3)—31no—
154C2×C4⋊(C3⋊D3)—34no—
155C2×C4⋊(C3⋊D3)—64no—
156C2×C4⋊(C3⋊D3)—64no—
157C2×C4×C3⋊D3—31no—
158C2×C4×C3⋊D3—31no—
159C2×#634C2×D311yescharacteristic, complemented
160C2×C3×#67—34no—
161C2×C3×#67C2×D314yes—
162C2×C3×#67C2×D314yescomplemented
163C2×C3×D12C2×D314yescomplemented
164C2×C3×C4×D3C2×D314yescomplemented
165C2×C3×Dic6—34no—
166#3811—616no—
167C2×#626—34no—
168C2×#626—34no—
169C2×#626—34no—
170C2×#626—34no—
171C2×#626—34no—
172C2×#626—34no—
173C2×#626—34no—
174C2×#625—34no—
175C2×#624—34no—
176C2×#624—34no—
177#3799—616no—
178C32×C4⋊C4—31no—
179C32×C22⋊C4—24no—
180C32×C22⋊C4—31no—
181C32×C22⋊C4C2×D314yescomplemented
182C32×C22⋊C4C2×D311yescharacteristic, complemented
183#3757—31no—
184#3757C2×D311yescharacteristic, complemented
185#3752—31no—
186#3752—31no—
187#3752—34no—
188#3752—34no—
189#3752—31no—
190#3752—31no—
191#3752—64no—
192#3752—64no—
193#3752C2×D311yescharacteristic, complemented
194#3752C2×D311yescharacteristic, complemented
195C4⋊(C3⋊Dic3)—31no—
196C4×C3⋊Dic3—31no—
197C4×C3⋊Dic3C2×D311yescharacteristic, complemented
198C3×#217—34no—
199C3×(C2×D3)⋊C4—34no—
200C3×(C2×D3)⋊C4—34no—
201C3×(C2×D3)⋊C4C2×D314yescomplemented
202C3×Dic3⋊C4C2×D314yescomplemented
203C3×C4×Dic3—34no—
204Dic3⋊Dic3—34no—
205#3722—34no—
206#3722—34no—
207(C2×D3)⋊Dic3—34no—
208Dic32—34no—
209C22×C33—21no—
210C22×C33—21no—
211C22×C33—21no—
212C22×C33C2411yescharacteristic
213C2×C3⋊(C3⋊D3)—21no—
214C2×C3⋊(C3⋊D3)—21no—
215C2×C3⋊(C3⋊D3)—21no—
216C2×C3⋊(C3⋊D3)—21no—
217C2×C3⋊(C3⋊D3)—21no—
218C2×C3⋊(C3⋊D3)—21no—
219C2×C3⋊(C3⋊D3)—21no—
220C2×C3⋊(C3⋊D3)—21no—
221C2×C3⋊(C3⋊D3)—44no—
222C2×C3⋊(C3⋊D3)C2×D412yes—
223C2×C3×C3⋊D3—21no—
224C2×C3×C3⋊D3—21no—
225C2×C3×C3⋊D3—21no—
226C2×C32×D3—21no—
227C2×C32×D3—21no—
228C2×C32×D3—21no—
229C2×C32×D3—21no—
230C2×C32×D3—21no—
231C2×C32×D3—21no—
232D3×C3⋊D3—44no—
233C33×C4—21no—
234C33×C4—21no—
235C3⋊(C3⋊Dic3)—21no—
236C3×C3⋊Dic3—21no—
237C3×C3⋊Dic3—21no—
238C3×C3⋊Dic3C2×D412yes—
239C32×Dic3—21no—
240C32×Dic3C2×D412yes—
241C2×#239—91no—
242C2×D3×D4—94no—
243C2×D3×D4—91no—
244C2×#235—94no—
245C3×#124—91no—
246C3×#121—34no—
247#947—91no—
248#940—94no—
249#940—94no—
250#940—91no—
251#938—94no—
252#937—94no—
253#937—94no—
254#930—94no—
255#895—94no—
256#892—94no—
257#885—34no—
258#885—94no—
259#884—91no—
260#884—91no—
261#884—91no—
262#884C3⋊D311yescharacteristic, complemented
263#882—94no—
264#882—91no—
265#882—91no—
266#882—94no—
267#882—91no—
268#882—91no—
269#882—184no—
270#874—91no—
271#872—91no—
272C23×C32—24no—
273C23×C32—31no—
274C23×C32—31no—
275C23×C32C22×D314yes—
276C23×C32C22×D311yescharacteristic
277C22×C3⋊D3—31no—
278C22×C3⋊D3—31no—
279C22×C3⋊D3—31no—
280C22×C3⋊D3—34no—
281C22×C3⋊D3—34no—
282C22×C3⋊D3—34no—
283C22×C3⋊D3—64no—
284C22×C3⋊D3—64no—
285C22×C3⋊D3—64no—
286C22×C3⋊D3—62no—
287C22×C3⋊D3—62no—
288C22×C3⋊D3—68no—
289C22×C3⋊D3—128no—
290C22×C3⋊D3—121no—
291C22×C3⋊D3—121no—
292C22×C3⋊D3—121no—
293C22×C3⋊D3—121no—
294C22×C3⋊D3—124no—
295C22×C3⋊D3—124no—
296C22×C3⋊D3—128no—
297C22×C3⋊D3—128no—
298C22×C3⋊D3C22×D311yescharacteristic
299C22×C3×D3—34no—
300C22×C3×D3C22×D314yes—
301C22×C3×D3C22×D314yes—
302C2×D32—68no—
303C2×D32—124no—
304C2×D32—124no—
305C32×D4—62no—
306C32×D4—121no—
307C32×D4—121no—
308C2×C32×C4—24no—
309C2×C32×C4—24no—
310C2×C32×C4—31no—
311C2×C32×C4—31no—
312C2×C32×C4—62no—
313C2×C32×C4C22×D314yes—
314C2×C32×C4C22×D314yes—
315C2×C32×C4C22×D311yescharacteristic
316C2×C32×C4C22×D311yescharacteristic
317#638—22no—
318#638—62no—
319#638—62no—
320#638—62no—
321#638—121no—
322#638—121no—
323#638—121no—
324#638—121no—
325#638—124no—
326#638—128no—
327C2×C3⋊Dic3—31no—
328C2×C3⋊Dic3—34no—
329C2×C3⋊Dic3—64no—
330C2×C3⋊Dic3C22×D311yescharacteristic
331C2×C3⋊Dic3C22×D311yescharacteristic
332C2×C3⋊Dic3C22×D311yescharacteristic
333C4⋊(C3⋊D3)—62no—
334C4⋊(C3⋊D3)—62no—
335C4⋊(C3⋊D3)—68no—
336C4⋊(C3⋊D3)—128no—
337C4⋊(C3⋊D3)—121no—
338C4⋊(C3⋊D3)—124no—
339C4⋊(C3⋊D3)—128no—
340C4⋊(C3⋊D3)—121no—
341C4×C3⋊D3—34no—
342C4×C3⋊D3—62no—
343#634—22no—
344C3×#67—28no—
345C3×#67—44no—
346C3×#67—68no—
347C2×C3×Dic3—34no—
348C2×C3×Dic3—34no—
349C2×C3×Dic3—34no—
350C2×C3×Dic3C22×D314yes—
351C2×C3×Dic3C22×D314yes—
352C3×D12—44no—
353C3×C4×D3—28no—
354C3×Dic6—68no—
355#626—68no—
356#626—68no—
357#626—68no—
358#626—68no—
359#626—124no—
360#626—124no—
361#626—124no—
362#625—124no—
363#624—316no—
364#624—68no—
365#535—271noSylow
366C2×C33—41no—
367C2×C33C22×D411yescharacteristic
368C2×C33H(5,𝔽2)11yescharacteristic
369C2×C33H(5,𝔽2)11yescharacteristic
370C3⋊(C3⋊D3)—22no—
371C3⋊(C3⋊D3)—41no—
372C3⋊(C3⋊D3)—41no—
373C3×C3⋊D3—41no—
374C32×D3—41no—
375C32×D3—41no—
376C23×D3—94no—
377C23×D3—94no—
378C23×D3—91no—
379C23×D3—91no—
380C23×D3—184no—
381C2×C3×Q8—91no—
382C2×C3×D4—34no—
383C2×C3×D4—34no—
384C2×C3×D4—34no—
385C2×C3×D4—91no—
386C22×C3×C4—34no—
387C2×#67—34no—
388C2×#67—94no—
389C2×#67—94no—
390C2×#67—94no—
391C2×#67—94no—
392C2×#67—94no—
393C2×#67—94no—
394C2×#67—94no—
395C2×#67—91no—
396C2×#67—91no—
397C2×#67—91no—
398C2×#67—91no—
399C2×#67—184no—
400C2×#67C2×C3⋊D311yescharacteristic
401C2×#67C2×C3⋊D311yescharacteristic, complemented
402#239—184no—
403D3×D4—184no—
404D3×D4—1816no—
405#235—1816no—
406C2×D12—94no—
407C2×D12—91no—
408C2×D12—91no—
409C2×D12—91no—
410C2×D12—94no—
411C2×D12—91no—
412C2×D12—94no—
413C2×D12—91no—
414C2×D12—91no—
415C2×D12—94no—
416C2×D12—91no—
417C2×D12—184no—
418C2×D12—184no—
419C2×D12C2×C3⋊D311yescharacteristic, complemented
420C2×C4×D3—94no—
421C2×C4×D3—91no—
422C2×C4×D3—94no—
423C2×C4×D3—91no—
424C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
425C2×Dic6—34no—
426C3×C4⋊C4—34no—
427C3×C22⋊C4—24no—
428C3×C22⋊C4—34no—
429C3×C22⋊C4—91no—
430C3×C22⋊C4—91no—
431C3×C22⋊C4—91no—
432C3×C22⋊C4D3214yescomplemented
433C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
434C3×C42—91no—
435#217—34no—
436#217—94no—
437(C2×D3)⋊C4—34no—
438(C2×D3)⋊C4—34no—
439(C2×D3)⋊C4—94no—
440(C2×D3)⋊C4—94no—
441(C2×D3)⋊C4—91no—
442(C2×D3)⋊C4—94no—
443(C2×D3)⋊C4—94no—
444(C2×D3)⋊C4—91no—
445(C2×D3)⋊C4—91no—
446(C2×D3)⋊C4—91no—
447(C2×D3)⋊C4—91no—
448(C2×D3)⋊C4—184no—
449(C2×D3)⋊C4—184no—
450(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
451C4⋊Dic3—94no—
452Dic3⋊C4—91no—
453Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
454C4×Dic3—34no—
455C4×Dic3—94no—
456C4×Dic3—91no—
457C22×C32—28no—
458C22×C32—21no—
459C22×C32—24no—
460C22×C32—21no—
461C22×C32—21no—
462C22×C32—24no—
463C22×C32—24no—
464C22×C32—24no—
465C22×C32—44no—
466C22×C32—44no—
467C22×C32—61no—
468C22×C32—61no—
469C22×C32—61no—
470C22×C32—61no—
471C22×C32—61no—
472C22×C32—61no—
473C22×C32C23×D314yes—
474C22×C32C23×D311yescharacteristic
475C2×C3⋊D3—21no—
476C2×C3⋊D3—21no—
477C2×C3⋊D3—21no—
478C2×C3⋊D3—32no—
479C2×C3⋊D3—38no—
480C2×C3⋊D3—68no—
481C2×C3⋊D3—61no—
482C2×C3⋊D3—61no—
483C2×C3⋊D3—68no—
484C2×C3⋊D3—61no—
485C2×C3⋊D3—61no—
486C2×C3⋊D3—64no—
487C2×C3⋊D3—61no—
488C2×C3⋊D3—61no—
489C2×C3⋊D3—61no—
490C2×C3⋊D3—61no—
491C2×C3⋊D3—64no—
492C2×C3⋊D3—64no—
493C2×C3⋊D3—64no—
494C2×C3⋊D3—64no—
495C2×C3⋊D3—64no—
496C2×C3⋊D3—64no—
497C2×C3⋊D3—64no—
498C2×C3⋊D3—124no—
499C2×C3⋊D3—124no—
500C2×C3⋊D3—124no—
501C2×C3⋊D3—124no—
502C2×C3⋊D3—124no—
503C2×C3⋊D3—124no—
504C2×C3⋊D3—124no—
505C2×C3⋊D3—124no—
506C2×C3⋊D3—124no—
507C2×C3⋊D3—1216no—
508C2×C3⋊D3—1232no—
509C2×C3×D3—24no—
510C2×C3×D3—24no—
511C2×C3×D3—24no—
512C2×C3×D3—24no—
513C2×C3×D3—24no—
514C2×C3×D3—24no—
515C2×C3×D3—64no—
516C2×C3×D3—64no—
517C2×C3×D3—64no—
518D32—1216no—
519C32×C4—21no—
520C32×C4—21no—
521C32×C4—24no—
522C32×C4—24no—
523C32×C4—32no—
524C32×C4—44no—
525C32×C4—44no—
526C32×C4—61no—
527C3⋊Dic3—21no—
528C3⋊Dic3—21no—
529C3⋊Dic3—61no—
530C3⋊Dic3—64no—
531C3⋊Dic3—124no—
532C3⋊Dic3D3×D412yes—
533C3×Dic3—24no—
534C3×Dic3—38no—
535C3×Dic3—64no—
536C3×Dic3—64no—
537C3×Dic3D3×D418yes—
538C2×#41—271no—
539C22×D4—271no—
540#127—271no—
541#127—271no—
542#124—91no—
543#124—271no—
544#121—31no—
545#121—271no—
546#121—271no—
547#121—271no—
548#120—271no—
549#120—271no—
550#120—271no—
551#120—271no—
552#117—271no—
553C33#53511yescharacteristic, complemented, Sylow
554C23×C3—24no—
555C23×C3—34no—
556C23×C3—34no—
557C23×C3—91no—
558C23×C3C2×D3214yes—
559C23×C3C22×C3⋊D311yescharacteristic
560C22×D3—34no—
561C22×D3—94no—
562C22×D3—91no—
563C22×D3—94no—
564C22×D3—94no—
565C22×D3—91no—
566C22×D3—91no—
567C22×D3—184no—
568C22×D3—184no—
569C22×D3—184no—
570C22×D3—182no—
571C22×D3—188no—
572C22×D3—182no—
573C22×D3—188no—
574C22×D3—368no—
575C22×D3—361no—
576C22×D3—361no—
577C22×D3—364no—
578C22×D3—364no—
579C22×D3—364no—
580C22×D3—364no—
581C22×D3—361no—
582C22×D3—361no—
583C22×D3—368no—
584C22×D3—368no—
585C22×D3C22×C3⋊D311yescharacteristic
586C22×D3C22×C3⋊D311yescharacteristic
587C3×Q8—182no—
588C3×D4—68no—
589C3×D4—124no—
590C3×D4—124no—
591C3×D4—182no—
592C2×C3×C4—24no—
593C2×C3×C4—24no—
594C2×C3×C4—34no—
595C2×C3×C4—34no—
596C2×C3×C4—68no—
597C2×C3×C4—91no—
598C2×C3×C4—91no—
599C2×C3×C4—91no—
600C2×C3×C4C2×D3214yes—
601C2×C3×C4C2×D3214yes—
602C2×C3×C4C22×C3⋊D311yescharacteristic
603C2×C3×C4C22×C3⋊D311yescharacteristic
604#67—22no—
605#67—41no—
606#67—68no—
607#67—188no—
608#67—188no—
609#67—188no—
610#67—182no—
611#67—361no—
612#67—364no—
613#67—364no—
614#67—361no—
615#67—364no—
616#67—364no—
617#67—361no—
618#67—368no—
619C2×Dic3—34no—
620C2×Dic3—34no—
621C2×Dic3—34no—
622C2×Dic3—94no—
623C2×Dic3—91no—
624C2×Dic3—184no—
625C2×Dic3C22×C3⋊D311yescharacteristic
626C2×Dic3C22×C3⋊D311yescharacteristic
627D12—41no—
628D12—182no—
629D12—188no—
630D12—188no—
631D12—182no—
632D12—182no—
633D12—182no—
634D12—368no—
635D12—364no—
636D12—361no—
637D12—368no—
638D12—364no—
639D12—361no—
640D12—361no—
641C4×D3—22no—
642C4×D3—916no—
643C4×D3—94no—
644C4×D3—188no—
645C4×D3—182no—
646Dic6—68no—
647C2×C32—24no—
648C2×C32—24no—
649C2×C32—24no—
650C2×C32—48no—
651C2×C32—41no—
652C2×C32—44no—
653C2×C32—121no—
654C2×C32—121no—
655C2×C32C2×D3×D414yes—
656C2×C32C2×D3×D411yescharacteristic
657C2×C32#100414yes—
658C2×C32#100914yes—
659C2×C32#100911yescharacteristic
660C2×C32#100911yescharacteristic
661C3⋊D3—41no—
662C3⋊D3—62no—
663C3⋊D3—68no—
664C3⋊D3—128no—
665C3⋊D3—128no—
666C3⋊D3—121no—
667C3⋊D3—121no—
668C3⋊D3—124no—
669C3⋊D3—124no—
670C3⋊D3—244no—
671C3×D3—44no—
672C3×D3—44no—
673C3×D3—124no—
674C24—271no—
675C24—271no—
676#41—544no—
677C2×Q8—91no—
678C2×D4—31no—
679C2×D4—31no—
680C2×D4—31no—
681C2×D4—91no—
682C2×D4—271no—
683C2×D4—271no—
684C2×D4—271no—
685C2×D4—271no—
686C2×D4—271no—
687C2×D4—271no—
688C2×D4—271no—
689C2×D4—271no—
690C2×D4—271no—
691C2×D4—271no—
692C2×D4—271no—
693C2×D4—544no—
694C22×C4—31no—
695C22×C4—271no—
696C22×C4—271no—
697C4⋊C4—31no—
698C4⋊C4—271no—
699C22⋊C4—31no—
700C22⋊C4—91no—
701C22⋊C4—91no—
702C22⋊C4—91no—
703C22⋊C4—271no—
704C22⋊C4—271no—
705C22⋊C4—271no—
706C22⋊C4—271no—
707C22⋊C4—271no—
708C22⋊C4D3×C3⋊D311yescharacteristic, complemented
709C42—91no—
710C42—271no—
711C22×C3—28no—
712C22×C3—24no—
713C22×C3—24no—
714C22×C3—24no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—24no—
719C22×C3—44no—
720C22×C3—44no—
721C22×C3—64no—
722C22×C3—64no—
723C22×C3—64no—
724C22×C3—64no—
725C22×C3—64no—
726C22×C3—64no—
727C22×C3—181no—
728C22×C3—181no—
729C22×C3—181no—
730C22×C3C22×D3214yes—
731C22×C3C23×C3⋊D311yescharacteristic
732C2×D3—21no—
733C2×D3—21no—
734C2×D3—21no—
735C2×D3—21no—
736C2×D3—21no—
737C2×D3—21no—
738C2×D3—64no—
739C2×D3—64no—
740C2×D3—64no—
741C2×D3—98no—
742C2×D3—92no—
743C2×D3—188no—
744C2×D3—184no—
745C2×D3—184no—
746C2×D3—181no—
747C2×D3—181no—
748C2×D3—188no—
749C2×D3—184no—
750C2×D3—184no—
751C2×D3—184no—
752C2×D3—184no—
753C2×D3—184no—
754C2×D3—184no—
755C2×D3—181no—
756C2×D3—181no—
757C2×D3—181no—
758C2×D3—181no—
759C2×D3—181no—
760C2×D3—181no—
761C2×D3—364no—
762C2×D3—364no—
763C2×D3—364no—
764C2×D3—364no—
765C2×D3—364no—
766C2×D3—364no—
767C2×D3—364no—
768C2×D3—364no—
769C2×D3—3616no—
770C2×D3—364no—
771C2×D3—3616no—
772C2×D3—3632no—
773C3×C4—24no—
774C3×C4—24no—
775C3×C4—21no—
776C3×C4—21no—
777C3×C4—38no—
778C3×C4—44no—
779C3×C4—44no—
780C3×C4—64no—
781C3×C4—92no—
782C3×C4—181no—
783C3×C4—181no—
784Dic3—21no—
785Dic3—38no—
786Dic3—64no—
787Dic3—64no—
788Dic3—184no—
789Dic3—181no—
790Dic3—364no—
791Dic3D4×C3⋊D312yes—
792C32—24no—
793C32#560714yescomplemented
794C32#567411yescharacteristic, complemented
795C23—31no—
796C23—31no—
797C23—91no—
798C23—271no—
799C23—271no—
800C23—271no—
801C23—542no—
802C23—542no—
803C23—1081no—
804C23—1081no—
805C23—1081no—
806C23—1081no—
807C23C2×D3×C3⋊D311yescharacteristic
808Q8—182no—
809D4—62no—
810D4—121no—
811D4—121no—
812D4—182no—
813D4—542no—
814D4—542no—
815D4—542no—
816D4—542no—
817D4—542no—
818D4—1081no—
819D4—1081no—
820D4—1081no—
821D4—1081no—
822D4—1081no—
823D4—1081no—
824C2×C4—31no—
825C2×C4—31no—
826C2×C4—62no—
827C2×C4—91no—
828C2×C4—91no—
829C2×C4—91no—
830C2×C4—274no—
831C2×C4—271no—
832C2×C4—542no—
833C2×C4C2×D3×C3⋊D311yescharacteristic
834C2×C4C2×D3×C3⋊D311yescharacteristic
835C2×C3—24no—
836C2×C3—24no—
837C2×C3—24no—
838C2×C3—48no—
839C2×C3—41no—
840C2×C3—44no—
841C2×C3—124no—
842C2×C3—124no—
843C2×C3—361no—
844C2×C3#6430814yes—
845C2×C3D32×D414yes—
846C2×C3#6431414yes—
847C2×C3C2×D4×C3⋊D311yescharacteristic
848C2×C3#6436111yescharacteristic
849C2×C3#6436611yescharacteristic
850D3—41no—
851D3—41no—
852D3—124no—
853D3—182no—
854D3—188no—
855D3—368no—
856D3—368no—
857D3—361no—
858D3—361no—
859D3—364no—
860D3—364no—
861D3—724no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—61no—
866C22—61no—
867C22—61no—
868C22—61no—
869C22—61no—
870C22—61no—
871C22—181no—
872C22—181no—
873C22—181no—
874C22—272no—
875C22—541no—
876C22—541no—
877C22—541no—
878C22—541no—
879C22—541no—
880C22—541no—
881C22—541no—
882C22—541no—
883C22—1084no—
884C22—1084no—
885C22C22×D3×C3⋊D311yescharacteristic
886C4—21no—
887C4—21no—
888C4—32no—
889C4—61no—
890C4—92no—
891C4—181no—
892C4—181no—
893C4—541no—
894C3—24no—
895C3#1059428714yescomplemented
896C3#1059607811yescharacteristic, complemented
897C2—41no—
898C2—121no—
899C2—121no—
900C2—361no—
901C2—542no—
902C2—1081no—
903C2—1081no—
904C2#1172458111yescharacteristic
905C2D3×D4×C3⋊D311yescharacteristic
906C2#1172458811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33#535
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#89039C2semidirect
2. C2×#89022C2semidirect
3. #11723923C2semidirect
4. C3×#64094C2semidirect
5. C32×#884C2semidirect
6. #11723638C2semidirect
7. #11723633C2semidirect
8. #11723599C2semidirect
9. #11723542C2semidirect
10. #11723540C2semidirect
11. #11723524C2semidirect
12. #11723521C2semidirect
13. #11723514C2semidirect
14. #11723486C2semidirect
15. #11723469C2semidirect
20. C2×#6312C22semidirect
22. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
24. C2×C3×#634C22semidirect
26. C2×C32×#67C22semidirect
27. C2×C32×D12C22semidirect
28. C2×C32×C4×D3C22semidirect
31. C2×#6292C22semidirect
34. C2×#6291C22semidirect
35. C2×#6291C22semidirect
36. C2×#6291C22semidirect
37. C2×#6290C22semidirect
39. C2×#6289C22semidirect
41. C33×C22⋊C4C22semidirect
43. #88859C22semidirect
44. C3×#3757C22semidirect
45. C3×#3752C22semidirect
46. C3×#3752C22semidirect
47. C3×C4×C3⋊Dic3C22semidirect
48. C32×(C2×D3)⋊C4C22semidirect
49. C32×Dic3⋊C4C22semidirect
50. Dic3⋊(C3⋊Dic3)C22semidirect
52. #88804C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
69. #64094D3semidirect
75. C3×#884D3semidirect
125. #6289D4semidirect
159. C2×#634C2×D3semidirect
162. C2×C3×#67C2×D3semidirect
163. C2×C3×D12C2×D3semidirect
164. C2×C3×C4×D3C2×D3semidirect
181. C32×C22⋊C4C2×D3semidirect
182. C32×C22⋊C4C2×D3semidirect
184. #3757C2×D3semidirect
193. #3752C2×D3semidirect
194. #3752C2×D3semidirect
197. C4×C3⋊Dic3C2×D3semidirect
201. C3×(C2×D3)⋊C4C2×D3semidirect
202. C3×Dic3⋊C4C2×D3semidirect
262. #884C3⋊D3semidirect
401. C2×#67C2×C3⋊D3semidirect
419. C2×D12C2×C3⋊D3semidirect
424. C2×C4×D3C2×C3⋊D3semidirect
432. C3×C22⋊C4D32semidirect
433. C3×C22⋊C4C2×C3⋊D3semidirect
450. (C2×D3)⋊C4C2×C3⋊D3semidirect
453. Dic3⋊C4C2×C3⋊D3semidirect
553. C33#535semidirect
708. C22⋊C4D3×C3⋊D3semidirect
793. C32#5607semidirect
794. C32#5674semidirect
895. C3#10594287semidirect
896. C3#10596078semidirect

Maximal subgroups

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

subgroupindex
C2×#890392
C2×#890222
#117239232
C3×#640942
C32×#8842
#117236382
#117236332
#117235992
#117235422
#117235402
#117235242
#117235212
#117235142
#117234862
#117234692
#105960783
#105942873