Finite Group Databasebeta

← #13175927

Subgroups — #13175927

Order 1728.

2596 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89039C211yesmaximal, characteristic, complemented
2C2×D3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3#11723923C211yesmaximal, characteristic, complemented
4C3×#64093C211yesmaximal, characteristic, complemented
5C32×#883C211yesmaximal, characteristic, complemented
6#11723643C211yesmaximal, characteristic, complemented
7#11723639C211yesmaximal, characteristic, complemented
8#11723624C211yesmaximal, characteristic, complemented
9#11723542C211yesmaximal, characteristic, complemented
10C3⋊D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11#11723526C211yesmaximal, characteristic, complemented
12#11723504C211yesmaximal, characteristic, complemented
13#11723498C211yesmaximal, characteristic, complemented
14#11723482C211yesmaximal, characteristic, complemented
15#11723414C211yesmaximal, characteristic, complemented
16#10596124—31nomaximal
17#10594264—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic, complemented
21C2×#6312C2211yescharacteristic, complemented
22C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
23C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
24C2×C3×#638C2211yescharacteristic, complemented
25C2×C3×#638C2211yescharacteristic, complemented
26C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
27C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
28C2×C32×#67C2211yescharacteristic
29C2×C32×C4×D3C2211yescharacteristic, complemented
30#89039—24no—
31C2×#6292C2211yescharacteristic
32C2×#6292C2211yescharacteristic, complemented
33C2×#6292C2211yescharacteristic, complemented
34C2×#6292C2211yescharacteristic, complemented
35C2×#6291C2211yescharacteristic
36C2×#6289C2211yescharacteristic, complemented
37C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
38D3×C4⋊(C3⋊D3)—24no—
39C33×C22⋊C4C2211yescharacteristic, complemented
40#88859C2211yescharacteristic, complemented
41#88859C2211yescharacteristic, complemented
42C3×#3752C2211yescharacteristic, complemented
43C3×#3750C2211yescharacteristic, complemented
44C32×#217C2211yescharacteristic, complemented
45C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C32×C4⋊Dic3C2211yescharacteristic, complemented
47C32×Dic3⋊C4C2211yescharacteristic, complemented
48#88806C2211yescharacteristic, complemented
49#88804C2211yescharacteristic, complemented
50#88804C2211yescharacteristic, complemented
51#88804C2211yescharacteristic, complemented
52#88804C2211yescharacteristic, complemented
53#88803C2211yescharacteristic, complemented
54(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
55C2×D4×C3⋊D3—31no—
56C22×C4⋊(C3⋊D3)—31no—
57C2×#3811—34no—
58C2×D3×D12—34no—
59C32×#123—31no—
60#64146—31no—
61#64138—31no—
62#64104—31no—
63#64104—31no—
64#64103—31no—
65#64103—31no—
66#64093—31no—
67#64093D311yescharacteristic, complemented
68#64091—31no—
69#64091—31no—
70#64091—31no—
71#64091—34no—
72#64091—64no—
73C22⋊C4×C3⋊D3—31no—
74C3×#884—34no—
75C3×#883D314yescomplemented
76#63983—34no—
77#63981—34no—
78#63971—34no—
79#63923—34no—
80D3×(C2×D3)⋊C4—34no—
81#63909—34no—
82#63897—34no—
83#63886—34no—
84#63854—34no—
85#63850—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×C3×C3⋊D3C2311yescharacteristic
95C22×C32×D3C2311yescharacteristic
96C2×D3×C3⋊D3—22no—
97C2×D3×C3⋊D3—41no—
98C2×D3×C3⋊D3—41no—
99C2×D3×C3⋊D3—41no—
100C2×D3×C3⋊D3—41no—
101C2×D3×C3⋊D3D414yescomplemented
102C2×C33×C4C2311yescharacteristic
103C2×C33×C4C2311yescharacteristic
104#6312—41no—
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C4⋊(C3⋊(C3⋊D3))—22no—
107C4⋊(C3⋊(C3⋊D3))—41no—
108C3×#638—22no—
109C3×#638—41no—
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C3×C4⋊(C3⋊D3)—22no—
113C3×C4×C3⋊D3—41no—
114C32×#67—22no—
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C32×C4×D3—22no—
119#6292—22no—
120#6292—22no—
121#6292—22no—
122#6292—41no—
123#6291—22no—
124#6289—22no—
125Dic3×C3⋊D3—41no—
126#5653—94no—
127#5605—91no—
128C23×C3⋊D3—31no—
129C23×C3⋊D3—31no—
130C23×C3⋊D3—34no—
131C23×C3⋊D3—31no—
132C23×C3⋊D3—64no—
133C22×D32—34no—
134C22×D32—34no—
135C2×C32×D4—31no—
136C22×C32×C4—31no—
137C2×#638—31no—
138C2×#638—34no—
139C2×#638—31no—
140C2×#638—64no—
141C2×#638C2×D311yescharacteristic, complemented
142C2×#638C2×D311yescharacteristic, complemented
143D4×C3⋊D3—64no—
144C2×C4⋊(C3⋊D3)—31no—
145C2×C4⋊(C3⋊D3)—31no—
146C2×C4⋊(C3⋊D3)—31no—
147C2×C4⋊(C3⋊D3)—31no—
148C2×C4⋊(C3⋊D3)—34no—
149C2×C4⋊(C3⋊D3)—31no—
150C2×C4⋊(C3⋊D3)—31no—
151C2×C4⋊(C3⋊D3)—34no—
152C2×C4⋊(C3⋊D3)—64no—
153C2×C4⋊(C3⋊D3)—64no—
154C2×C4⋊(C3⋊D3)—64no—
155C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
156C2×C4×C3⋊D3—31no—
157C2×C4×C3⋊D3—31no—
158C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
159C2×C3×#67—34no—
160C2×C3×#67—34no—
161C2×C3×#67C2×D314yes—
162C2×C3×D12—34no—
163C2×C3×C4×D3—34no—
164C2×C3×C4×D3C2×D314yescomplemented
165#3811—616no—
166C2×#626—34no—
167C2×#626—34no—
168C2×#626—34no—
169C2×#626—34no—
170C2×#626—34no—
171C2×#624—34no—
172C2×D3×Dic3—34no—
173D3×D12—616no—
174C32×C4⋊C4—31no—
175C32×C4⋊C4—31no—
176C32×C22⋊C4—24no—
177C32×C22⋊C4—31no—
178C32×C22⋊C4—31no—
179C32×C22⋊C4C2×D314yescomplemented
180C32×C22⋊C4C2×D311yescharacteristic, complemented
181#3757—31no—
182#3752—31no—
183#3752—31no—
184#3752—31no—
185#3752—34no—
186#3752—34no—
187#3752—31no—
188#3752—31no—
189#3752—31no—
190#3752—31no—
191#3752—64no—
192#3752—64no—
193#3752C2×D311yescharacteristic, complemented
194#3750—31no—
195#3750C2×D311yescharacteristic, complemented
196C3×#217C2×D314yescomplemented
197C3×(C2×D3)⋊C4—34no—
198C3×(C2×D3)⋊C4C2×D314yescomplemented
199C3×C4⋊Dic3C2×D314yescomplemented
200C3×Dic3⋊C4—34no—
201C3×Dic3⋊C4C2×D314yescomplemented
202#3724—34no—
203#3722—34no—
204#3722—34no—
205#3722—34no—
206#3722—34no—
207(C2×D3)⋊Dic3—34no—
208(C2×D3)⋊Dic3—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×C3×C3⋊D3—21no—
227C2×C3×C3⋊D3—21no—
228C2×C3×C3⋊D3C2×D412yes—
229C2×C32×D3—21no—
230C2×C32×D3—21no—
231C2×C32×D3C2×D412yes—
232D3×C3⋊D3—44no—
233D3×C3⋊D3—44no—
234C33×C4—21no—
235C33×C4—21no—
236C3⋊(C3⋊Dic3)—21no—
237C3×C3⋊Dic3—21no—
238C3×C3⋊Dic3—21no—
239C32×Dic3—21no—
240C32×Dic3—21no—
241C32×Dic3—21no—
242C2×D3×D4—94no—
243C2×D3×D4—91no—
244C2×D3×D4—91no—
245C22×D12—94no—
246C3×#123—34no—
247C3×#121—91no—
248#939—91no—
249#939—91no—
250#937—94no—
251#937—91no—
252#937—91no—
253#930—91no—
254#929—94no—
255C2×(C2×D3)⋊C4—91no—
256#895—94no—
257#895—94no—
258#894—94no—
259#894—94no—
260#894—91no—
261#894—91no—
262#884—34no—
263#884—94no—
264#883—91no—
265#883C3⋊D311yescharacteristic, complemented
266#882—94no—
267#882—94no—
268#882—94no—
269#882—91no—
270#882—91no—
271#882—184no—
272D3×C22⋊C4—94no—
273C23×C32—24no—
274C23×C32—31no—
275C23×C32C22×D314yes—
276C23×C32C22×D311yescharacteristic
277C22×C3⋊D3—31no—
278C22×C3⋊D3—34no—
279C22×C3⋊D3—31no—
280C22×C3⋊D3—31no—
281C22×C3⋊D3—34no—
282C22×C3⋊D3—34no—
283C22×C3⋊D3—34no—
284C22×C3⋊D3—64no—
285C22×C3⋊D3—64no—
286C22×C3⋊D3—64no—
287C22×C3⋊D3—62no—
288C22×C3⋊D3—62no—
289C22×C3⋊D3—68no—
290C22×C3⋊D3—128no—
291C22×C3⋊D3—121no—
292C22×C3⋊D3—121no—
293C22×C3⋊D3—121no—
294C22×C3⋊D3—121no—
295C22×C3⋊D3—121no—
296C22×C3⋊D3—121no—
297C22×C3⋊D3—124no—
298C22×C3⋊D3—124no—
299C22×C3⋊D3—128no—
300C22×C3⋊D3—128no—
301C22×C3⋊D3C22×D311yescharacteristic
302C22×C3⋊D3C22×D311yescharacteristic
303C22×C3×D3—34no—
304C22×C3×D3—34no—
305C22×C3×D3C22×D314yes—
306C2×D32—316no—
307C2×D32—68no—
308C2×D32—124no—
309C2×D32—124no—
310C2×D32—124no—
311C2×D32—124no—
312C32×D4—62no—
313C2×C32×C4—24no—
314C2×C32×C4—24no—
315C2×C32×C4—31no—
316C2×C32×C4—31no—
317C2×C32×C4—31no—
318C2×C32×C4—62no—
319C2×C32×C4C22×D314yes—
320C2×C32×C4C22×D314yes—
321C2×C32×C4C22×D311yescharacteristic
322C2×C32×C4C22×D311yescharacteristic
323#638—22no—
324#638—41no—
325#638—62no—
326#638—121no—
327#638—124no—
328#638—128no—
329C2×C3⋊Dic3—31no—
330C2×C3⋊Dic3—34no—
331C2×C3⋊Dic3—64no—
332C2×C3⋊Dic3C22×D311yescharacteristic
333C2×C3⋊Dic3C22×D311yescharacteristic
334C4⋊(C3⋊D3)—22no—
335C4⋊(C3⋊D3)—62no—
336C4⋊(C3⋊D3)—62no—
337C4⋊(C3⋊D3)—62no—
338C4⋊(C3⋊D3)—62no—
339C4⋊(C3⋊D3)—68no—
340C4⋊(C3⋊D3)—128no—
341C4⋊(C3⋊D3)—121no—
342C4⋊(C3⋊D3)—124no—
343C4⋊(C3⋊D3)—128no—
344C4⋊(C3⋊D3)—121no—
345C4×C3⋊D3—41no—
346C4×C3⋊D3—62no—
347C4×C3⋊D3—121no—
348C3×#67—28no—
349C3×#67—68no—
350C3×#67—124no—
351C2×C3×Dic3—34no—
352C2×C3×Dic3—34no—
353C2×C3×Dic3C22×D314yes—
354C2×C3×Dic3C22×D314yes—
355C2×C3×Dic3C22×D314yes—
356C3×D12—68no—
357C3×C4×D3—28no—
358C3×C4×D3—124no—
359#626—68no—
360#626—68no—
361#626—68no—
362#626—68no—
363#626—124no—
364#624—68no—
365D3×Dic3—124no—
366#534—271noSylow
367C2×C33—41no—
368C2×C33C22×D411yescharacteristic
369C2×C33H(5,𝔽2)11yescharacteristic
370C2×C33H(5,𝔽2)11yescharacteristic
371C3⋊(C3⋊D3)—22no—
372C3⋊(C3⋊D3)—41no—
373C3⋊(C3⋊D3)—41no—
374C3×C3⋊D3—22no—
375C3×C3⋊D3—41no—
376C32×D3—22no—
377C23×D3—94no—
378C23×D3—94no—
379C23×D3—91no—
380C23×D3—94no—
381C23×D3—91no—
382C23×D3—91no—
383C23×D3—184no—
384C2×C3×D4—34no—
385C2×C3×D4—91no—
386C2×C3×D4—91no—
387C2×C3×D4—91no—
388C22×C3×C4—34no—
389C22×C3×C4—91no—
390C2×#67—34no—
391C2×#67—34no—
392C2×#67—94no—
393C2×#67—94no—
394C2×#67—91no—
395C2×#67—91no—
396C2×#67—91no—
397C2×#67—91no—
398C2×#67—91no—
399C2×#67—184no—
400C2×#67C2×C3⋊D311yescharacteristic
401C22×Dic3—91no—
402D3×D4—184no—
403D3×D4—184no—
404D3×D4—1816no—
405C2×D12—34no—
406C2×D12—94no—
407C2×D12—94no—
408C2×D12—94no—
409C2×D12—91no—
410C2×D12—94no—
411C2×D12—91no—
412C2×D12—94no—
413C2×D12—94no—
414C2×D12—91no—
415C2×D12—184no—
416C2×D12—184no—
417C2×D12—1816no—
418C2×C4×D3—34no—
419C2×C4×D3—94no—
420C2×C4×D3—91no—
421C2×C4×D3—94no—
422C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
423C3×C4⋊C4—34no—
424C3×C4⋊C4—34no—
425C3×C4⋊C4—91no—
426C3×C22⋊C4—24no—
427C3×C22⋊C4—34no—
428C3×C22⋊C4—34no—
429C3×C22⋊C4—91no—
430C3×C22⋊C4D3214yescomplemented
431C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
432#217—94no—
433#217—91no—
434#217C2×C3⋊D311yescharacteristic, complemented
435(C2×D3)⋊C4—34no—
436(C2×D3)⋊C4—94no—
437(C2×D3)⋊C4—94no—
438(C2×D3)⋊C4—94no—
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—91no—
449(C2×D3)⋊C4—91no—
450(C2×D3)⋊C4—184no—
451(C2×D3)⋊C4—184no—
452(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
453C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
454Dic3⋊C4—34no—
455Dic3⋊C4—94no—
456Dic3⋊C4—91no—
457Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
458C22×C32—28no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32—24no—
462C22×C32—21no—
463C22×C32—24no—
464C22×C32—24no—
465C22×C32—24no—
466C22×C32—32no—
467C22×C32—44no—
468C22×C32—44no—
469C22×C32—61no—
470C22×C32—61no—
471C22×C32C23×D314yes—
472C22×C32C23×D311yescharacteristic
473C2×C3⋊D3—21no—
474C2×C3⋊D3—21no—
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—61no—
487C2×C3⋊D3—61no—
488C2×C3⋊D3—64no—
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—124no—
508C2×C3⋊D3—1216no—
509C2×C3⋊D3—1232no—
510C2×C3⋊D3D3×D412yes—
511C2×C3×D3—24no—
512C2×C3×D3—24no—
513C2×C3×D3—38no—
514C2×C3×D3—64no—
515C2×C3×D3—64no—
516C2×C3×D3—64no—
517C2×C3×D3—64no—
518C2×C3×D3—64no—
519C2×C3×D3D3×D418yes—
520D32—1216no—
521D32—1216no—
522C32×C4—21no—
523C32×C4—21no—
524C32×C4—24no—
525C32×C4—24no—
526C32×C4—44no—
527C32×C4—44no—
528C32×C4—61no—
529C32×C4—61no—
530C32×C4—61no—
531C3⋊Dic3—21no—
532C3⋊Dic3—21no—
533C3⋊Dic3—61no—
534C3⋊Dic3—64no—
535C3⋊Dic3—124no—
536C3×Dic3—24no—
537C3×Dic3—24no—
538C3×Dic3—24no—
539C3×Dic3—64no—
540C3×Dic3—64no—
541C22×D4—271no—
542C22×D4—271no—
543#123—31no—
544#123—271no—
545#123—271no—
546#123—271no—
547#121—91no—
548#121—271no—
549#121—271no—
550#121—271no—
551#120—271no—
552#120—271no—
553#120—271no—
554#120—271no—
555C2×C22⋊C4—271no—
556C33#53411yescharacteristic, complemented, Sylow
557C23×C3—24no—
558C23×C3—34no—
559C23×C3—91no—
560C23×C3—91no—
561C23×C3C2×D3214yes—
562C23×C3C22×C3⋊D311yescharacteristic
563C22×D3—34no—
564C22×D3—34no—
565C22×D3—916no—
566C22×D3—94no—
567C22×D3—91no—
568C22×D3—94no—
569C22×D3—94no—
570C22×D3—94no—
571C22×D3—91no—
572C22×D3—91no—
573C22×D3—184no—
574C22×D3—184no—
575C22×D3—184no—
576C22×D3—188no—
577C22×D3—182no—
578C22×D3—188no—
579C22×D3—182no—
580C22×D3—368no—
581C22×D3—361no—
582C22×D3—361no—
583C22×D3—361no—
584C22×D3—361no—
585C22×D3—364no—
586C22×D3—364no—
587C22×D3—364no—
588C22×D3—364no—
589C22×D3—364no—
590C22×D3—364no—
591C22×D3—361no—
592C22×D3—361no—
593C22×D3—368no—
594C22×D3—368no—
595C22×D3C22×C3⋊D311yescharacteristic
596C3×D4—68no—
597C3×D4—182no—
598C3×D4—182no—
599C3×D4—361no—
600C2×C3×C4—24no—
601C2×C3×C4—24no—
602C2×C3×C4—34no—
603C2×C3×C4—34no—
604C2×C3×C4—34no—
605C2×C3×C4—68no—
606C2×C3×C4—91no—
607C2×C3×C4—91no—
608C2×C3×C4—361no—
609C2×C3×C4C2×D3214yes—
610C2×C3×C4C2×D3214yes—
611C2×C3×C4C22×C3⋊D311yescharacteristic
612C2×C3×C4C22×C3⋊D311yescharacteristic
613#67—22no—
614#67—68no—
615#67—124no—
616#67—182no—
617#67—182no—
618#67—182no—
619#67—188no—
620#67—361no—
621#67—364no—
622#67—361no—
623#67—368no—
624C2×Dic3—34no—
625C2×Dic3—34no—
626C2×Dic3—94no—
627C2×Dic3—91no—
628C2×Dic3—184no—
629C2×Dic3—361no—
630C2×Dic3C22×C3⋊D311yescharacteristic
631C2×Dic3C22×C3⋊D311yescharacteristic
632C2×Dic3C22×C3⋊D311yescharacteristic
633D12—68no—
634D12—182no—
635D12—188no—
636D12—188no—
637D12—188no—
638D12—188no—
639D12—182no—
640D12—368no—
641D12—364no—
642D12—361no—
643D12—368no—
644D12—364no—
645C4×D3—22no—
646C4×D3—124no—
647C4×D3—182no—
648C4×D3—188no—
649C4×D3—364no—
650C2×C32—24no—
651C2×C32—24no—
652C2×C32—24no—
653C2×C32—48no—
654C2×C32—44no—
655C2×C32—41no—
656C2×C32—62no—
657C2×C32C2×D3×D414yes—
658C2×C32C2×D3×D411yescharacteristic
659C2×C32#100411yescharacteristic
660C2×C32#100914yes—
661C2×C32#100914yes—
662C2×C32#100911yescharacteristic
663C3⋊D3—22no—
664C3⋊D3—41no—
665C3⋊D3—62no—
666C3⋊D3—68no—
667C3⋊D3—128no—
668C3⋊D3—128no—
669C3⋊D3—124no—
670C3⋊D3—121no—
671C3⋊D3—121no—
672C3⋊D3—124no—
673C3⋊D3—244no—
674C3×D3—28no—
675C3×D3—68no—
676C3×D3—124no—
677C24—271no—
678C24—271no—
679C24—271no—
680C2×D4—31no—
681C2×D4—91no—
682C2×D4—91no—
683C2×D4—91no—
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—544no—
693C2×D4—544no—
694C22×C4—31no—
695C22×C4—91no—
696C22×C4—271no—
697C22×C4—271no—
698C4⋊C4—31no—
699C4⋊C4—31no—
700C4⋊C4—91no—
701C4⋊C4—271no—
702C22⋊C4—31no—
703C22⋊C4—31no—
704C22⋊C4—91no—
705C22⋊C4—271no—
706C22⋊C4—271no—
707C22⋊C4—271no—
708C22⋊C4—271no—
709C22⋊C4—271no—
710C22⋊C4—271no—
711C22⋊C4—271no—
712C22⋊C4—271no—
713C22⋊C4D3×C3⋊D311yescharacteristic, complemented
714C22×C3—28no—
715C22×C3—24no—
716C22×C3—24no—
717C22×C3—24no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—24no—
722C22×C3—38no—
723C22×C3—44no—
724C22×C3—44no—
725C22×C3—64no—
726C22×C3—64no—
727C22×C3—92no—
728C22×C3—181no—
729C22×C3—181no—
730C22×C3—181no—
731C22×C3—181no—
732C22×C3—181no—
733C22×C3C22×D3214yes—
734C22×C3C23×C3⋊D311yescharacteristic
735C2×D3—21no—
736C2×D3—21no—
737C2×D3—38no—
738C2×D3—64no—
739C2×D3—64no—
740C2×D3—64no—
741C2×D3—64no—
742C2×D3—64no—
743C2×D3—98no—
744C2×D3—92no—
745C2×D3—188no—
746C2×D3—184no—
747C2×D3—184no—
748C2×D3—181no—
749C2×D3—181no—
750C2×D3—188no—
751C2×D3—184no—
752C2×D3—184no—
753C2×D3—184no—
754C2×D3—184no—
755C2×D3—184no—
756C2×D3—184no—
757C2×D3—181no—
758C2×D3—181no—
759C2×D3—181no—
760C2×D3—181no—
761C2×D3—181no—
762C2×D3—181no—
763C2×D3—364no—
764C2×D3—364no—
765C2×D3—364no—
766C2×D3—364no—
767C2×D3—364no—
768C2×D3—364no—
769C2×D3—364no—
770C2×D3—364no—
771C2×D3—364no—
772C2×D3—3616no—
773C2×D3—3616no—
774C2×D3—364no—
775C2×D3—3616no—
776C2×D3—3632no—
777C2×D3D4×C3⋊D312yes—
778C3×C4—24no—
779C3×C4—24no—
780C3×C4—21no—
781C3×C4—21no—
782C3×C4—44no—
783C3×C4—44no—
784C3×C4—64no—
785C3×C4—64no—
786C3×C4—64no—
787C3×C4—181no—
788C3×C4—181no—
789Dic3—21no—
790Dic3—21no—
791Dic3—21no—
792Dic3—64no—
793Dic3—64no—
794Dic3—184no—
795Dic3—181no—
796Dic3—364no—
797C32—24no—
798C32#560511yescharacteristic, complemented
799C32#565314yescomplemented
800C23—31no—
801C23—91no—
802C23—91no—
803C23—274no—
804C23—271no—
805C23—271no—
806C23—271no—
807C23—542no—
808C23—542no—
809C23—1081no—
810C23—1081no—
811C23—1081no—
812C23—1081no—
813C23—1081no—
814C23—1081no—
815C23C2×D3×C3⋊D311yescharacteristic
816D4—62no—
817D4—182no—
818D4—182no—
819D4—361no—
820D4—542no—
821D4—542no—
822D4—542no—
823D4—542no—
824D4—542no—
825D4—1081no—
826D4—1081no—
827D4—1081no—
828C2×C4—31no—
829C2×C4—31no—
830C2×C4—31no—
831C2×C4—62no—
832C2×C4—91no—
833C2×C4—91no—
834C2×C4—271no—
835C2×C4—361no—
836C2×C4—542no—
837C2×C4—1081no—
838C2×C4C2×D3×C3⋊D311yescharacteristic
839C2×C4C2×D3×C3⋊D311yescharacteristic
840C2×C3—24no—
841C2×C3—24no—
842C2×C3—24no—
843C2×C3—48no—
844C2×C3—41no—
845C2×C3—44no—
846C2×C3—68no—
847C2×C3—182no—
848C2×C3—361no—
849C2×C3#6430814yes—
850C2×C3D32×D414yes—
851C2×C3#6431414yes—
852C2×C3C2×D4×C3⋊D311yescharacteristic
853C2×C3#6436611yescharacteristic
854C2×C3#6436611yescharacteristic
855D3—22no—
856D3—68no—
857D3—124no—
858D3—182no—
859D3—188no—
860D3—368no—
861D3—368no—
862D3—361no—
863D3—361no—
864D3—364no—
865D3—364no—
866D3—724no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—32no—
871C22—61no—
872C22—61no—
873C22—92no—
874C22—181no—
875C22—181no—
876C22—181no—
877C22—181no—
878C22—181no—
879C22—272no—
880C22—541no—
881C22—541no—
882C22—541no—
883C22—541no—
884C22—541no—
885C22—541no—
886C22—541no—
887C22—541no—
888C22—1084no—
889C22—1084no—
890C22—1084no—
891C22C22×D3×C3⋊D311yescharacteristic
892C4—21no—
893C4—21no—
894C4—61no—
895C4—61no—
896C4—61no—
897C4—181no—
898C4—181no—
899C4—541no—
900C3—24no—
901C3#1059426414yescomplemented
902C3#1059612411yescharacteristic, complemented
903C2—41no—
904C2—62no—
905C2—182no—
906C2—361no—
907C2—542no—
908C2—1081no—
909C2—1081no—
910C2#1172458111yescharacteristic
911C2D3×D4×C3⋊D311yescharacteristic
912C2#1172458911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33#534
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×D3×C4⋊(C3⋊D3)C2semidirect
3. #11723923C2semidirect
4. C3×#64093C2semidirect
5. C32×#883C2semidirect
6. #11723643C2semidirect
7. #11723639C2semidirect
8. #11723624C2semidirect
9. #11723542C2semidirect
10. C3⋊D3×(C2×D3)⋊C4C2semidirect
11. #11723526C2semidirect
12. #11723504C2semidirect
13. #11723498C2semidirect
14. #11723482C2semidirect
15. #11723414C2semidirect
18. C23×C3⋊(C3⋊D3)C22semidirect
20. C22×D3×C3⋊D3C22semidirect
21. C2×#6312C22semidirect
23. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
24. C2×C3×#638C22semidirect
25. C2×C3×#638C22semidirect
26. C2×C3×C4⋊(C3⋊D3)C22semidirect
27. C2×C3×C4×C3⋊D3C22semidirect
29. C2×C32×C4×D3C22semidirect
32. C2×#6292C22semidirect
33. C2×#6292C22semidirect
34. C2×#6292C22semidirect
36. C2×#6289C22semidirect
37. C2×Dic3×C3⋊D3C22semidirect
39. C33×C22⋊C4C22semidirect
40. #88859C22semidirect
41. #88859C22semidirect
42. C3×#3752C22semidirect
43. C3×#3750C22semidirect
44. C32×#217C22semidirect
45. C32×(C2×D3)⋊C4C22semidirect
46. C32×C4⋊Dic3C22semidirect
47. C32×Dic3⋊C4C22semidirect
48. #88806C22semidirect
49. #88804C22semidirect
50. #88804C22semidirect
51. #88804C22semidirect
52. #88804C22semidirect
53. #88803C22semidirect
54. (C2×D3)⋊(C3⋊Dic3)C22semidirect
67. #64093D3semidirect
75. C3×#883D3semidirect
101. C2×D3×C3⋊D3D4semidirect
141. C2×#638C2×D3semidirect
142. C2×#638C2×D3semidirect
155. C2×C4⋊(C3⋊D3)C2×D3semidirect
158. C2×C4×C3⋊D3C2×D3semidirect
164. C2×C3×C4×D3C2×D3semidirect
179. C32×C22⋊C4C2×D3semidirect
180. C32×C22⋊C4C2×D3semidirect
193. #3752C2×D3semidirect
195. #3750C2×D3semidirect
196. C3×#217C2×D3semidirect
198. C3×(C2×D3)⋊C4C2×D3semidirect
199. C3×C4⋊Dic3C2×D3semidirect
201. C3×Dic3⋊C4C2×D3semidirect
265. #883C3⋊D3semidirect
422. C2×C4×D3C2×C3⋊D3semidirect
430. C3×C22⋊C4D32semidirect
431. C3×C22⋊C4C2×C3⋊D3semidirect
434. #217C2×C3⋊D3semidirect
452. (C2×D3)⋊C4C2×C3⋊D3semidirect
453. C4⋊Dic3C2×C3⋊D3semidirect
457. Dic3⋊C4C2×C3⋊D3semidirect
556. C33#534semidirect
713. C22⋊C4D3×C3⋊D3semidirect
798. C32#5605semidirect
799. C32#5653semidirect
901. C3#10594264semidirect
902. C3#10596124semidirect

Maximal subgroups

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

subgroupindex
C2×#890392
C2×D3×C4⋊(C3⋊D3)2
#117239232
C3×#640932
C32×#8832
#117236432
#117236392
#117236242
#117235422
C3⋊D3×(C2×D3)⋊C42
#117235262
#117235042
#117234982
#117234822
#117234142
#105961243
#105942643