Finite Group Databasebeta

← #13175938

Subgroups — #13175938

Order 1728.

2524 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89039C211yesmaximal, characteristic, complemented
2C2×#89028C211yesmaximal, characteristic, complemented
3#11723923C211yesmaximal, characteristic, complemented
4C3×#64095C211yesmaximal, characteristic, complemented
5C32×#67⋊C4C211yesmaximal, characteristic, complemented
6#11723632C211yesmaximal, characteristic, complemented
7C2×#88804C211yesmaximal, characteristic, complemented
8#11723542C211yesmaximal, characteristic, complemented
9D3×#3752C211yesmaximal, characteristic, complemented
10#11723516C211yesmaximal, characteristic, complemented
11#11723486C211yesmaximal, characteristic, complemented
12#11723485C211yesmaximal, characteristic, complemented
13#11723484C211yesmaximal, characteristic, complemented
14#11723479C211yesmaximal, characteristic, complemented
15#11723416C211yesmaximal, characteristic, complemented
16#10596025—31nomaximal
17#10594293—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
24C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic
26C22×C32×Dic3C2211yescharacteristic, complemented
27C2×C32×C4×D3C2211yescharacteristic, complemented
28#89039—24no—
29C2×#6293C2211yescharacteristic, complemented
30C2×#6292C2211yescharacteristic
31C2×#6292C2211yescharacteristic, complemented
32C2×#6291C2211yescharacteristic
33C2×#6291C2211yescharacteristic, complemented
34C2×#6289C2211yescharacteristic
35C2×#6289C2211yescharacteristic, complemented
36#89028—24no—
37C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
38C33×C22⋊C4C2211yescharacteristic, complemented
39#88859C2211yescharacteristic
40#88859C2211yescharacteristic, complemented
41C3×#3752C2211yescharacteristic, complemented
42C3×#3752C2211yescharacteristic, complemented
43C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C32×Dic3⋊C4C2211yescharacteristic, complemented
47C32×C4×Dic3C2211yescharacteristic, complemented
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49#88804C2211yescharacteristic
50#88804C2211yescharacteristic
51#88804C2211yescharacteristic, complemented
52#88804C2211yescharacteristic, complemented
53#88804C2211yescharacteristic, complemented
54#88803C2211yescharacteristic, complemented
55C2×#3830—31no—
56C2×D4×C3⋊D3—31no—
57C2×#3811—34no—
58C2×#3804—34no—
59C32×C4×D4—31no—
60#64139—31no—
61#64139—31no—
62C2×#3752—31no—
63C2×#3752—31no—
64#64106—31no—
65#64104—31no—
66#64095—31no—
67#64095D311yescharacteristic, complemented
68#64091—31no—
69#64091—31no—
70#64091—34no—
71#64091—64no—
72#64084—31no—
73C4×C4⋊(C3⋊D3)—31no—
74C3×#886—34no—
75C3×#67⋊C4D314yescomplemented
76#63978—34no—
77C2×#3722—34no—
78#63923—34no—
79D3×(C2×D3)⋊C4—34no—
80#63910—34no—
81#63909—34no—
82#63895—34no—
83#63894—34no—
84#63890—34no—
85#63852—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)—22no—
88C22×C3⋊(C3⋊D3)—22no—
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
95C2×D3×C3⋊D3—22no—
96C2×D3×C3⋊D3—22no—
97C2×D3×C3⋊D3—41no—
98C2×C33×C4C2311yescharacteristic
99C2×C33×C4C2311yescharacteristic
100#6312—22no—
101C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
102C4⋊(C3⋊(C3⋊D3))—22no—
103C4⋊(C3⋊(C3⋊D3))—41no—
104C3×#638—22no—
105C2×C3×C3⋊Dic3—22no—
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C32×#67D414yescomplemented
110C2×C32×Dic3—41no—
111C2×C32×Dic3C2311yescharacteristic
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C32×C4×D3—41no—
115#6293—22no—
116#6292—22no—
117#6292—41no—
118#6291—22no—
119#6291—22no—
120#6289—22no—
121#6289—22no—
122D3×C3⋊Dic3—22no—
123#5654—91no—
124#5554—94no—
125C23×C3⋊D3—31no—
126C23×C3⋊D3—34no—
127C23×C3⋊D3—31no—
128C23×C3⋊D3—64no—
129C22×D32—34no—
130C2×C32×D4—31no—
131C22×C32×C4—31no—
132C22×C32×C4—31no—
133C2×#638—31no—
134C2×#638—34no—
135C2×#638—31no—
136C2×#638—31no—
137C2×#638—64no—
138C2×#638C2×D311yescharacteristic
139C22×C3⋊Dic3—31no—
140C22×C3⋊Dic3C2×D311yescharacteristic, complemented
141#3830—64no—
142D4×C3⋊D3—64no—
143C2×C4⋊(C3⋊D3)—31no—
144C2×C4⋊(C3⋊D3)—31no—
145C2×C4⋊(C3⋊D3)—34no—
146C2×C4⋊(C3⋊D3)—31no—
147C2×C4⋊(C3⋊D3)—31no—
148C2×C4⋊(C3⋊D3)—34no—
149C2×C4⋊(C3⋊D3)—64no—
150C2×C4⋊(C3⋊D3)—64no—
151C2×C4×C3⋊D3—31no—
152C2×C4×C3⋊D3—31no—
153C2×#634—31no—
154C2×C3×#67—34no—
155C2×C3×#67C2×D314yes—
156C22×C3×Dic3—34no—
157C22×C3×Dic3C2×D314yescomplemented
158C2×C3×C4×D3C2×D314yescomplemented
159#3811—616no—
160C2×#627—34no—
161C2×#626—34no—
162C2×#626—34no—
163C2×#626—34no—
164C2×#626—34no—
165C2×#624—34no—
166C2×#624—34no—
167#3804—616no—
168C2×D3×Dic3—34no—
169C32×C4⋊C4—31no—
170C32×C22⋊C4—24no—
171C32×C22⋊C4—31no—
172C32×C22⋊C4C2×D314yescomplemented
173C32×C22⋊C4C2×D311yescharacteristic, complemented
174C32×C42—31no—
175#3752—31no—
176#3752—31no—
177#3752—31no—
178#3752—34no—
179#3752—34no—
180#3752—31no—
181#3752—31no—
182#3752—31no—
183#3752—31no—
184#3752—31no—
185#3752—64no—
186#3752—64no—
187#3752C2×D311yescharacteristic, complemented
188#3752C2×D311yescharacteristic, complemented
189C4⋊(C3⋊Dic3)—31no—
190C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
191C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
192C3×(C2×D3)⋊C4—34no—
193C3×(C2×D3)⋊C4—34no—
194C3×(C2×D3)⋊C4C2×D314yescomplemented
195C3×C4⋊Dic3—34no—
196C3×C4⋊Dic3—34no—
197C3×Dic3⋊C4C2×D314yescomplemented
198C3×C4×Dic3C2×D314yescomplemented
199Dic3⋊Dic3—34no—
200#3722—34no—
201#3722—34no—
202#3722—34no—
203#3722—34no—
204#3722—34no—
205(C2×D3)⋊Dic3—34no—
206C22×C33—21no—
207C22×C33—21no—
208C22×C33C2×D412yes—
209C22×C33C2411yescharacteristic
210C2×C3⋊(C3⋊D3)—21no—
211C2×C3⋊(C3⋊D3)—21no—
212C2×C3⋊(C3⋊D3)—21no—
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)—44no—
219C2×C3⋊(C3⋊D3)#4112yescomplemented
220C2×C3×C3⋊D3—21no—
221C2×C3×C3⋊D3—21no—
222C2×C3×C3⋊D3—21no—
223C2×C32×D3—21no—
224C2×C32×D3—21no—
225C2×C32×D3C2×D412yes—
226D3×C3⋊D3—44no—
227C33×C4—21no—
228C33×C4—21no—
229C3⋊(C3⋊Dic3)—21no—
230C3×C3⋊Dic3—21no—
231C3×C3⋊Dic3—21no—
232C3×C3⋊Dic3—21no—
233C32×Dic3—21no—
234C32×Dic3—21no—
235C32×Dic3C2×D412yes—
236C2×#237—94no—
237C2×D3×D4—94no—
238C2×D3×D4—91no—
239C2×#235—91no—
240C3×#123—91no—
241C3×C4×D4—34no—
242#939—91no—
243#930—94no—
244#930—94no—
245C2×(C2×D3)⋊C4—94no—
246C2×(C2×D3)⋊C4—94no—
247C2×(C2×D3)⋊C4—91no—
248#897—94no—
249#896—91no—
250#895—94no—
251#895—91no—
252#894—91no—
253#893—91no—
254#886—34no—
255#886—94no—
256#885—91no—
257#884—91no—
258#882—94no—
259#882—94no—
260#882—91no—
261#882—91no—
262#882—184no—
263#67⋊C4C3⋊D311yescharacteristic, complemented
264D3×C22⋊C4—91no—
265#875—94no—
266C4×D12—94no—
267C23×C32—24no—
268C23×C32—31no—
269C23×C32C22×D314yes—
270C23×C32C22×D311yescharacteristic
271C22×C3⋊D3—31no—
272C22×C3⋊D3—31no—
273C22×C3⋊D3—31no—
274C22×C3⋊D3—34no—
275C22×C3⋊D3—34no—
276C22×C3⋊D3—34no—
277C22×C3⋊D3—64no—
278C22×C3⋊D3—64no—
279C22×C3⋊D3—64no—
280C22×C3⋊D3—62no—
281C22×C3⋊D3—62no—
282C22×C3⋊D3—62no—
283C22×C3⋊D3—62no—
284C22×C3⋊D3—68no—
285C22×C3⋊D3—68no—
286C22×C3⋊D3—128no—
287C22×C3⋊D3—128no—
288C22×C3⋊D3—121no—
289C22×C3⋊D3—121no—
290C22×C3⋊D3—124no—
291C22×C3⋊D3—128no—
292C22×C3⋊D3C22×D311yescharacteristic
293C22×C3×D3—34no—
294C22×C3×D3C22×D314yes—
295C2×D32—68no—
296C2×D32—68no—
297C2×D32—124no—
298C32×D4—34no—
299C2×C32×C4—24no—
300C2×C32×C4—24no—
301C2×C32×C4—31no—
302C2×C32×C4—31no—
303C2×C32×C4—31no—
304C2×C32×C4—121no—
305C2×C32×C4—121no—
306C2×C32×C4C22×D314yes—
307C2×C32×C4C22×D314yes—
308C2×C32×C4C22×D311yescharacteristic
309C2×C32×C4C22×D311yescharacteristic
310#638—22no—
311#638—62no—
312#638—62no—
313#638—62no—
314#638—68no—
315#638—128no—
316C2×C3⋊Dic3—22no—
317C2×C3⋊Dic3—31no—
318C2×C3⋊Dic3—34no—
319C2×C3⋊Dic3—64no—
320C2×C3⋊Dic3—62no—
321C2×C3⋊Dic3C22×D311yescharacteristic
322C2×C3⋊Dic3C22×D311yescharacteristic
323C2×C3⋊Dic3C22×D311yescharacteristic
324C4⋊(C3⋊D3)—62no—
325C4⋊(C3⋊D3)—62no—
326C4⋊(C3⋊D3)—68no—
327C4⋊(C3⋊D3)—128no—
328C4⋊(C3⋊D3)—121no—
329C4⋊(C3⋊D3)—124no—
330C4⋊(C3⋊D3)—128no—
331C4⋊(C3⋊D3)—121no—
332C4×C3⋊D3—62no—
333C4×C3⋊D3—62no—
334#634—62no—
335C3×#67—68no—
336C3×#67D12116yescomplemented
337C2×C3×Dic3—34no—
338C2×C3×Dic3—34no—
339C2×C3×Dic3—34no—
340C2×C3×Dic3—44no—
341C2×C3×Dic3—68no—
342C2×C3×Dic3C22×D314yes—
343C2×C3×Dic3C22×D314yes—
344C2×C3×Dic3C22×D314yes—
345C3×C4×D3—44no—
346#627—68no—
347#626—68no—
348#626—68no—
349#626—68no—
350#626—124no—
351#624—68no—
352#624—68no—
353D3×Dic3—68no—
354#546—271noSylow
355C2×C33—22no—
356C2×C33C22×D411yescharacteristic
357C2×C33C2×#4111yescharacteristic
358C2×C33H(5,𝔽2)11yescharacteristic
359C3⋊(C3⋊D3)—22no—
360C3⋊(C3⋊D3)—41no—
361C3⋊(C3⋊D3)—41no—
362C3×C3⋊D3—41no—
363C32×D3—22no—
364C23×D3—94no—
365C23×D3—94no—
366C23×D3—91no—
367C23×D3—91no—
368C23×D3—184no—
369C2×C3×D4—34no—
370C2×C3×D4—91no—
371C22×C3×C4—34no—
372C22×C3×C4—34no—
373C22×C3×C4—91no—
374C2×#67—34no—
375C2×#67—94no—
376C2×#67—94no—
377C2×#67—94no—
378C2×#67—91no—
379C2×#67—91no—
380C2×#67—91no—
381C2×#67—184no—
382C2×#67C2×C3⋊D311yescharacteristic
383C22×Dic3—34no—
384C22×Dic3—94no—
385C22×Dic3C2×C3⋊D311yescharacteristic, complemented
386#237—1816no—
387D3×D4—1816no—
388D3×D4—184no—
389#235—184no—
390C2×D12—94no—
391C2×D12—91no—
392C2×D12—91no—
393C2×D12—94no—
394C2×D12—91no—
395C2×D12—94no—
396C2×D12—94no—
397C2×D12—91no—
398C2×D12—184no—
399C2×D12—184no—
400C2×C4×D3—94no—
401C2×C4×D3—94no—
402C2×C4×D3—91no—
403C2×C4×D3—91no—
404C2×C4×D3—91no—
405C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
406C2×Dic6—94no—
407C2×Dic6—91no—
408C3×C4⋊C4—34no—
409C3×C4⋊C4—91no—
410C3×C4⋊C4—91no—
411C3×C22⋊C4—24no—
412C3×C22⋊C4—34no—
413C3×C22⋊C4—91no—
414C3×C22⋊C4—91no—
415C3×C22⋊C4D3214yescomplemented
416C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
417C3×C42—34no—
418#217—91no—
419(C2×D3)⋊C4—34no—
420(C2×D3)⋊C4—34no—
421(C2×D3)⋊C4—94no—
422(C2×D3)⋊C4—94no—
423(C2×D3)⋊C4—94no—
424(C2×D3)⋊C4—94no—
425(C2×D3)⋊C4—94no—
426(C2×D3)⋊C4—94no—
427(C2×D3)⋊C4—94no—
428(C2×D3)⋊C4—94no—
429(C2×D3)⋊C4—91no—
430(C2×D3)⋊C4—91no—
431(C2×D3)⋊C4—91no—
432(C2×D3)⋊C4—91no—
433(C2×D3)⋊C4—91no—
434(C2×D3)⋊C4—91no—
435(C2×D3)⋊C4—91no—
436(C2×D3)⋊C4—184no—
437(C2×D3)⋊C4—184no—
438(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
439C4⋊Dic3—34no—
440C4⋊Dic3—34no—
441C4⋊Dic3—94no—
442Dic3⋊C4—91no—
443Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
444C4×Dic3C2×C3⋊D311yescharacteristic, complemented
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—24no—
448C22×C32—28no—
449C22×C32—24no—
450C22×C32—24no—
451C22×C32—32no—
452C22×C32—44no—
453C22×C32—44no—
454C22×C32—61no—
455C22×C32—61no—
456C22×C32C2×D1218yes—
457C22×C32D3×D412yes—
458C22×C32C23×D314yes—
459C22×C32C23×D311yescharacteristic
460C2×C3⋊D3—21no—
461C2×C3⋊D3—21no—
462C2×C3⋊D3—21no—
463C2×C3⋊D3—32no—
464C2×C3⋊D3—38no—
465C2×C3⋊D3—68no—
466C2×C3⋊D3—61no—
467C2×C3⋊D3—61no—
468C2×C3⋊D3—68no—
469C2×C3⋊D3—61no—
470C2×C3⋊D3—61no—
471C2×C3⋊D3—64no—
472C2×C3⋊D3—61no—
473C2×C3⋊D3—61no—
474C2×C3⋊D3—61no—
475C2×C3⋊D3—61no—
476C2×C3⋊D3—64no—
477C2×C3⋊D3—64no—
478C2×C3⋊D3—64no—
479C2×C3⋊D3—64no—
480C2×C3⋊D3—64no—
481C2×C3⋊D3—64no—
482C2×C3⋊D3—64no—
483C2×C3⋊D3—124no—
484C2×C3⋊D3—124no—
485C2×C3⋊D3—124no—
486C2×C3⋊D3—124no—
487C2×C3⋊D3—124no—
488C2×C3⋊D3—124no—
489C2×C3⋊D3—124no—
490C2×C3⋊D3—124no—
491C2×C3⋊D3—124no—
492C2×C3⋊D3—1216no—
493C2×C3⋊D3—1232no—
494C2×C3×D3—24no—
495C2×C3×D3—24no—
496C2×C3×D3—64no—
497C2×C3×D3—64no—
498C2×C3×D3—64no—
499C2×C3×D3C2×D1218yes—
500D32—1216no—
501C32×C4—21no—
502C32×C4—21no—
503C32×C4—24no—
504C32×C4—24no—
505C32×C4—32no—
506C32×C4—44no—
507C32×C4—44no—
508C32×C4—61no—
509C32×C4—61no—
510C3⋊Dic3—21no—
511C3⋊Dic3—21no—
512C3⋊Dic3—21no—
513C3⋊Dic3—61no—
514C3⋊Dic3—64no—
515C3⋊Dic3—124no—
516C3×Dic3—24no—
517C3×Dic3—24no—
518C3×Dic3—64no—
519C3×Dic3—64no—
520C3×Dic3—64no—
521C3×Dic3C2×D1218yes—
522C2×#41—271no—
523C22×D4—271no—
524#124—271no—
525#123—91no—
526#123—271no—
527C22⋊Q8—271no—
528#121—271no—
529#121—271no—
530#121—271no—
531#120—271no—
532#120—271no—
533C4×D4—31no—
534C4×D4—271no—
535C2×C22⋊C4—271no—
536C2×C22⋊C4—271no—
537C33#54611yescharacteristic, complemented, Sylow
538C23×C3—24no—
539C23×C3—34no—
540C23×C3—91no—
541C23×C3C2×D3214yes—
542C23×C3C22×C3⋊D311yescharacteristic
543C22×D3—34no—
544C22×D3—94no—
545C22×D3—91no—
546C22×D3—94no—
547C22×D3—94no—
548C22×D3—91no—
549C22×D3—91no—
550C22×D3—184no—
551C22×D3—184no—
552C22×D3—184no—
553C22×D3—182no—
554C22×D3—188no—
555C22×D3—188no—
556C22×D3—182no—
557C22×D3—188no—
558C22×D3—188no—
559C22×D3—182no—
560C22×D3—182no—
561C22×D3—368no—
562C22×D3—368no—
563C22×D3—361no—
564C22×D3—364no—
565C22×D3—364no—
566C22×D3—361no—
567C22×D3—368no—
568C22×D3C22×C3⋊D311yescharacteristic
569C3×D4—316no—
570C3×D4—182no—
571C2×C3×C4—24no—
572C2×C3×C4—24no—
573C2×C3×C4—34no—
574C2×C3×C4—34no—
575C2×C3×C4—34no—
576C2×C3×C4—91no—
577C2×C3×C4—91no—
578C2×C3×C4—91no—
579C2×C3×C4—124no—
580C2×C3×C4—124no—
581C2×C3×C4—182no—
582C2×C3×C4C2×D3214yes—
583C2×C3×C4C2×D3214yes—
584C2×C3×C4C22×C3⋊D311yescharacteristic
585C2×C3×C4C22×C3⋊D311yescharacteristic
586#67—68no—
587#67—188no—
588#67—188no—
589#67—188no—
590#67—182no—
591#67—182no—
592#67—368no—
593#67—361no—
594#67C4⋊(C3⋊D3)14yescomplemented
595C2×Dic3—34no—
596C2×Dic3—34no—
597C2×Dic3—34no—
598C2×Dic3—41no—
599C2×Dic3—68no—
600C2×Dic3—94no—
601C2×Dic3—91no—
602C2×Dic3—184no—
603C2×Dic3—188no—
604C2×Dic3C22×C3⋊D311yescharacteristic
605C2×Dic3C22×C3⋊D311yescharacteristic
606C2×Dic3C22×C3⋊D311yescharacteristic
607D12—182no—
608D12—188no—
609D12—188no—
610D12—182no—
611D12—182no—
612D12—368no—
613D12—364no—
614D12—361no—
615D12—368no—
616D12—364no—
617C4×D3—41no—
618C4×D3—188no—
619C4×D3—188no—
620C4×D3—182no—
621C4×D3—182no—
622C4×D3—182no—
623Dic6—188no—
624Dic6—182no—
625C2×C32—22no—
626C2×C32—24no—
627C2×C32—24no—
628C2×C32—24no—
629C2×C32—28no—
630C2×C32—48no—
631C2×C32—62no—
632C2×C32C22×D1214yes—
633C2×C32C2×D3×D411yescharacteristic
634C2×C32#100414yes—
635C2×C32D3×#4114yes—
636C2×C32D3×#4111yescharacteristic
637C2×C32#100911yescharacteristic
638C3⋊D3—41no—
639C3⋊D3—62no—
640C3⋊D3—68no—
641C3⋊D3—128no—
642C3⋊D3—128no—
643C3⋊D3—121no—
644C3⋊D3—121no—
645C3⋊D3—124no—
646C3⋊D3—124no—
647C3⋊D3—244no—
648C3×D3—28no—
649C3×D3—124no—
650C24—271no—
651C24—271no—
652#41—544no—
653C2×Q8—271no—
654C2×D4—31no—
655C2×D4—91no—
656C2×D4—271no—
657C2×D4—271no—
658C2×D4—271no—
659C2×D4—271no—
660C2×D4—271no—
661C2×D4—271no—
662C2×D4—271no—
663C2×D4—544no—
664C22×C4—31no—
665C22×C4—31no—
666C22×C4—91no—
667C22×C4—271no—
668C22×C4—271no—
669C22×C4—271no—
670C4⋊C4—31no—
671C4⋊C4—91no—
672C4⋊C4—91no—
673C4⋊C4—271no—
674C22⋊C4—31no—
675C22⋊C4—91no—
676C22⋊C4—91no—
677C22⋊C4—271no—
678C22⋊C4—271no—
679C22⋊C4—271no—
680C22⋊C4—271no—
681C22⋊C4—271no—
682C22⋊C4—271no—
683C22⋊C4—271no—
684C22⋊C4—271no—
685C22⋊C4D3×C3⋊D311yescharacteristic, complemented
686C42—31no—
687C22×C3—24no—
688C22×C3—24no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—24no—
692C22×C3—28no—
693C22×C3—38no—
694C22×C3—44no—
695C22×C3—44no—
696C22×C3—64no—
697C22×C3—64no—
698C22×C3—181no—
699C22×C3—181no—
700C22×C3—181no—
701C22×C3D3×D1218yes—
702C22×C3C2×C4⋊(C3⋊D3)12yes—
703C22×C3C22×D3214yes—
704C22×C3C23×C3⋊D311yescharacteristic
705C2×D3—21no—
706C2×D3—21no—
707C2×D3—64no—
708C2×D3—64no—
709C2×D3—64no—
710C2×D3—98no—
711C2×D3—92no—
712C2×D3—188no—
713C2×D3—184no—
714C2×D3—184no—
715C2×D3—181no—
716C2×D3—181no—
717C2×D3—188no—
718C2×D3—184no—
719C2×D3—184no—
720C2×D3—184no—
721C2×D3—184no—
722C2×D3—184no—
723C2×D3—184no—
724C2×D3—181no—
725C2×D3—181no—
726C2×D3—181no—
727C2×D3—181no—
728C2×D3—181no—
729C2×D3—181no—
730C2×D3—364no—
731C2×D3—364no—
732C2×D3—364no—
733C2×D3—364no—
734C2×D3—364no—
735C2×D3—364no—
736C2×D3—364no—
737C2×D3—364no—
738C2×D3—3616no—
739C2×D3—364no—
740C2×D3—3616no—
741C2×D3—3632no—
742C2×D3C2×C4⋊(C3⋊D3)12yes—
743C3×C4—24no—
744C3×C4—24no—
745C3×C4—21no—
746C3×C4—21no—
747C3×C4—38no—
748C3×C4—44no—
749C3×C4—44no—
750C3×C4—64no—
751C3×C4—64no—
752C3×C4—181no—
753C3×C4—181no—
754C3×C4—181no—
755Dic3—21no—
756Dic3—21no—
757Dic3—64no—
758Dic3—64no—
759Dic3—64no—
760Dic3—184no—
761Dic3—181no—
762Dic3—364no—
763Dic3C2×C4⋊(C3⋊D3)12yes—
764C32—24no—
765C32#555414yescomplemented
766C32#565411yescharacteristic, complemented
767C23—31no—
768C23—91no—
769C23—271no—
770C23—271no—
771C23—271no—
772C23—542no—
773C23—542no—
774C23—542no—
775C23—542no—
776C23—1081no—
777C23—1081no—
778C23C2×D3×C3⋊D311yescharacteristic
779Q8—542no—
780D4—34no—
781D4—182no—
782D4—542no—
783D4—542no—
784D4—542no—
785D4—542no—
786D4—542no—
787D4—1081no—
788D4—1081no—
789C2×C4—31no—
790C2×C4—31no—
791C2×C4—31no—
792C2×C4—91no—
793C2×C4—91no—
794C2×C4—91no—
795C2×C4—121no—
796C2×C4—121no—
797C2×C4—182no—
798C2×C4—271no—
799C2×C4—542no—
800C2×C4—542no—
801C2×C4—542no—
802C2×C4C2×D3×C3⋊D311yescharacteristic
803C2×C4C2×D3×C3⋊D311yescharacteristic
804C2×C3—22no—
805C2×C3—28no—
806C2×C3—24no—
807C2×C3—24no—
808C2×C3—24no—
809C2×C3—48no—
810C2×C3—68no—
811C2×C3—361no—
812C2×C3C2×D3×D1214yes—
813C2×C3#6431214yes—
814C2×C3#6431414yes—
815C2×C3C22×C4⋊(C3⋊D3)11yescharacteristic
816C2×C3#6436111yescharacteristic
817C2×C3#41×C3⋊D311yescharacteristic
818D3—22no—
819D3—124no—
820D3—182no—
821D3—188no—
822D3—368no—
823D3—368no—
824D3—361no—
825D3—361no—
826D3—364no—
827D3—364no—
828D3—724no—
829C22—21no—
830C22—21no—
831C22—32no—
832C22—61no—
833C22—61no—
834C22—181no—
835C22—181no—
836C22—181no—
837C22—272no—
838C22—541no—
839C22—541no—
840C22—541no—
841C22—541no—
842C22—541no—
843C22—541no—
844C22—541no—
845C22—541no—
846C22—1084no—
847C22—1084no—
848C22D3×C4⋊(C3⋊D3)12yes—
849C22C22×D3×C3⋊D311yescharacteristic
850C4—21no—
851C4—21no—
852C4—32no—
853C4—61no—
854C4—61no—
855C4—181no—
856C4—181no—
857C4—181no—
858C4—541no—
859C3—24no—
860C3#1059429314yescomplemented
861C3#1059602511yescharacteristic, complemented
862C2—22no—
863C2—62no—
864C2—361no—
865C2—542no—
866C2—1081no—
867C2—1081no—
868C2C2×D3×C4⋊(C3⋊D3)11yescharacteristic
869C2#1172458611yescharacteristic
870C2#1172458811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33#546
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×#89028C2semidirect
3. #11723923C2semidirect
4. C3×#64095C2semidirect
5. C32×#67⋊C4C2semidirect
6. #11723632C2semidirect
7. C2×#88804C2semidirect
8. #11723542C2semidirect
9. D3×#3752C2semidirect
10. #11723516C2semidirect
11. #11723486C2semidirect
12. #11723485C2semidirect
13. #11723484C2semidirect
14. #11723479C2semidirect
15. #11723416C2semidirect
20. C2×#6312C22semidirect
22. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
24. C22×C3×C3⋊Dic3C22semidirect
26. C22×C32×Dic3C22semidirect
27. C2×C32×C4×D3C22semidirect
29. C2×#6293C22semidirect
31. C2×#6292C22semidirect
33. C2×#6291C22semidirect
35. C2×#6289C22semidirect
37. C2×D3×C3⋊Dic3C22semidirect
38. C33×C22⋊C4C22semidirect
40. #88859C22semidirect
41. C3×#3752C22semidirect
42. C3×#3752C22semidirect
43. C3×C4⋊(C3⋊Dic3)C22semidirect
44. C3×C4⋊(C3⋊Dic3)C22semidirect
45. C32×(C2×D3)⋊C4C22semidirect
46. C32×Dic3⋊C4C22semidirect
47. C32×C4×Dic3C22semidirect
48. Dic3⋊(C3⋊Dic3)C22semidirect
51. #88804C22semidirect
52. #88804C22semidirect
53. #88804C22semidirect
54. #88803C22semidirect
67. #64095D3semidirect
75. C3×#67⋊C4D3semidirect
109. C32×#67D4semidirect
140. C22×C3⋊Dic3C2×D3semidirect
157. C22×C3×Dic3C2×D3semidirect
158. C2×C3×C4×D3C2×D3semidirect
172. C32×C22⋊C4C2×D3semidirect
173. C32×C22⋊C4C2×D3semidirect
187. #3752C2×D3semidirect
188. #3752C2×D3semidirect
190. C4⋊(C3⋊Dic3)C2×D3semidirect
191. C4⋊(C3⋊Dic3)C2×D3semidirect
194. C3×(C2×D3)⋊C4C2×D3semidirect
197. C3×Dic3⋊C4C2×D3semidirect
198. C3×C4×Dic3C2×D3semidirect
219. C2×C3⋊(C3⋊D3)#41semidirect
263. #67⋊C4C3⋊D3semidirect
336. C3×#67D12semidirect
385. C22×Dic3C2×C3⋊D3semidirect
405. C2×C4×D3C2×C3⋊D3semidirect
415. C3×C22⋊C4D32semidirect
416. C3×C22⋊C4C2×C3⋊D3semidirect
438. (C2×D3)⋊C4C2×C3⋊D3semidirect
443. Dic3⋊C4C2×C3⋊D3semidirect
444. C4×Dic3C2×C3⋊D3semidirect
537. C33#546semidirect
594. #67C4⋊(C3⋊D3)semidirect
685. C22⋊C4D3×C3⋊D3semidirect
765. C32#5554semidirect
766. C32#5654semidirect
860. C3#10594293semidirect
861. C3#10596025semidirect

Maximal subgroups

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

subgroupindex
C2×#890392
C2×#890282
#117239232
C3×#640952
C32×#67⋊C42
#117236322
C2×#888042
#117235422
D3×#37522
#117235162
#117234862
#117234852
#117234842
#117234792
#117234162
#105960253
#105942933