Finite Group Databasebeta

← #13176609

Subgroups — #13176609

Order 1728.

1824 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723935C211yesmaximal, characteristic, complemented
2C3×#64107C211yesmaximal, characteristic, complemented
3C32×#895C211yesmaximal, characteristic, complemented
4#11723542C211yesmaximal, characteristic, complemented
5#11723540C211yesmaximal, characteristic, complemented
6#11723540C211yesmaximal, characteristic, complemented
7#11723531C211yesmaximal, characteristic, complemented
8#11723527C211yesmaximal, characteristic, complemented
9#11723524C211yesmaximal, characteristic, complemented
10#11723514C211yesmaximal, characteristic, complemented
11#11723479C211yesmaximal, characteristic, complemented
12#11723475C211yesmaximal, characteristic, complemented
13#11723474C211yesmaximal, characteristic, complemented
14#11723428C211yesmaximal, characteristic, complemented
15#11723414C211yesmaximal, characteristic, complemented
16#10596091—31nomaximal
17#10594661—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
21C2×C32×D12C2211yescharacteristic
22C2×C32×D12C2211yescharacteristic
23C2×C32×D12C2211yescharacteristic, complemented
24C2×C32×C4×D3C2211yescharacteristic, complemented
25C2×#6292C2211yescharacteristic
26C2×#6291C2211yescharacteristic
27C2×#6291C2211yescharacteristic
28C2×#6291C2211yescharacteristic
29C2×#6291C2211yescharacteristic, complemented
30C2×#6291C2211yescharacteristic, complemented
31C2×#6290C2211yescharacteristic
32C2×#6290C2211yescharacteristic
33C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
34C33×C4⋊C4C2211yescharacteristic, complemented
35#88859C2211yescharacteristic
36#88859C2211yescharacteristic
37#88859C2211yescharacteristic, complemented
38#88857C2211yescharacteristic, complemented
39C3×#3752C2211yescharacteristic
40C3×#3752C2211yescharacteristic
41C3×#3752C2211yescharacteristic
42C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
43C3×#3750C2211yescharacteristic, complemented
44C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
45C32×(C2×D3)⋊C4C2211yescharacteristic
46C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
47#88806C2211yescharacteristic, complemented
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49#88804C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
53C32×#121—31no—
54#64149—31no—
55#64148—31no—
56#64148—31no—
57#64147—31no—
58#64146—31no—
59#64146—31no—
60#64139—31no—
61#64138—31no—
62#64107D311yescharacteristic, complemented
63#64103—31no—
64#64103—34no—
65#64103—64no—
66#64095—31no—
67#64093—31no—
68#64091—31no—
69#64088—31no—
70C3×#898—34no—
71C3×#895D314yescomplemented
72#63923—34no—
73#63922—34no—
74#63922—34no—
75#63916—34no—
76#63912—34no—
77#63911—34no—
78#63906—34no—
79#63890—34no—
80#63886—34no—
81#63885—34no—
82#63859—34no—
83#63850—34no—
84C22×C3⋊(C3⋊D3)C2311yescharacteristic
85C22×C3⋊(C3⋊D3)C2311yescharacteristic
86C22×C3×C3⋊D3C2311yescharacteristic
87C22×C32×D3C2311yescharacteristic
88C22×C32×D3C2311yescharacteristic
89C22×C32×D3C2311yescharacteristic
90C2×D3×C3⋊D3—41no—
91C2×D3×C3⋊D3—41no—
92C2×D3×C3⋊D3—41no—
93C2×C33×C4C2311yescharacteristic
94C2×C33×C4C2311yescharacteristic
95C2×C33×C4C2311yescharacteristic
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C4⋊(C3⋊(C3⋊D3))—41no—
99C4×C3⋊(C3⋊D3)—41no—
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C2×C32×Dic3C2311yescharacteristic
104C32×D12—41no—
105C32×D12—41no—
106C32×D12—41no—
107C32×C4×D3—41no—
108#6292—41no—
109#6291—41no—
110#6291—41no—
111#6291—41no—
112#6291—41no—
113#6291—41no—
114#6290—41no—
115#6290—41no—
116D3×C3⋊Dic3—41no—
117#5711—91no—
118#5620—94no—
119C23×C3⋊D3—31no—
120C22×D32—34no—
121C2×C32×D4—31no—
122C2×C32×D4—31no—
123C2×C32×D4—31no—
124C22×C32×C4—31no—
125C2×#638—31no—
126C2×#638—31no—
127C2×#638—31no—
128C2×#638—31no—
129C2×#638—31no—
130C2×#638—31no—
131C2×#638—31no—
132C22×C3⋊Dic3—31no—
133C2×C4⋊(C3⋊D3)—31no—
134C2×C4⋊(C3⋊D3)—31no—
135C2×C4⋊(C3⋊D3)—34no—
136C2×C4⋊(C3⋊D3)—64no—
137C2×C4×C3⋊D3—31no—
138C2×C4×C3⋊D3—34no—
139C2×C4×C3⋊D3—64no—
140C2×C3×D12C2×D314yes—
141C2×C3×D12C2×D314yes—
142C2×C3×D12C2×D314yescomplemented
143C2×C3×C4×D3C2×D314yescomplemented
144C2×#626—34no—
145C2×#626—34no—
146C2×#626—34no—
147C2×#626—34no—
148C2×#626—34no—
149C2×#626—34no—
150C2×#625—34no—
151C2×#625—34no—
152C2×D3×Dic3—34no—
153C32×C4⋊C4—24no—
154C32×C4⋊C4C2×D314yescomplemented
155C32×C4⋊C4C2×D311yescharacteristic, complemented
156C32×C22⋊C4—31no—
157C32×C22⋊C4—31no—
158#3757—31no—
159#3757—31no—
160#3757—31no—
161#3752—31no—
162#3752—31no—
163#3752—31no—
164#3752—34no—
165#3752—34no—
166#3752—34no—
167#3752—31no—
168#3752—64no—
169#3752—64no—
170#3752—64no—
171#3752C2×D311yescharacteristic
172#3752C2×D311yescharacteristic
173#3752C2×D311yescharacteristic
174C4⋊(C3⋊Dic3)—31no—
175C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
176#3750—31no—
177#3750—34no—
178#3750—31no—
179#3750—64no—
180#3750C2×D311yescharacteristic, complemented
181C4×C3⋊Dic3C2×D311yescharacteristic, complemented
182C3×(C2×D3)⋊C4—34no—
183C3×(C2×D3)⋊C4—34no—
184C3×(C2×D3)⋊C4—34no—
185C3×(C2×D3)⋊C4C2×D314yes—
186C3×(C2×D3)⋊C4C2×D314yescomplemented
187C3×C4⋊Dic3—34no—
188C3×Dic3⋊C4—34no—
189C3×C4×Dic3—34no—
190#3724—34no—
191Dic3⋊Dic3—34no—
192#3722—34no—
193(C2×D3)⋊Dic3—34no—
194(C2×D3)⋊Dic3—34no—
195(C2×D3)⋊Dic3—34no—
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—21no—
209C2×C32×D3—21no—
210C2×C32×D3—21no—
211C2×C32×D3—21no—
212C2×C32×D3—21no—
213C2×C32×D3—21no—
214C2×C32×D3—21no—
215D3×C3⋊D3—44no—
216C33×C4—21no—
217C33×C4—21no—
218C33×C4—21no—
219C3⋊(C3⋊Dic3)—21no—
220C3⋊(C3⋊Dic3)—21no—
221C3×C3⋊Dic3—21no—
222C3×C3⋊Dic3—21no—
223C3×C3⋊Dic3—21no—
224C32×Dic3—21no—
225C3×#126—91no—
226C3×#121—34no—
227#940—94no—
228#939—94no—
229#939—94no—
230#938—94no—
231#937—94no—
232#937—94no—
233#930—94no—
234#929—94no—
235#898—34no—
236#895—91no—
237#895—91no—
238#895C3⋊D311yescharacteristic, complemented
239#894—91no—
240#894—94no—
241#894—91no—
242#894—91no—
243#894—184no—
244#886—94no—
245#884—94no—
246#884—91no—
247#884—91no—
248#884—91no—
249#882—94no—
250#882—91no—
251#882—91no—
252#882—91no—
253#879—94no—
254#876—91no—
255#874—91no—
256C23×C32—31no—
257C23×C32—31no—
258C23×C32—31no—
259C22×C3⋊D3—31no—
260C22×C3⋊D3—31no—
261C22×C3⋊D3—34no—
262C22×C3⋊D3—34no—
263C22×C3⋊D3—64no—
264C22×C3⋊D3—64no—
265C22×C3⋊D3—121no—
266C22×C3⋊D3—121no—
267C22×C3⋊D3—121no—
268C22×C3⋊D3C22×D311yescharacteristic
269C22×C3×D3—34no—
270C22×C3×D3C22×D314yes—
271C22×C3×D3C22×D314yes—
272C22×C3×D3C22×D314yes—
273C2×D32—124no—
274C2×D32—124no—
275C2×D32—124no—
276C32×D4—121no—
277C32×D4—121no—
278C32×D4—121no—
279C2×C32×C4—24no—
280C2×C32×C4—24no—
281C2×C32×C4—24no—
282C2×C32×C4—31no—
283C2×C32×C4—121no—
284C2×C32×C4C22×D314yes—
285C2×C32×C4C22×D314yes—
286C2×C32×C4C22×D314yes—
287C2×C32×C4C22×D311yescharacteristic
288C2×C32×C4C22×D311yescharacteristic
289C2×C32×C4C22×D311yescharacteristic
290#638—121no—
291#638—121no—
292#638—121no—
293#638—121no—
294#638—121no—
295#638—121no—
296#638—121no—
297C2×C3⋊Dic3—31no—
298C2×C3⋊Dic3—31no—
299C2×C3⋊Dic3—34no—
300C2×C3⋊Dic3—34no—
301C2×C3⋊Dic3—64no—
302C2×C3⋊Dic3—64no—
303C2×C3⋊Dic3—121no—
304C2×C3⋊Dic3C22×D311yescharacteristic
305C2×C3⋊Dic3C22×D311yescharacteristic
306C2×C3⋊Dic3C22×D311yescharacteristic
307C4⋊(C3⋊D3)—121no—
308C4⋊(C3⋊D3)—124no—
309C4⋊(C3⋊D3)—128no—
310C4⋊(C3⋊D3)—121no—
311C4×C3⋊D3—121no—
312C4×C3⋊D3—124no—
313C4×C3⋊D3—128no—
314C2×C3×Dic3—34no—
315C2×C3×Dic3—34no—
316C2×C3×Dic3—34no—
317C2×C3×Dic3C22×D314yes—
318C3×D12—44no—
319C3×D12—44no—
320C3×D12—44no—
321C3×C4×D3—44no—
322#626—124no—
323#626—124no—
324#626—124no—
325#626—124no—
326#626—124no—
327#626—124no—
328#625—124no—
329#625—124no—
330D3×Dic3—124no—
331#560—271noSylow
332C2×C33H(5,𝔽2)11yescharacteristic
333C2×C33H(5,𝔽2)11yescharacteristic
334C2×C33H(5,𝔽2)11yescharacteristic
335C3⋊(C3⋊D3)—41no—
336C3⋊(C3⋊D3)—41no—
337C3×C3⋊D3—41no—
338C32×D3—41no—
339C32×D3—41no—
340C32×D3—41no—
341C23×D3—94no—
342C23×D3—91no—
343C2×C3×D4—34no—
344C2×C3×D4—34no—
345C2×C3×D4—34no—
346C22×C3×C4—34no—
347C2×#67—94no—
348C2×#67—94no—
349C2×#67—94no—
350C2×#67—94no—
351C2×#67—94no—
352C2×#67—94no—
353C2×#67—94no—
354C2×#67—91no—
355C2×#67—91no—
356C2×#67—91no—
357C22×Dic3—94no—
358C2×D12—94no—
359C2×D12—91no—
360C2×D12—91no—
361C2×D12—91no—
362C2×D12—91no—
363C2×D12—91no—
364C2×D12—94no—
365C2×D12—91no—
366C2×D12—184no—
367C2×D12C2×C3⋊D311yescharacteristic
368C2×D12C2×C3⋊D311yescharacteristic
369C2×D12C2×C3⋊D311yescharacteristic, complemented
370C2×C4×D3—91no—
371C2×C4×D3—94no—
372C2×C4×D3—91no—
373C2×C4×D3—184no—
374C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
375C3×C4⋊C4—24no—
376C3×C4⋊C4—91no—
377C3×C4⋊C4—91no—
378C3×C4⋊C4D3214yescomplemented
379C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
380C3×C22⋊C4—34no—
381C3×C22⋊C4—34no—
382C3×C22⋊C4—91no—
383C3×C22⋊C4—91no—
384C3×C22⋊C4—91no—
385C3×C42—91no—
386#217—94no—
387#217—94no—
388#217—94no—
389(C2×D3)⋊C4—34no—
390(C2×D3)⋊C4—34no—
391(C2×D3)⋊C4—34no—
392(C2×D3)⋊C4—94no—
393(C2×D3)⋊C4—91no—
394(C2×D3)⋊C4—91no—
395(C2×D3)⋊C4—91no—
396(C2×D3)⋊C4—94no—
397(C2×D3)⋊C4—94no—
398(C2×D3)⋊C4—94no—
399(C2×D3)⋊C4—91no—
400(C2×D3)⋊C4—91no—
401(C2×D3)⋊C4—91no—
402(C2×D3)⋊C4—91no—
403(C2×D3)⋊C4—184no—
404(C2×D3)⋊C4—184no—
405(C2×D3)⋊C4—184no—
406(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
407(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
408C4⋊Dic3—34no—
409C4⋊Dic3—94no—
410Dic3⋊C4—34no—
411Dic3⋊C4—94no—
412Dic3⋊C4—94no—
413Dic3⋊C4—91no—
414Dic3⋊C4—91no—
415Dic3⋊C4—91no—
416Dic3⋊C4—184no—
417C4×Dic3—34no—
418C22×C32—24no—
419C22×C32—61no—
420C22×C32—61no—
421C22×C32—61no—
422C22×C32—61no—
423C22×C32—61no—
424C22×C32—61no—
425C22×C32—61no—
426C22×C32—61no—
427C22×C32—61no—
428C22×C32C23×D314yes—
429C22×C32C23×D311yescharacteristic
430C2×C3⋊D3—21no—
431C2×C3⋊D3—21no—
432C2×C3⋊D3—21no—
433C2×C3⋊D3—68no—
434C2×C3⋊D3—64no—
435C2×C3⋊D3—61no—
436C2×C3⋊D3—61no—
437C2×C3⋊D3—61no—
438C2×C3⋊D3—61no—
439C2×C3⋊D3—61no—
440C2×C3⋊D3—61no—
441C2×C3⋊D3—64no—
442C2×C3⋊D3—64no—
443C2×C3⋊D3—64no—
444C2×C3⋊D3—64no—
445C2×C3⋊D3—64no—
446C2×C3⋊D3—124no—
447C2×C3⋊D3—124no—
448C2×C3⋊D3—124no—
449C2×C3⋊D3—124no—
450C2×C3⋊D3—124no—
451C2×C3⋊D3—124no—
452C2×C3×D3—24no—
453C2×C3×D3—24no—
454C2×C3×D3—24no—
455C2×C3×D3—24no—
456C2×C3×D3—24no—
457C2×C3×D3—24no—
458C2×C3×D3—24no—
459C2×C3×D3—24no—
460C2×C3×D3—24no—
461C2×C3×D3—64no—
462C2×C3×D3—64no—
463C2×C3×D3—64no—
464D32—1216no—
465C32×C4—21no—
466C32×C4—21no—
467C32×C4—21no—
468C32×C4—24no—
469C32×C4—24no—
470C32×C4—24no—
471C32×C4—44no—
472C32×C4—44no—
473C32×C4—44no—
474C32×C4—61no—
475C3⋊Dic3—21no—
476C3⋊Dic3—21no—
477C3⋊Dic3—21no—
478C3⋊Dic3—61no—
479C3⋊Dic3—61no—
480C3⋊Dic3—64no—
481C3⋊Dic3—64no—
482C3⋊Dic3—124no—
483C3⋊Dic3—124no—
484C3×Dic3—24no—
485C3×Dic3—64no—
486C3×Dic3—64no—
487C3×Dic3—64no—
488#127—271no—
489#126—91no—
490#126—271no—
491#123—271no—
492#123—271no—
493#123—271no—
494#121—31no—
495#121—271no—
496#121—271no—
497#121—271no—
498#121—271no—
499#121—271no—
500#120—271no—
501#120—271no—
502#120—271no—
503C33#56011yescharacteristic, complemented, Sylow
504C23×C3—34no—
505C23×C3—34no—
506C23×C3—34no—
507C23×C3—91no—
508C22×D3—34no—
509C22×D3—94no—
510C22×D3—94no—
511C22×D3—91no—
512C22×D3—91no—
513C22×D3—184no—
514C22×D3—184no—
515C22×D3—361no—
516C22×D3—361no—
517C22×D3—361no—
518C22×D3—364no—
519C22×D3—364no—
520C22×D3—364no—
521C22×D3C22×C3⋊D311yescharacteristic
522C22×D3C22×C3⋊D311yescharacteristic
523C22×D3C22×C3⋊D311yescharacteristic
524C3×D4—124no—
525C3×D4—124no—
526C3×D4—124no—
527C2×C3×C4—24no—
528C2×C3×C4—24no—
529C2×C3×C4—24no—
530C2×C3×C4—34no—
531C2×C3×C4—91no—
532C2×C3×C4—91no—
533C2×C3×C4—91no—
534C2×C3×C4—124no—
535C2×C3×C4C2×D3214yes—
536C2×C3×C4C2×D3214yes—
537C2×C3×C4C2×D3214yes—
538C2×C3×C4C22×C3⋊D311yescharacteristic
539C2×C3×C4C22×C3⋊D311yescharacteristic
540C2×C3×C4C22×C3⋊D311yescharacteristic
541#67—361no—
542#67—364no—
543#67—364no—
544#67—364no—
545#67—364no—
546#67—364no—
547#67—361no—
548#67—361no—
549#67—364no—
550#67—364no—
551C2×Dic3—34no—
552C2×Dic3—34no—
553C2×Dic3—34no—
554C2×Dic3—94no—
555C2×Dic3—94no—
556C2×Dic3—91no—
557C2×Dic3—91no—
558C2×Dic3—184no—
559C2×Dic3—184no—
560C2×Dic3—364no—
561C2×Dic3C22×C3⋊D311yescharacteristic
562D12—41no—
563D12—41no—
564D12—41no—
565D12—364no—
566D12—361no—
567D12—368no—
568D12—364no—
569D12—361no—
570D12—361no—
571D12—361no—
572D12—361no—
573D12—361no—
574C4×D3—41no—
575C4×D3—364no—
576C4×D3—361no—
577C4×D3—361no—
578C4×D3—368no—
579C2×C32—24no—
580C2×C32—24no—
581C2×C32—24no—
582C2×C32—121no—
583C2×C32—121no—
584C2×C32—121no—
585C2×C32#100414yes—
586C2×C32#100414yes—
587C2×C32#100914yes—
588C2×C32#100911yescharacteristic
589C2×C32#100911yescharacteristic
590C2×C32#100911yescharacteristic
591C3⋊D3—41no—
592C3⋊D3—128no—
593C3⋊D3—121no—
594C3⋊D3—121no—
595C3⋊D3—124no—
596C3⋊D3—124no—
597C3⋊D3—244no—
598C3×D3—44no—
599C3×D3—44no—
600C3×D3—44no—
601C3×D3—124no—
602C24—271no—
603C2×D4—31no—
604C2×D4—31no—
605C2×D4—31no—
606C2×D4—271no—
607C2×D4—271no—
608C2×D4—271no—
609C2×D4—271no—
610C2×D4—271no—
611C2×D4—271no—
612C2×D4—271no—
613C2×D4—271no—
614C2×D4—271no—
615C22×C4—31no—
616C22×C4—271no—
617C22×C4—271no—
618C4⋊C4—91no—
619C4⋊C4—91no—
620C4⋊C4—271no—
621C4⋊C4—271no—
622C4⋊C4—271no—
623C4⋊C4D3×C3⋊D311yescharacteristic, complemented
624C22⋊C4—31no—
625C22⋊C4—31no—
626C22⋊C4—91no—
627C22⋊C4—91no—
628C22⋊C4—91no—
629C22⋊C4—271no—
630C22⋊C4—271no—
631C22⋊C4—271no—
632C22⋊C4—271no—
633C22⋊C4—271no—
634C22⋊C4—271no—
635C22⋊C4—271no—
636C42—91no—
637C22×C3—24no—
638C22×C3—64no—
639C22×C3—64no—
640C22×C3—64no—
641C22×C3—64no—
642C22×C3—64no—
643C22×C3—64no—
644C22×C3—64no—
645C22×C3—64no—
646C22×C3—64no—
647C22×C3—181no—
648C22×C3—181no—
649C22×C3—181no—
650C22×C3C22×D3214yes—
651C22×C3C23×C3⋊D311yescharacteristic
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—64no—
662C2×D3—64no—
663C2×D3—64no—
664C2×D3—188no—
665C2×D3—184no—
666C2×D3—184no—
667C2×D3—184no—
668C2×D3—184no—
669C2×D3—184no—
670C2×D3—184no—
671C2×D3—181no—
672C2×D3—181no—
673C2×D3—181no—
674C2×D3—181no—
675C2×D3—181no—
676C2×D3—181no—
677C2×D3—364no—
678C2×D3—364no—
679C2×D3—364no—
680C2×D3—364no—
681C2×D3—364no—
682C2×D3—364no—
683C2×D3—3616no—
684C3×C4—24no—
685C3×C4—24no—
686C3×C4—24no—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—44no—
691C3×C4—44no—
692C3×C4—44no—
693C3×C4—64no—
694C3×C4—181no—
695C3×C4—181no—
696C3×C4—181no—
697Dic3—21no—
698Dic3—64no—
699Dic3—64no—
700Dic3—64no—
701Dic3—184no—
702Dic3—184no—
703Dic3—181no—
704Dic3—181no—
705Dic3—364no—
706Dic3—364no—
707C32—24no—
708C32#562014yescomplemented
709C32#571111yescharacteristic, complemented
710C23—31no—
711C23—31no—
712C23—31no—
713C23—91no—
714C23—271no—
715C23—271no—
716C23—1081no—
717C23—1081no—
718C23—1081no—
719D4—121no—
720D4—121no—
721D4—121no—
722D4—1081no—
723D4—1081no—
724D4—1081no—
725D4—1081no—
726D4—1081no—
727D4—1081no—
728D4—1081no—
729D4—1081no—
730D4—1081no—
731C2×C4—31no—
732C2×C4—91no—
733C2×C4—91no—
734C2×C4—91no—
735C2×C4—121no—
736C2×C4—271no—
737C2×C4—271no—
738C2×C4—1081no—
739C2×C4—1081no—
740C2×C4C2×D3×C3⋊D311yescharacteristic
741C2×C4C2×D3×C3⋊D311yescharacteristic
742C2×C4C2×D3×C3⋊D311yescharacteristic
743C2×C3—24no—
744C2×C3—24no—
745C2×C3—24no—
746C2×C3—124no—
747C2×C3—124no—
748C2×C3—124no—
749C2×C3—361no—
750C2×C3#6430714yes—
751C2×C3#6431414yes—
752C2×C3#6432014yes—
753C2×C3#6436111yescharacteristic
754C2×C3#6436111yescharacteristic
755C2×C3#6436611yescharacteristic
756D3—41no—
757D3—41no—
758D3—41no—
759D3—124no—
760D3—368no—
761D3—364no—
762D3—364no—
763D3—361no—
764D3—361no—
765D3—724no—
766C22—61no—
767C22—61no—
768C22—61no—
769C22—61no—
770C22—61no—
771C22—61no—
772C22—61no—
773C22—61no—
774C22—61no—
775C22—181no—
776C22—181no—
777C22—181no—
778C22—541no—
779C22—541no—
780C22—541no—
781C22—541no—
782C22—541no—
783C22—541no—
784C22—1084no—
785C22C22×D3×C3⋊D311yescharacteristic
786C4—21no—
787C4—21no—
788C4—21no—
789C4—61no—
790C4—181no—
791C4—181no—
792C4—181no—
793C4—541no—
794C4—541no—
795C3—24no—
796C3#1059466114yescomplemented
797C3#1059609111yescharacteristic, complemented
798C2—121no—
799C2—121no—
800C2—121no—
801C2—361no—
802C2—1081no—
803C2—1081no—
804C2#1172457911yescharacteristic
805C2#1172458811yescharacteristic
806C2#1172459711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
hypercenterC4⋊C4D3×C3⋊D3
hypocenterC33#560
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #11723935C2semidirect
2. C3×#64107C2semidirect
3. C32×#895C2semidirect
4. #11723542C2semidirect
5. #11723540C2semidirect
6. #11723540C2semidirect
7. #11723531C2semidirect
8. #11723527C2semidirect
9. #11723524C2semidirect
10. #11723514C2semidirect
11. #11723479C2semidirect
12. #11723475C2semidirect
13. #11723474C2semidirect
14. #11723428C2semidirect
15. #11723414C2semidirect
20. C2×C4×C3⋊(C3⋊D3)C22semidirect
23. C2×C32×D12C22semidirect
24. C2×C32×C4×D3C22semidirect
29. C2×#6291C22semidirect
30. C2×#6291C22semidirect
33. C2×D3×C3⋊Dic3C22semidirect
34. C33×C4⋊C4C22semidirect
37. #88859C22semidirect
38. #88857C22semidirect
42. C3×C4⋊(C3⋊Dic3)C22semidirect
43. C3×#3750C22semidirect
44. C3×C4×C3⋊Dic3C22semidirect
46. C32×(C2×D3)⋊C4C22semidirect
47. #88806C22semidirect
48. Dic3⋊(C3⋊Dic3)C22semidirect
52. (C2×D3)⋊(C3⋊Dic3)C22semidirect
62. #64107D3semidirect
71. C3×#895D3semidirect
142. C2×C3×D12C2×D3semidirect
143. C2×C3×C4×D3C2×D3semidirect
154. C32×C4⋊C4C2×D3semidirect
155. C32×C4⋊C4C2×D3semidirect
175. C4⋊(C3⋊Dic3)C2×D3semidirect
180. #3750C2×D3semidirect
181. C4×C3⋊Dic3C2×D3semidirect
186. C3×(C2×D3)⋊C4C2×D3semidirect
238. #895C3⋊D3semidirect
369. C2×D12C2×C3⋊D3semidirect
374. C2×C4×D3C2×C3⋊D3semidirect
378. C3×C4⋊C4D32semidirect
379. C3×C4⋊C4C2×C3⋊D3semidirect
407. (C2×D3)⋊C4C2×C3⋊D3semidirect
503. C33#560semidirect
623. C4⋊C4D3×C3⋊D3semidirect
708. C32#5620semidirect
709. C32#5711semidirect
796. C3#10594661semidirect
797. C3#10596091semidirect

Maximal subgroups

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

subgroupindex
#117239352
C3×#641072
C32×#8952
#117235422
#117235402
#117235312
#117235272
#117235242
#117235142
#117234792
#117234752
#117234742
#117234282
#117234142
#105960913
#105946613