Finite Group Databasebeta

← #13176447

Subgroups — #13176447

Order 1728.

1544 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723931C211yesmaximal, characteristic, complemented
2C3×#64103C211yesmaximal, characteristic, complemented
3C32×#894C211yesmaximal, characteristic, complemented
4#11723530C211yesmaximal, characteristic, complemented
5#11723530C211yesmaximal, characteristic, complemented
6#11723523C211yesmaximal, characteristic, complemented
7#11723522C211yesmaximal, characteristic, complemented
8#11723519C211yesmaximal, characteristic, complemented
9#11723515C211yesmaximal, characteristic, complemented
10#11723491C211yesmaximal, characteristic, complemented
11#11723483C211yesmaximal, characteristic, complemented
12#11723480C211yesmaximal, characteristic, complemented
13#11723474C211yesmaximal, characteristic, complemented
14#11723418C211yesmaximal, characteristic, complemented
15#11723415C211yesmaximal, characteristic, complemented
16#10596138—31nomaximal
17#10594497—34nomaximal
18C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C3×C4×C3⋊D3C2211yescharacteristic
20C2×C32×D12C2211yescharacteristic
21C2×C32×C4×D3C2211yescharacteristic
22C2×#6293C2211yescharacteristic
23C2×#6293C2211yescharacteristic
24C2×#6290C2211yescharacteristic
25C2×#6290C2211yescharacteristic
26C2×#6290C2211yescharacteristic
27C2×#6290C2211yescharacteristic
28C2×Dic3×C3⋊D3C2211yescharacteristic
29C2×D3×C3⋊Dic3C2211yescharacteristic
30C33×C4⋊C4C2211yescharacteristic
31C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
32C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
33C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
34#88857C2211yescharacteristic
35#88857C2211yescharacteristic
36C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
37C3×#3752C2211yescharacteristic
38C3×#3752C2211yescharacteristic
39C3×#3752C2211yescharacteristic
40C3×#3750C2211yescharacteristic
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×(C2×D3)⋊C4C2211yescharacteristic
43C32×(C2×D3)⋊C4C2211yescharacteristic
44C32×Dic3⋊C4C2211yescharacteristic
45#88807C2211yescharacteristic
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic
47#88803C2211yescharacteristic
48#88803C2211yescharacteristic
49#88803C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
53C32×#123—31no—
54#64148—31no—
55#64147—31no—
56#64139—31no—
57#64133—31no—
58#64106—31no—
59#64105—31no—
60#64103D311yescharacteristic, complemented
61#64099—31no—
62#64099—34no—
63#64099—64no—
64#64095—31no—
65#64094—31no—
66#64094—31no—
67#64093—31no—
68#64092—31no—
69#64087—31no—
70C3×#894—34no—
71C3×#894D314yescomplemented
72#63915—34no—
73#63915—34no—
74#63908—34no—
75#63908—34no—
76#63893—34no—
77#63893—34no—
78#63891—34no—
79#63891—34no—
80#63885—34no—
81#63885—34no—
82#63851—34no—
83#63851—34no—
84C22×C3×C3⋊D3C2311yescharacteristic
85C22×C3×C3⋊D3C2311yescharacteristic
86C22×C32×D3C2311yescharacteristic
87C22×C32×D3C2311yescharacteristic
88C2×C33×C4C2311yescharacteristic
89C2×C33×C4C2311yescharacteristic
90C2×C33×C4C2311yescharacteristic
91C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
92C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
93C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95C2×C3×C3⋊Dic3C2311yescharacteristic
96C2×C3×C3⋊Dic3C2311yescharacteristic
97C3×C4⋊(C3⋊D3)—41no—
98C3×C4×C3⋊D3—41no—
99C2×C32×Dic3C2311yescharacteristic
100C2×C32×Dic3C2311yescharacteristic
101C32×D12—41no—
102C32×C4×D3—41no—
103#6293—41no—
104#6293—41no—
105#6290—41no—
106#6290—41no—
107#6290—41no—
108#6290—41no—
109Dic3×C3⋊D3—41no—
110D3×C3⋊Dic3—41no—
111#5667—94no—
112#5667—91no—
113C2×C32×D4—31no—
114C22×C32×C4—31no—
115C2×#638—31no—
116C2×#638—31no—
117C2×#638—31no—
118C2×#638—31no—
119C22×C3⋊Dic3—31no—
120C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
121C2×C4×C3⋊D3—31no—
122C2×C4×C3⋊D3C2×D311yescharacteristic
123C2×#634—31no—
124C2×#634—31no—
125C2×C3×D12—34no—
126C2×C3×D12C2×D314yes—
127C2×C3×C4×D3—34no—
128C2×C3×C4×D3C2×D314yes—
129C2×#627—34no—
130C2×#627—34no—
131C2×#625—34no—
132C2×#625—34no—
133C2×#625—34no—
134C2×#625—34no—
135C2×D3×Dic3—34no—
136C2×D3×Dic3—34no—
137C32×C4⋊C4—24no—
138C32×C4⋊C4—31no—
139C32×C4⋊C4C2×D314yes—
140C32×C4⋊C4C2×D311yescharacteristic
141C32×C22⋊C4—31no—
142C32×C22⋊C4—31no—
143C32×C22⋊C4—31no—
144#3757—31no—
145#3757—31no—
146#3757—31no—
147#3752—31no—
148#3752—31no—
149#3752—31no—
150#3752C2×D311yescharacteristic
151#3752C2×D311yescharacteristic
152#3752C2×D311yescharacteristic
153C4⋊(C3⋊Dic3)—31no—
154C4⋊(C3⋊Dic3)—31no—
155C4⋊(C3⋊Dic3)—31no—
156C4⋊(C3⋊Dic3)—34no—
157C4⋊(C3⋊Dic3)—34no—
158C4⋊(C3⋊Dic3)—34no—
159C4⋊(C3⋊Dic3)—31no—
160C4⋊(C3⋊Dic3)—64no—
161C4⋊(C3⋊Dic3)—64no—
162C4⋊(C3⋊Dic3)—64no—
163#3750—31no—
164#3750—31no—
165#3750—34no—
166#3750—34no—
167#3750—31no—
168#3750—64no—
169#3750—64no—
170#3750C2×D311yescharacteristic
171C4×C3⋊Dic3—31no—
172C4×C3⋊Dic3—34no—
173C4×C3⋊Dic3—64no—
174C3×(C2×D3)⋊C4—34no—
175C3×(C2×D3)⋊C4—34no—
176C3×(C2×D3)⋊C4—34no—
177C3×(C2×D3)⋊C4C2×D314yes—
178C3×(C2×D3)⋊C4C2×D314yes—
179C3×(C2×D3)⋊C4C2×D314yes—
180C3×Dic3⋊C4—34no—
181C3×Dic3⋊C4C2×D314yes—
182Dic3⋊Dic3—34no—
183Dic3⋊Dic3—34no—
184(C2×D3)⋊Dic3—34no—
185(C2×D3)⋊Dic3—34no—
186(C2×D3)⋊Dic3—34no—
187(C2×D3)⋊Dic3—34no—
188(C2×D3)⋊Dic3—34no—
189(C2×D3)⋊Dic3—34no—
190C22×C33C2411yescharacteristic
191C2×C3×C3⋊D3—21no—
192C2×C3×C3⋊D3—21no—
193C2×C3×C3⋊D3—21no—
194C2×C3×C3⋊D3—21no—
195C2×C3×C3⋊D3—21no—
196C2×C3×C3⋊D3—21no—
197C2×C32×D3—21no—
198C2×C32×D3—21no—
199C2×C32×D3—21no—
200C2×C32×D3—21no—
201C2×C32×D3—21no—
202C2×C32×D3—21no—
203C33×C4—21no—
204C33×C4—21no—
205C33×C4—21no—
206C3⋊(C3⋊Dic3)—21no—
207C3⋊(C3⋊Dic3)—21no—
208C3⋊(C3⋊Dic3)—21no—
209C3⋊(C3⋊Dic3)—21no—
210C3×C3⋊Dic3—21no—
211C3×C3⋊Dic3—21no—
212C32×Dic3—21no—
213C32×Dic3—21no—
214C3×#123—34no—
215C3×#123—91no—
216#939—94no—
217#939—91no—
218#938—94no—
219#938—91no—
220#930—94no—
221#930—91no—
222#924—94no—
223#924—91no—
224#897—94no—
225#897—91no—
226#896—94no—
227#896—91no—
228#894—34no—
229#894C3⋊D311yescharacteristic, complemented
230#890—94no—
231#890—91no—
232#890—184no—
233#886—94no—
234#886—91no—
235#885—94no—
236#885—94no—
237#885—91no—
238#885—91no—
239#884—94no—
240#884—91no—
241#883—94no—
242#883—91no—
243#878—94no—
244#878—91no—
245C23×C32—31no—
246C23×C32—31no—
247C22×C3⋊D3C22×D311yescharacteristic
248C22×C3⋊D3C22×D311yescharacteristic
249C22×C3×D3—34no—
250C22×C3×D3—34no—
251C22×C3×D3C22×D314yes—
252C22×C3×D3C22×D314yes—
253C32×D4—121no—
254C2×C32×C4—24no—
255C2×C32×C4—24no—
256C2×C32×C4—24no—
257C2×C32×C4—31no—
258C2×C32×C4—31no—
259C2×C32×C4—121no—
260C2×C32×C4C22×D314yes—
261C2×C32×C4C22×D314yes—
262C2×C32×C4C22×D314yes—
263C2×C32×C4C22×D311yescharacteristic
264C2×C32×C4C22×D311yescharacteristic
265C2×C32×C4C22×D311yescharacteristic
266#638—121no—
267#638—121no—
268#638—121no—
269#638—121no—
270C2×C3⋊Dic3—31no—
271C2×C3⋊Dic3—31no—
272C2×C3⋊Dic3—31no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—34no—
275C2×C3⋊Dic3—34no—
276C2×C3⋊Dic3—34no—
277C2×C3⋊Dic3—34no—
278C2×C3⋊Dic3—64no—
279C2×C3⋊Dic3—64no—
280C2×C3⋊Dic3—64no—
281C2×C3⋊Dic3—64no—
282C2×C3⋊Dic3—121no—
283C2×C3⋊Dic3C22×D311yescharacteristic
284C2×C3⋊Dic3C22×D311yescharacteristic
285C4⋊(C3⋊D3)—41no—
286C4×C3⋊D3—41no—
287C4×C3⋊D3—121no—
288#634—121no—
289#634—121no—
290C2×C3×Dic3—34no—
291C2×C3×Dic3—34no—
292C2×C3×Dic3C22×D314yes—
293C2×C3×Dic3C22×D314yes—
294C3×D12—44no—
295C3×D12—124no—
296C3×C4×D3—44no—
297C3×C4×D3—124no—
298#627—124no—
299#627—124no—
300#625—124no—
301#625—124no—
302#625—124no—
303#625—124no—
304D3×Dic3—124no—
305D3×Dic3—124no—
306#562—271noSylow
307C2×C33H(5,𝔽2)11yescharacteristic
308C2×C33H(5,𝔽2)11yescharacteristic
309C2×C332−1+411yescharacteristic
310C3×C3⋊D3—41no—
311C3×C3⋊D3—41no—
312C32×D3—41no—
313C32×D3—41no—
314C2×C3×D4—34no—
315C2×C3×D4—91no—
316C22×C3×C4—34no—
317C22×C3×C4—91no—
318C2×#67—94no—
319C2×#67—94no—
320C2×#67—94no—
321C2×#67—94no—
322C2×#67—91no—
323C2×#67—91no—
324C2×#67—91no—
325C2×#67—91no—
326C22×Dic3—94no—
327C22×Dic3—91no—
328C2×D12—34no—
329C2×D12C2×C3⋊D311yescharacteristic
330C2×C4×D3—34no—
331C2×C4×D3—94no—
332C2×C4×D3—91no—
333C2×C4×D3C2×C3⋊D311yescharacteristic
334C2×Dic6—94no—
335C2×Dic6—94no—
336C2×Dic6—91no—
337C2×Dic6—91no—
338C3×C4⋊C4—24no—
339C3×C4⋊C4—34no—
340C3×C4⋊C4—91no—
341C3×C4⋊C4D3214yes—
342C3×C4⋊C4C2×C3⋊D311yescharacteristic
343C3×C22⋊C4—34no—
344C3×C22⋊C4—34no—
345C3×C22⋊C4—34no—
346C3×C22⋊C4—91no—
347C3×C22⋊C4—91no—
348C3×C22⋊C4—91no—
349#217—94no—
350#217—94no—
351#217—94no—
352#217—91no—
353#217—91no—
354#217—91no—
355(C2×D3)⋊C4—34no—
356(C2×D3)⋊C4—34no—
357(C2×D3)⋊C4—34no—
358(C2×D3)⋊C4—94no—
359(C2×D3)⋊C4—94no—
360(C2×D3)⋊C4—94no—
361(C2×D3)⋊C4—91no—
362(C2×D3)⋊C4—91no—
363(C2×D3)⋊C4—91no—
364(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
365(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
366(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
367C4⋊Dic3—94no—
368C4⋊Dic3—94no—
369C4⋊Dic3—94no—
370C4⋊Dic3—94no—
371C4⋊Dic3—91no—
372C4⋊Dic3—91no—
373C4⋊Dic3—91no—
374C4⋊Dic3—91no—
375C4⋊Dic3—184no—
376C4⋊Dic3—184no—
377C4⋊Dic3—184no—
378Dic3⋊C4—34no—
379Dic3⋊C4—94no—
380Dic3⋊C4—94no—
381Dic3⋊C4—94no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—91no—
385Dic3⋊C4—184no—
386Dic3⋊C4—184no—
387Dic3⋊C4C2×C3⋊D311yescharacteristic
388C4×Dic3—94no—
389C4×Dic3—91no—
390C4×Dic3—184no—
391C22×C32—24no—
392C22×C32—61no—
393C22×C32—61no—
394C22×C32—61no—
395C22×C32—61no—
396C22×C32—61no—
397C22×C32—61no—
398C22×C32C23×D314yes—
399C22×C32C23×D311yescharacteristic
400C2×C3⋊D3—21no—
401C2×C3⋊D3—21no—
402C2×C3⋊D3—21no—
403C2×C3⋊D3—21no—
404C2×C3⋊D3—21no—
405C2×C3⋊D3—21no—
406C2×C3×D3—24no—
407C2×C3×D3—24no—
408C2×C3×D3—24no—
409C2×C3×D3—24no—
410C2×C3×D3—24no—
411C2×C3×D3—24no—
412C2×C3×D3—64no—
413C2×C3×D3—64no—
414C2×C3×D3—64no—
415C2×C3×D3—64no—
416C2×C3×D3—64no—
417C2×C3×D3—64no—
418C32×C4—28no—
419C32×C4—21no—
420C32×C4—21no—
421C32×C4—24no—
422C32×C4—21no—
423C32×C4—24no—
424C32×C4—24no—
425C32×C4—44no—
426C32×C4—44no—
427C32×C4—61no—
428C32×C4—61no—
429C3⋊Dic3—21no—
430C3⋊Dic3—21no—
431C3⋊Dic3—61no—
432C3⋊Dic3—61no—
433C3⋊Dic3—61no—
434C3⋊Dic3—61no—
435C3⋊Dic3—64no—
436C3⋊Dic3—64no—
437C3⋊Dic3—64no—
438C3⋊Dic3—64no—
439C3⋊Dic3—124no—
440C3⋊Dic3—124no—
441C3⋊Dic3—124no—
442C3⋊Dic3—124no—
443C3×Dic3—24no—
444C3×Dic3—24no—
445C3×Dic3—64no—
446C3×Dic3—64no—
447#125—271no—
448#124—271no—
449#124—271no—
450#123—31no—
451#123—91no—
452#123—271no—
453#123—271no—
454C22⋊Q8—271no—
455C22⋊Q8—271no—
456C22⋊Q8—271no—
457C22⋊Q8—271no—
458#121—271no—
459#121—271no—
460#121—271no—
461#121—271no—
462C33#56211yescharacteristic, complemented, Sylow
463C23×C3—34no—
464C23×C3—34no—
465C23×C3—91no—
466C23×C3—91no—
467C22×D3—34no—
468C22×D3—34no—
469C22×D3C22×C3⋊D311yescharacteristic
470C22×D3C22×C3⋊D311yescharacteristic
471C3×D4—124no—
472C3×D4—361no—
473C2×C3×C4—24no—
474C2×C3×C4—24no—
475C2×C3×C4—24no—
476C2×C3×C4—34no—
477C2×C3×C4—34no—
478C2×C3×C4—91no—
479C2×C3×C4—91no—
480C2×C3×C4—124no—
481C2×C3×C4—361no—
482C2×C3×C4C2×D3214yes—
483C2×C3×C4C2×D3214yes—
484C2×C3×C4C2×D3214yes—
485C2×C3×C4C22×C3⋊D311yescharacteristic
486C2×C3×C4C22×C3⋊D311yescharacteristic
487C2×C3×C4C22×C3⋊D311yescharacteristic
488#67—361no—
489#67—361no—
490#67—361no—
491#67—361no—
492#67—364no—
493#67—364no—
494#67—364no—
495#67—364no—
496C2×Dic3—34no—
497C2×Dic3—34no—
498C2×Dic3—94no—
499C2×Dic3—94no—
500C2×Dic3—94no—
501C2×Dic3—94no—
502C2×Dic3—91no—
503C2×Dic3—91no—
504C2×Dic3—91no—
505C2×Dic3—91no—
506C2×Dic3—184no—
507C2×Dic3—184no—
508C2×Dic3—184no—
509C2×Dic3—184no—
510C2×Dic3—361no—
511C2×Dic3—364no—
512C2×Dic3C22×C3⋊D311yescharacteristic
513C2×Dic3C22×C3⋊D311yescharacteristic
514D12—41no—
515D12—124no—
516C4×D3—41no—
517C4×D3—124no—
518C4×D3—364no—
519C4×D3—361no—
520Dic6—361no—
521Dic6—361no—
522Dic6—364no—
523Dic6—364no—
524C2×C32—24no—
525C2×C32—24no—
526C2×C32—24no—
527C2×C32—121no—
528C2×C32—121no—
529C2×C32#100414yes—
530C2×C32#100411yescharacteristic
531C2×C32#100914yes—
532C2×C32#100911yescharacteristic
533C2×C32#101014yes—
534C2×C32#101011yescharacteristic
535C3⋊D3—41no—
536C3⋊D3—41no—
537C3×D3—44no—
538C3×D3—44no—
539C3×D3—124no—
540C3×D3—124no—
541C2×Q8—271no—
542C2×Q8—271no—
543C2×D4—31no—
544C2×D4—91no—
545C2×D4—271no—
546C2×D4—271no—
547C2×D4—271no—
548C2×D4—271no—
549C22×C4—31no—
550C22×C4—91no—
551C22×C4—271no—
552C22×C4—271no—
553C4⋊C4—31no—
554C4⋊C4—91no—
555C4⋊C4—271no—
556C4⋊C4—271no—
557C4⋊C4—271no—
558C4⋊C4—271no—
559C4⋊C4—271no—
560C4⋊C4—271no—
561C4⋊C4—271no—
562C4⋊C4D3×C3⋊D311yescharacteristic
563C22⋊C4—31no—
564C22⋊C4—31no—
565C22⋊C4—31no—
566C22⋊C4—91no—
567C22⋊C4—91no—
568C22⋊C4—91no—
569C22⋊C4—271no—
570C22⋊C4—271no—
571C22⋊C4—271no—
572C22⋊C4—271no—
573C22⋊C4—271no—
574C22⋊C4—271no—
575C42—271no—
576C22×C3—24no—
577C22×C3—64no—
578C22×C3—64no—
579C22×C3—64no—
580C22×C3—64no—
581C22×C3—64no—
582C22×C3—64no—
583C22×C3—181no—
584C22×C3—181no—
585C22×C3—181no—
586C22×C3—181no—
587C22×C3—181no—
588C22×C3—181no—
589C22×C3C22×D3214yes—
590C22×C3C23×C3⋊D311yescharacteristic
591C2×D3—21no—
592C2×D3—21no—
593C2×D3—21no—
594C2×D3—21no—
595C2×D3—21no—
596C2×D3—21no—
597C2×D3—64no—
598C2×D3—64no—
599C2×D3—64no—
600C2×D3—64no—
601C2×D3—64no—
602C2×D3—64no—
603C3×C4—28no—
604C3×C4—24no—
605C3×C4—24no—
606C3×C4—24no—
607C3×C4—21no—
608C3×C4—21no—
609C3×C4—21no—
610C3×C4—44no—
611C3×C4—44no—
612C3×C4—64no—
613C3×C4—64no—
614C3×C4—181no—
615C3×C4—181no—
616Dic3—21no—
617Dic3—21no—
618Dic3—64no—
619Dic3—64no—
620Dic3—184no—
621Dic3—184no—
622Dic3—184no—
623Dic3—184no—
624Dic3—181no—
625Dic3—181no—
626Dic3—181no—
627Dic3—181no—
628Dic3—364no—
629Dic3—364no—
630Dic3—364no—
631Dic3—364no—
632C32—24no—
633C32#566714yescomplemented
634C32#566711yescharacteristic, complemented
635C23—31no—
636C23—31no—
637C23—91no—
638C23—91no—
639Q8—1081no—
640Q8—1081no—
641D4—121no—
642D4—361no—
643D4—1081no—
644D4—1081no—
645D4—1081no—
646D4—1081no—
647C2×C4—31no—
648C2×C4—31no—
649C2×C4—91no—
650C2×C4—91no—
651C2×C4—121no—
652C2×C4—271no—
653C2×C4—271no—
654C2×C4—271no—
655C2×C4—271no—
656C2×C4—361no—
657C2×C4—1081no—
658C2×C4—1081no—
659C2×C4C2×D3×C3⋊D311yescharacteristic
660C2×C4C2×D3×C3⋊D311yescharacteristic
661C2×C4C2×D3×C3⋊D311yescharacteristic
662C2×C3—24no—
663C2×C3—24no—
664C2×C3—24no—
665C2×C3—124no—
666C2×C3—124no—
667C2×C3—361no—
668C2×C3—361no—
669C2×C3#6429814yes—
670C2×C3#6431314yes—
671C2×C3#6432014yes—
672C2×C3#6436111yescharacteristic
673C2×C3#6436611yescharacteristic
674C2×C3#6436711yescharacteristic
675D3—41no—
676D3—41no—
677D3—124no—
678D3—124no—
679C22—61no—
680C22—61no—
681C22—61no—
682C22—61no—
683C22—61no—
684C22—61no—
685C22—181no—
686C22—181no—
687C22—181no—
688C22—181no—
689C22—181no—
690C22—181no—
691C22C22×D3×C3⋊D311yescharacteristic
692C4—21no—
693C4—21no—
694C4—21no—
695C4—61no—
696C4—61no—
697C4—181no—
698C4—181no—
699C4—541no—
700C4—541no—
701C4—541no—
702C4—541no—
703C3—24no—
704C3#1059449714yescomplemented
705C3#1059613811yescharacteristic, complemented
706C2—121no—
707C2—121no—
708C2—361no—
709C2—361no—
710C2#1172456311yescharacteristic
711C2#1172458711yescharacteristic
712C2#1172459711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
hypercenterC4⋊C4D3×C3⋊D3
hypocenterC33#562
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #11723931C2semidirect
2. C3×#64103C2semidirect
3. C32×#894C2semidirect
4. #11723530C2semidirect
5. #11723530C2semidirect
6. #11723523C2semidirect
7. #11723522C2semidirect
8. #11723519C2semidirect
9. #11723515C2semidirect
10. #11723491C2semidirect
11. #11723483C2semidirect
12. #11723480C2semidirect
13. #11723474C2semidirect
14. #11723418C2semidirect
15. #11723415C2semidirect
60. #64103D3semidirect
71. C3×#894D3semidirect
229. #894C3⋊D3semidirect
462. C33#562semidirect
633. C32#5667semidirect
634. C32#5667semidirect
704. C3#10594497semidirect
705. C3#10596138semidirect

Maximal subgroups

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

subgroupindex
#117239312
C3×#641032
C32×#8942
#117235302
#117235232
#117235222
#117235192
#117235152
#117234912
#117234832
#117234802
#117234742
#117234182
#117234152
#105961383
#105944973