Finite Group Databasebeta

← #13175336

Subgroups — #13175336

Order 1728.

1732 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723913C211yesmaximal, characteristic, complemented
2C3×#64085C211yesmaximal, characteristic, complemented
3C32×C4×D12C211yesmaximal, characteristic, complemented
4#11723527C211yesmaximal, characteristic, complemented
5#11723514C211yesmaximal, characteristic, complemented
6#11723508C211yesmaximal, characteristic, complemented
7#11723506C211yesmaximal, characteristic, complemented
8#11723493C211yesmaximal, characteristic, complemented
9#11723475C211yesmaximal, characteristic, complemented
10#11723474C211yesmaximal, characteristic, complemented
11#11723462C211yesmaximal, characteristic, complemented
12D3×#3750C211yesmaximal, characteristic, complemented
13#11723432C211yesmaximal, characteristic, complemented
14#11723414C211yesmaximal, characteristic, complemented
15#11723405C211yesmaximal, characteristic, complemented
16#10596011—31nomaximal
17#10593924—34nomaximal
18C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
19C2×C32×D12C2211yescharacteristic
20C2×C32×C4×D3C2211yescharacteristic
21C2×C32×C4×D3C2211yescharacteristic
22C2×#6292C2211yescharacteristic
23C2×#6291C2211yescharacteristic
24C2×#6291C2211yescharacteristic
25C2×#6290C2211yescharacteristic
26C2×#6290C2211yescharacteristic
27C2×Dic3×C3⋊D3C2211yescharacteristic
28C2×D3×C3⋊Dic3C2211yescharacteristic
29C2×D3×C3⋊Dic3C2211yescharacteristic
30C33×C42C2211yescharacteristic
31#88859C2211yescharacteristic
32#88859C2211yescharacteristic
33#88857C2211yescharacteristic
34#88857C2211yescharacteristic
35C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
36C3×#3752C2211yescharacteristic
37C3×#3752C2211yescharacteristic
38C3×#3752C2211yescharacteristic
39C3×#3750C2211yescharacteristic
40C3×#3750C2211yescharacteristic
41C3×#3750C2211yescharacteristic
42C32×(C2×D3)⋊C4C2211yescharacteristic
43C32×(C2×D3)⋊C4C2211yescharacteristic
44C32×C4⋊Dic3C2211yescharacteristic
45#88807C2211yescharacteristic
46#88806C2211yescharacteristic
47#88806C2211yescharacteristic
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic
49#88804C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
52Dic3×C3⋊Dic3C2211yescharacteristic
53C32×C4×D4—31no—
54#64148—31no—
55#64148—31no—
56#64139—31no—
57#64138—31no—
58C4×#638—31no—
59C2×#3750—31no—
60#64103—31no—
61#64098—31no—
62#64093—31no—
63#64090—31no—
64#64090—31no—
65#64088—31no—
66#64085D311yescharacteristic, complemented
67#64081—31no—
68#64081—34no—
69#64081—64no—
70C3×#876—34no—
71C3×C4×D12D314yescomplemented
72#63912—34no—
73#63906—34no—
74#63902—34no—
75#63890—34no—
76#63886—34no—
77#63885—34no—
78#63881—34no—
79#63879—34no—
80D3×Dic3⋊C4—34no—
81#63862—34no—
82#63850—34no—
83#63847—34no—
84C22×C3⋊(C3⋊D3)C2311yescharacteristic
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
94C4×C3⋊(C3⋊D3)—22no—
95C2×C3×C3⋊Dic3C2311yescharacteristic
96C2×C3×C3⋊Dic3C2311yescharacteristic
97C2×C3×C3⋊Dic3C2311yescharacteristic
98C2×C32×Dic3C2311yescharacteristic
99C2×C32×Dic3C2311yescharacteristic
100C32×D12—22no—
101C32×C4×D3—41no—
102C32×C4×D3—41no—
103#6292—41no—
104#6291—22no—
105#6291—41no—
106#6290—22no—
107#6290—22no—
108Dic3×C3⋊D3—41no—
109D3×C3⋊Dic3—22no—
110D3×C3⋊Dic3—41no—
111#5709—91no—
112#5540—94no—
113C2×C32×D4—31no—
114C22×C32×C4—31no—
115C22×C32×C4—31no—
116C2×#638—31no—
117C2×#638—31no—
118C2×#638—31no—
119C2×#638—31no—
120C22×C3⋊Dic3—31no—
121C22×C3⋊Dic3—31no—
122C2×C4⋊(C3⋊D3)—31no—
123C2×C4×C3⋊D3—31no—
124C2×C4×C3⋊D3—34no—
125C2×C4×C3⋊D3—31no—
126C2×C4×C3⋊D3—64no—
127C2×C3×D12C2×D314yes—
128C2×C3×C4×D3C2×D314yes—
129C2×C3×C4×D3C2×D314yes—
130C2×#626—34no—
131C2×#626—34no—
132C2×#626—34no—
133C2×#625—34no—
134C2×#625—34no—
135C2×D3×Dic3—34no—
136C2×D3×Dic3—34no—
137C2×D3×Dic3—34no—
138C32×C4⋊C4—31no—
139C32×C22⋊C4—31no—
140C32×C22⋊C4—31no—
141C32×C42—24no—
142C32×C42C2×D314yes—
143C32×C42C2×D311yescharacteristic
144#3757—31no—
145#3757—31no—
146#3752—31no—
147#3752—31no—
148#3752—34no—
149#3752—34no—
150#3752—31no—
151#3752—64no—
152#3752—64no—
153#3752C2×D311yescharacteristic
154#3752C2×D311yescharacteristic
155#3752C2×D311yescharacteristic
156C4⋊(C3⋊Dic3)—31no—
157#3750—31no—
158#3750—31no—
159#3750—34no—
160#3750—34no—
161#3750—31no—
162#3750—31no—
163#3750—31no—
164#3750—64no—
165#3750—64no—
166#3750C2×D311yescharacteristic
167#3750C2×D311yescharacteristic
168#3750C2×D311yescharacteristic
169C4×C3⋊Dic3—31no—
170C4×C3⋊Dic3—34no—
171C4×C3⋊Dic3—31no—
172C4×C3⋊Dic3—64no—
173C3×(C2×D3)⋊C4—34no—
174C3×(C2×D3)⋊C4—34no—
175C3×(C2×D3)⋊C4—34no—
176C3×(C2×D3)⋊C4C2×D314yes—
177C3×(C2×D3)⋊C4C2×D314yes—
178C3×C4⋊Dic3C2×D314yes—
179C3×Dic3⋊C4—34no—
180C3×Dic3⋊C4—34no—
181C3×Dic3⋊C4—34no—
182#3724—34no—
183#3724—34no—
184Dic3⋊Dic3—34no—
185Dic3⋊Dic3—34no—
186#3722—34no—
187(C2×D3)⋊Dic3—34no—
188(C2×D3)⋊Dic3—34no—
189Dic32—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#4112yes—
203C33×C4—21no—
204C33×C4—21no—
205C33×C4—21no—
206C3⋊(C3⋊Dic3)—21no—
207C3⋊(C3⋊Dic3)—21no—
208C3⋊(C3⋊Dic3)#4112yes—
209C3×C3⋊Dic3—21no—
210C3×C3⋊Dic3—21no—
211C3×C3⋊Dic3—21no—
212C32×Dic3—21no—
213C32×Dic3—21no—
214C3×#126—91no—
215C3×C4×D4—34no—
216#939—94no—
217#939—94no—
218#930—94no—
219#929—94no—
220C4×#67—94no—
221C2×Dic3⋊C4—94no—
222#898—91no—
223#895—91no—
224#894—94no—
225#894—91no—
226#893—91no—
227D3×C4⋊C4—91no—
228#889—94no—
229#889—91no—
230#886—91no—
231#884—94no—
232#884—91no—
233#884—91no—
234#884—91no—
235#67⋊C4—94no—
236#67⋊C4—94no—
237#67⋊C4—91no—
238#67⋊C4—91no—
239#879—94no—
240#876—34no—
241C4×D12C3⋊D311yescharacteristic, complemented
242#872—94no—
243#872—91no—
244#872—184no—
245C23×C32—31no—
246C23×C32—31no—
247C22×C3⋊D3—31no—
248C22×C3⋊D3—34no—
249C22×C3⋊D3—64no—
250C22×C3⋊D3C22×D311yescharacteristic
251C22×C3×D3—34no—
252C22×C3×D3C22×D314yes—
253C22×C3×D3C22×D314yes—
254C32×D4—62no—
255C2×C32×C4—24no—
256C2×C32×C4—24no—
257C2×C32×C4—24no—
258C2×C32×C4—31no—
259C2×C32×C4—31no—
260C2×C32×C4—121no—
261C2×C32×C4—121no—
262C2×C32×C4C22×D314yes—
263C2×C32×C4C22×D314yes—
264C2×C32×C4C22×D314yes—
265C2×C32×C4C22×D311yescharacteristic
266C2×C32×C4C22×D311yescharacteristic
267C2×C32×C4C22×D311yescharacteristic
268#638—62no—
269#638—62no—
270#638—62no—
271#638—121no—
272C2×C3⋊Dic3—31no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—31no—
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—62no—
282C2×C3⋊Dic3—121no—
283C2×C3⋊Dic3C22×D311yescharacteristic
284C2×C3⋊Dic3C22×D311yescharacteristic
285C2×C3⋊Dic3C22×D311yescharacteristic
286C4⋊(C3⋊D3)—121no—
287C4×C3⋊D3—62no—
288C4×C3⋊D3—68no—
289C4×C3⋊D3—616no—
290C4×C3⋊D3—121no—
291C2×C3×Dic3—34no—
292C2×C3×Dic3—34no—
293C2×C3×Dic3—34no—
294C2×C3×Dic3C22×D314yes—
295C2×C3×Dic3C22×D314yes—
296C3×D12—28no—
297C3×C4×D3—44no—
298C3×C4×D3—44no—
299#626—68no—
300#626—124no—
301#626—124no—
302#625—68no—
303#625—68no—
304D3×Dic3—68no—
305D3×Dic3—124no—
306D3×Dic3—124no—
307#553—271noSylow
308C2×C33C2×#4111yescharacteristic
309C2×C33C2×#4111yescharacteristic
310C2×C33H(5,𝔽2)11yescharacteristic
311C3⋊(C3⋊D3)—41no—
312C3×C3⋊D3—41no—
313C32×D3—22no—
314C32×D3—41no—
315C2×C3×D4—34no—
316C22×C3×C4—34no—
317C22×C3×C4—34no—
318C2×#67—94no—
319C2×#67—94no—
320C2×#67—94no—
321C2×#67—94no—
322C2×#67—91no—
323C2×#67—91no—
324C2×#67—91no—
325C22×Dic3—94no—
326C22×Dic3—94no—
327C22×Dic3—91no—
328C2×D12—91no—
329C2×D12—94no—
330C2×D12—91no—
331C2×D12C2×C3⋊D311yescharacteristic
332C2×C4×D3—91no—
333C2×C4×D3—94no—
334C2×C4×D3—91no—
335C2×C4×D3—94no—
336C2×C4×D3—91no—
337C2×C4×D3—184no—
338C2×C4×D3C2×C3⋊D311yescharacteristic
339C2×C4×D3C2×C3⋊D311yescharacteristic
340C3×C4⋊C4—34no—
341C3×C4⋊C4—91no—
342C3×C4⋊C4—91no—
343C3×C4⋊C4—91no—
344C3×C22⋊C4—34no—
345C3×C22⋊C4—34no—
346C3×C22⋊C4—91no—
347C3×C22⋊C4—91no—
348C3×C22⋊C4—91no—
349C3×C42—24no—
350C3×C42D3214yes—
351C3×C42C2×C3⋊D311yescharacteristic
352#217—94no—
353#217—94no—
354(C2×D3)⋊C4—34no—
355(C2×D3)⋊C4—34no—
356(C2×D3)⋊C4—34no—
357(C2×D3)⋊C4—94no—
358(C2×D3)⋊C4—91no—
359(C2×D3)⋊C4—91no—
360(C2×D3)⋊C4—94no—
361(C2×D3)⋊C4—94no—
362(C2×D3)⋊C4—91no—
363(C2×D3)⋊C4—91no—
364(C2×D3)⋊C4—91no—
365(C2×D3)⋊C4—184no—
366(C2×D3)⋊C4—184no—
367(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
368(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
369C4⋊Dic3—94no—
370C4⋊Dic3—91no—
371C4⋊Dic3C2×C3⋊D311yescharacteristic
372Dic3⋊C4—34no—
373Dic3⋊C4—34no—
374Dic3⋊C4—34no—
375Dic3⋊C4—94no—
376Dic3⋊C4—94no—
377Dic3⋊C4—94no—
378Dic3⋊C4—94no—
379Dic3⋊C4—94no—
380Dic3⋊C4—91no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—91no—
385Dic3⋊C4—184no—
386Dic3⋊C4—184no—
387C4×Dic3—94no—
388C4×Dic3—94no—
389C4×Dic3—91no—
390C4×Dic3—91no—
391C4×Dic3—184no—
392C22×C32—24no—
393C22×C32—32no—
394C22×C32—61no—
395C22×C32—61no—
396C22×C32—61no—
397C22×C32—61no—
398C22×C32—61no—
399C22×C32C23×D314yes—
400C22×C32C23×D311yescharacteristic
401C2×C3⋊D3—21no—
402C2×C3⋊D3—21no—
403C2×C3⋊D3—21no—
404C2×C3⋊D3—68no—
405C2×C3⋊D3—64no—
406C2×C3⋊D3—61no—
407C2×C3⋊D3—61no—
408C2×C3⋊D3—61no—
409C2×C3⋊D3—64no—
410C2×C3⋊D3—64no—
411C2×C3⋊D3—124no—
412C2×C3⋊D3—124no—
413C2×C3×D3—24no—
414C2×C3×D3—24no—
415C2×C3×D3—24no—
416C2×C3×D3—24no—
417C2×C3×D3—24no—
418C2×C3×D3—64no—
419C2×C3×D3—64no—
420C2×C3×D3—64no—
421C2×C3×D3#23518yes—
422C32×C4—28no—
423C32×C4—24no—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4—24no—
428C32×C4—24no—
429C32×C4—44no—
430C32×C4—44no—
431C32×C4—61no—
432C32×C4—61no—
433C3⋊Dic3—21no—
434C3⋊Dic3—21no—
435C3⋊Dic3—21no—
436C3⋊Dic3—32no—
437C3⋊Dic3—38no—
438C3⋊Dic3—68no—
439C3⋊Dic3—61no—
440C3⋊Dic3—61no—
441C3⋊Dic3—64no—
442C3⋊Dic3—64no—
443C3⋊Dic3—124no—
444C3⋊Dic3—124no—
445C3×Dic3—24no—
446C3×Dic3—24no—
447C3×Dic3—64no—
448C3×Dic3—64no—
449C3×Dic3—64no—
450#126—91no—
451#126—271no—
452#125—271no—
453#123—271no—
454#123—271no—
455#121—271no—
456#121—271no—
457#121—271no—
458#121—271no—
459C4×D4—31no—
460C4×D4—271no—
461C4×D4—271no—
462C4×D4—271no—
463#117—271no—
464C2×C4⋊C4—271no—
465C33#55311yescharacteristic, complemented, Sylow
466C23×C3—34no—
467C23×C3—34no—
468C23×C3—91no—
469C22×D3—34no—
470C22×D3—94no—
471C22×D3—91no—
472C22×D3—184no—
473C22×D3C22×C3⋊D311yescharacteristic
474C22×D3C22×C3⋊D311yescharacteristic
475C3×D4—68no—
476C2×C3×C4—24no—
477C2×C3×C4—24no—
478C2×C3×C4—24no—
479C2×C3×C4—34no—
480C2×C3×C4—34no—
481C2×C3×C4—91no—
482C2×C3×C4—91no—
483C2×C3×C4—91no—
484C2×C3×C4—124no—
485C2×C3×C4—124no—
486C2×C3×C4C2×D3214yes—
487C2×C3×C4C2×D3214yes—
488C2×C3×C4C2×D3214yes—
489C2×C3×C4C22×C3⋊D311yescharacteristic
490C2×C3×C4C22×C3⋊D311yescharacteristic
491C2×C3×C4C22×C3⋊D311yescharacteristic
492#67—188no—
493#67—182no—
494#67—188no—
495#67—188no—
496#67—182no—
497#67—361no—
498#67—364no—
499C2×Dic3—34no—
500C2×Dic3—34no—
501C2×Dic3—34no—
502C2×Dic3—94no—
503C2×Dic3—91no—
504C2×Dic3—94no—
505C2×Dic3—94no—
506C2×Dic3—91no—
507C2×Dic3—91no—
508C2×Dic3—184no—
509C2×Dic3—184no—
510C2×Dic3—184no—
511C2×Dic3—188no—
512C2×Dic3—361no—
513C2×Dic3—364no—
514C2×Dic3C22×C3⋊D311yescharacteristic
515C2×Dic3C22×C3⋊D311yescharacteristic
516D12—22no—
517D12—182no—
518D12—364no—
519D12—361no—
520C4×D3—41no—
521C4×D3—41no—
522C4×D3—188no—
523C4×D3—182no—
524C4×D3—182no—
525C4×D3—1816no—
526C4×D3—364no—
527C4×D3—361no—
528C2×C32—24no—
529C2×C32—24no—
530C2×C32—24no—
531C2×C32—62no—
532C2×C32—121no—
533C2×C32C2×#23514yes—
534C2×C32#100414yes—
535C2×C32D3×#4114yes—
536C2×C32D3×#4111yescharacteristic
537C2×C32D3×#4111yescharacteristic
538C2×C32#100911yescharacteristic
539C3⋊D3—41no—
540C3⋊D3—128no—
541C3⋊D3—121no—
542C3⋊D3—124no—
543C3×D3—28no—
544C3×D3—44no—
545C3×D3—124no—
546C2×D4—31no—
547C2×D4—271no—
548C2×D4—271no—
549C2×D4—271no—
550C2×D4—271no—
551C2×D4—271no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—271no—
555C22×C4—271no—
556C22×C4—271no—
557C22×C4—271no—
558C4⋊C4—31no—
559C4⋊C4—91no—
560C4⋊C4—91no—
561C4⋊C4—91no—
562C4⋊C4—271no—
563C4⋊C4—271no—
564C4⋊C4—271no—
565C4⋊C4—271no—
566C4⋊C4—271no—
567C4⋊C4—271no—
568C22⋊C4—31no—
569C22⋊C4—31no—
570C22⋊C4—91no—
571C22⋊C4—91no—
572C22⋊C4—91no—
573C22⋊C4—271no—
574C22⋊C4—271no—
575C22⋊C4—271no—
576C22⋊C4—271no—
577C22⋊C4—271no—
578C42—271no—
579C42—271no—
580C42D3×C3⋊D311yescharacteristic
581C22×C3—24no—
582C22×C3—38no—
583C22×C3—64no—
584C22×C3—64no—
585C22×C3—64no—
586C22×C3—64no—
587C22×C3—64no—
588C22×C3—181no—
589C22×C3—181no—
590C22×C3—181no—
591C22×C3C22×D3214yes—
592C22×C3C23×C3⋊D311yescharacteristic
593C2×D3—21no—
594C2×D3—21no—
595C2×D3—21no—
596C2×D3—21no—
597C2×D3—21no—
598C2×D3—64no—
599C2×D3—64no—
600C2×D3—64no—
601C2×D3—188no—
602C2×D3—184no—
603C2×D3—184no—
604C2×D3—184no—
605C2×D3—181no—
606C2×D3—181no—
607C2×D3—181no—
608C2×D3—364no—
609C2×D3—364no—
610C2×D3#382812yes—
611C3×C4—28no—
612C3×C4—24no—
613C3×C4—24no—
614C3×C4—24no—
615C3×C4—21no—
616C3×C4—21no—
617C3×C4—21no—
618C3×C4—44no—
619C3×C4—44no—
620C3×C4—64no—
621C3×C4—64no—
622C3×C4—181no—
623C3×C4—181no—
624C3×C4—181no—
625Dic3—21no—
626Dic3—21no—
627Dic3—64no—
628Dic3—64no—
629Dic3—64no—
630Dic3—98no—
631Dic3—92no—
632Dic3—188no—
633Dic3—184no—
634Dic3—184no—
635Dic3—181no—
636Dic3—181no—
637Dic3—364no—
638Dic3—364no—
639C32—24no—
640C32#554014yescomplemented
641C32#570911yescharacteristic, complemented
642C23—31no—
643C23—31no—
644C23—91no—
645C23—271no—
646D4—62no—
647D4—542no—
648D4—542no—
649D4—542no—
650D4—1081no—
651D4—1081no—
652C2×C4—31no—
653C2×C4—31no—
654C2×C4—91no—
655C2×C4—91no—
656C2×C4—91no—
657C2×C4—121no—
658C2×C4—121no—
659C2×C4—271no—
660C2×C4—271no—
661C2×C4—271no—
662C2×C4—542no—
663C2×C4—542no—
664C2×C4—1081no—
665C2×C4—1081no—
666C2×C4C2×D3×C3⋊D311yescharacteristic
667C2×C4C2×D3×C3⋊D311yescharacteristic
668C2×C4C2×D3×C3⋊D311yescharacteristic
669C2×C3—24no—
670C2×C3—24no—
671C2×C3—24no—
672C2×C3—68no—
673C2×C3—124no—
674C2×C3—361no—
675C2×C3D3×#23514yes—
676C2×C3#6430614yes—
677C2×C3#6430714yes—
678C2×C3C2×#382811yescharacteristic
679C2×C3#6436111yescharacteristic
680C2×C3#41×C3⋊D311yescharacteristic
681D3—22no—
682D3—41no—
683D3—124no—
684D3—368no—
685D3—364no—
686D3—361no—
687C22—32no—
688C22—61no—
689C22—61no—
690C22—61no—
691C22—61no—
692C22—61no—
693C22—181no—
694C22—181no—
695C22—181no—
696C22—541no—
697C22—541no—
698C22—541no—
699C22C22×D3×C3⋊D311yescharacteristic
700C4—21no—
701C4—21no—
702C4—21no—
703C4—61no—
704C4—61no—
705C4—181no—
706C4—181no—
707C4—181no—
708C4—272no—
709C4—541no—
710C4—541no—
711C3—24no—
712C3#1059392414yescomplemented
713C3#1059601111yescharacteristic, complemented
714C2—62no—
715C2—121no—
716C2—361no—
717C2—1081no—
718C2D3×#382811yescharacteristic
719C2#1172457811yescharacteristic
720C2#1172457911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C42C22
hypercenterC42D3×C3⋊D3
hypocenterC33#553
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. #11723913C2semidirect
2. C3×#64085C2semidirect
3. C32×C4×D12C2semidirect
4. #11723527C2semidirect
5. #11723514C2semidirect
6. #11723508C2semidirect
7. #11723506C2semidirect
8. #11723493C2semidirect
9. #11723475C2semidirect
10. #11723474C2semidirect
11. #11723462C2semidirect
12. D3×#3750C2semidirect
13. #11723432C2semidirect
14. #11723414C2semidirect
15. #11723405C2semidirect
66. #64085D3semidirect
71. C3×C4×D12D3semidirect
241. C4×D12C3⋊D3semidirect
465. C33#553semidirect
640. C32#5540semidirect
641. C32#5709semidirect
712. C3#10593924semidirect
713. C3#10596011semidirect

Maximal subgroups

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

subgroupindex
#117239132
C3×#640852
C32×C4×D122
#117235272
#117235142
#117235082
#117235062
#117234932
#117234752
#117234742
#117234622
D3×#37502
#117234322
#117234142
#117234052
#105960113
#105939243