Finite Group Databasebeta

← #13177238

Subgroups — #13177238

Order 1728.

2028 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88859C211yesmaximal, characteristic, complemented
2C3×C4×#638C211yesmaximal, characteristic, complemented
3C32×C4×#67C211yesmaximal, characteristic, complemented
4#11723642C211yesmaximal, characteristic, complemented
5#11723639C211yesmaximal, characteristic, complemented
6#11723638C211yesmaximal, characteristic, complemented
7#11723637C211yesmaximal, characteristic, complemented
8#11723520C211yesmaximal, characteristic, complemented
9#11723514C211yesmaximal, characteristic, complemented
10#11723453C211yesmaximal, characteristic, complemented
11#11723446C211yesmaximal, characteristic, complemented
12#11723419C211yesmaximal, characteristic, complemented
13#11723417C211yesmaximal, characteristic, complemented
14#11723416C211yesmaximal, characteristic, complemented
15#11723414C211yesmaximal, characteristic, complemented
16#10596031—31nomaximal
17#10595039—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C22×C33×C4C2211yescharacteristic
20C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
23C2×C32×#67C2211yescharacteristic
24C2×C32×C4×D3C2211yescharacteristic, complemented
25C2×#6293C2211yescharacteristic, complemented
26C2×#6292C2211yescharacteristic
27C2×#6292C2211yescharacteristic
28C2×#6291C2211yescharacteristic
29C2×#6291C2211yescharacteristic
30C2×#6290C2211yescharacteristic, complemented
31#88859C2211yescharacteristic
32#88859C2211yescharacteristic
33#88859C2211yescharacteristic
34#88859C2211yescharacteristic
35C3×#3757C2211yescharacteristic
36C3×#3752C2211yescharacteristic, complemented
37C3×#3750C2211yescharacteristic, complemented
38C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
39C32×#217C2211yescharacteristic
40C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C32×Dic3⋊C4C2211yescharacteristic, complemented
42C32×C4×Dic3C2211yescharacteristic, complemented
43#88807C2211yescharacteristic, complemented
44#88806C2211yescharacteristic, complemented
45#88806C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47#88804C2211yescharacteristic
48#88804C2211yescharacteristic
49#88804C2211yescharacteristic
50#88804C2211yescharacteristic
51#88803C2211yescharacteristic, complemented
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
53C32×C4×D4—31no—
54#64148—31no—
55#64146—31no—
56#64139—31no—
57#64138—31no—
58C4×#638D311yescharacteristic, complemented
59C2×#3752—31no—
60C2×#3752—34no—
61C2×#3752—64no—
62#64107—31no—
63#64103—31no—
64#64094—31no—
65#64093—31no—
66#64091—31no—
67#64087—31no—
68#64085—31no—
69#64084—31no—
70C3×C4×#67—34no—
71C3×C4×#67D314yescomplemented
72#63982—34no—
73#63981—34no—
74#63981—34no—
75#63980—34no—
76#63906—34no—
77#63906—34no—
78#63868—34no—
79#63868—34no—
80#63852—34no—
81#63852—34no—
82#63850—34no—
83#63850—34no—
84C23×C33C2311yescharacteristic
85C22×C3⋊(C3⋊D3)—22no—
86C22×C3⋊(C3⋊D3)—41no—
87C22×C3⋊(C3⋊D3)—41no—
88C22×C3⋊(C3⋊D3)C2311yescharacteristic
89C22×C3⋊(C3⋊D3)C2311yescharacteristic
90C22×C3×C3⋊D3C2311yescharacteristic
91C22×C32×D3C2311yescharacteristic
92C2×C33×C4—41no—
93C2×C33×C4C2311yescharacteristic
94C2×C33×C4C2311yescharacteristic
95C2×C3⋊(C3⋊Dic3)—41no—
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C3×#638—22no—
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C3×C4×C3⋊D3—41no—
103C32×#67—22no—
104C2×C32×Dic3C2311yescharacteristic
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C32×C4×D3—41no—
108#6293—41no—
109#6292—41no—
110#6292—41no—
111#6291—41no—
112#6291—41no—
113#6290—41no—
114#5560—94no—
115#5560—91no—
116C23×C3⋊D3—31no—
117C23×C3⋊D3—34no—
118C23×C3⋊D3—64no—
119C2×C32×D4—31no—
120C22×C32×C4—24no—
121C22×C32×C4—31no—
122C22×C32×C4C2×D314yes—
123C22×C32×C4C2×D311yescharacteristic
124C2×#638—31no—
125C2×#638—31no—
126C2×#638—31no—
127C2×#638C2×D311yescharacteristic
128C22×C3⋊Dic3—31no—
129C22×C3⋊Dic3—34no—
130C22×C3⋊Dic3—64no—
131C2×C4⋊(C3⋊D3)—31no—
132C2×C4⋊(C3⋊D3)—31no—
133C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
134C2×#634—31no—
135C2×C3×#67—34no—
136C2×C3×#67C2×D314yes—
137C2×C3×C4×D3—34no—
138C2×C3×C4×D3C2×D314yescomplemented
139C2×#627—34no—
140C2×#626—34no—
141C2×#626—34no—
142C2×#626—34no—
143C2×#626—34no—
144C2×#625—34no—
145C32×C4⋊C4—31no—
146C32×C22⋊C4—31no—
147C32×C22⋊C4—31no—
148C32×C42—31no—
149#3757—31no—
150#3757C2×D311yescharacteristic
151#3752—31no—
152#3752—31no—
153#3752—31no—
154#3752—31no—
155#3752—31no—
156#3752—34no—
157#3752—34no—
158#3752—34no—
159#3752—34no—
160#3752—31no—
161#3752—31no—
162#3752—31no—
163#3752—31no—
164#3752—64no—
165#3752—64no—
166#3752—64no—
167#3752—64no—
168#3752C2×D311yescharacteristic, complemented
169C4⋊(C3⋊Dic3)—31no—
170#3750—31no—
171#3750—31no—
172#3750—31no—
173#3750C2×D311yescharacteristic, complemented
174C4×C3⋊Dic3C2×D311yescharacteristic, complemented
175C3×#217—34no—
176C3×#217C2×D314yes—
177C3×(C2×D3)⋊C4—34no—
178C3×(C2×D3)⋊C4C2×D314yescomplemented
179C3×Dic3⋊C4—34no—
180C3×Dic3⋊C4C2×D314yescomplemented
181C3×C4×Dic3—34no—
182C3×C4×Dic3C2×D314yescomplemented
183#3724—34no—
184#3724—34no—
185Dic3⋊Dic3—34no—
186Dic3⋊Dic3—34no—
187#3722—34no—
188#3722—34no—
189#3722—34no—
190#3722—34no—
191(C2×D3)⋊Dic3—34no—
192(C2×D3)⋊Dic3—34no—
193C22×C33—21no—
194C22×C33—21no—
195C22×C33#4112yes—
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)—44no—
204C2×C3×C3⋊D3—21no—
205C2×C3×C3⋊D3—21no—
206C2×C3×C3⋊D3—21no—
207C2×C32×D3—21no—
208C2×C32×D3—21no—
209C2×C32×D3—21no—
210C33×C4—21no—
211C33×C4—21no—
212C3⋊(C3⋊Dic3)—21no—
213C3⋊(C3⋊Dic3)—21no—
214C3×C3⋊Dic3—21no—
215C3×C3⋊Dic3—21no—
216C3×C3⋊Dic3—21no—
217C32×Dic3—21no—
218C32×Dic3—21no—
219C32×Dic3—21no—
220C3×C4×D4—34no—
221C3×C4×D4—91no—
222#939—94no—
223#939—91no—
224#937—94no—
225#937—91no—
226#930—94no—
227#930—91no—
228#929—94no—
229#929—91no—
230C4×#67—34no—
231C4×#67C3⋊D311yescharacteristic, complemented
232C2×(C2×D3)⋊C4—94no—
233C2×(C2×D3)⋊C4—91no—
234C2×(C2×D3)⋊C4—184no—
235#898—94no—
236#898—91no—
237#894—94no—
238#894—91no—
239#885—94no—
240#885—91no—
241#884—94no—
242#884—91no—
243#882—94no—
244#882—91no—
245#878—94no—
246#878—91no—
247#876—94no—
248#876—91no—
249#875—94no—
250#875—91no—
251C23×C32—24no—
252C23×C32—31no—
253C23×C32C22×D314yes—
254C23×C32C22×D311yescharacteristic
255C22×C3⋊D3—31no—
256C22×C3⋊D3—31no—
257C22×C3⋊D3—34no—
258C22×C3⋊D3—34no—
259C22×C3⋊D3—64no—
260C22×C3⋊D3—64no—
261C22×C3⋊D3—616no—
262C22×C3⋊D3—68no—
263C22×C3⋊D3—62no—
264C22×C3⋊D3—121no—
265C22×C3⋊D3—121no—
266C22×C3⋊D3—124no—
267C22×C3⋊D3—124no—
268C22×C3⋊D3—128no—
269C22×C3⋊D3—128no—
270C22×C3⋊D3C22×D311yescharacteristic
271C22×C3×D3—34no—
272C22×C3×D3C22×D314yes—
273C32×D4—62no—
274C2×C32×C4—24no—
275C2×C32×C4—24no—
276C2×C32×C4—31no—
277C2×C32×C4—31no—
278C2×C32×C4—31no—
279C2×C32×C4—41no—
280C2×C32×C4—44no—
281C2×C32×C4—48no—
282C2×C32×C4—121no—
283C2×C32×C4C22×D314yes—
284C2×C32×C4C22×D314yes—
285C2×C32×C4C22×D311yescharacteristic
286C2×C32×C4C22×D311yescharacteristic
287#638—22no—
288#638—121no—
289#638—121no—
290#638—121no—
291C2×C3⋊Dic3—31no—
292C2×C3⋊Dic3—31no—
293C2×C3⋊Dic3—34no—
294C2×C3⋊Dic3—34no—
295C2×C3⋊Dic3—64no—
296C2×C3⋊Dic3—64no—
297C2×C3⋊Dic3—121no—
298C2×C3⋊Dic3—124no—
299C2×C3⋊Dic3—128no—
300C2×C3⋊Dic3C22×D311yescharacteristic
301C2×C3⋊Dic3C22×D311yescharacteristic
302C2×C3⋊Dic3C22×D311yescharacteristic
303C4⋊(C3⋊D3)—121no—
304C4⋊(C3⋊D3)—121no—
305C4×C3⋊D3—41no—
306#634—121no—
307C3×#67—28no—
308C3×#67—68no—
309C2×C3×Dic3—34no—
310C2×C3×Dic3—34no—
311C2×C3×Dic3—34no—
312C2×C3×Dic3C22×D314yes—
313C2×C3×Dic3C22×D314yes—
314C2×C3×Dic3C22×D314yes—
315C3×C4×D3—44no—
316C3×C4×D3—124no—
317#627—124no—
318#626—124no—
319#626—124no—
320#626—124no—
321#626—124no—
322#625—124no—
323#538—271noSylow
324C2×C33—22no—
325C2×C33C2×#4111yescharacteristic
326C2×C33H(5,𝔽2)11yescharacteristic
327C2×C33H(5,𝔽2)11yescharacteristic
328C3⋊(C3⋊D3)—41no—
329C3⋊(C3⋊D3)—41no—
330C3×C3⋊D3—41no—
331C32×D3—41no—
332C23×D3—94no—
333C23×D3—91no—
334C23×D3—184no—
335C2×C3×D4—34no—
336C2×C3×D4—91no—
337C22×C3×C4—24no—
338C22×C3×C4—34no—
339C22×C3×C4—91no—
340C22×C3×C4D3214yes—
341C22×C3×C4C2×C3⋊D311yescharacteristic
342C2×#67—34no—
343C2×#67—94no—
344C2×#67—94no—
345C2×#67—94no—
346C2×#67—91no—
347C2×#67—91no—
348C2×#67—91no—
349C2×#67C2×C3⋊D311yescharacteristic
350C22×Dic3—94no—
351C22×Dic3—91no—
352C22×Dic3—184no—
353C2×D12—94no—
354C2×D12—94no—
355C2×D12—91no—
356C2×D12—91no—
357C2×C4×D3—34no—
358C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
359C2×Dic6—94no—
360C2×Dic6—91no—
361C3×C4⋊C4—34no—
362C3×C4⋊C4—91no—
363C3×C22⋊C4—34no—
364C3×C22⋊C4—34no—
365C3×C22⋊C4—91no—
366C3×C22⋊C4—91no—
367C3×C42—34no—
368C3×C42—91no—
369#217—34no—
370#217—94no—
371#217—91no—
372#217C2×C3⋊D311yescharacteristic
373(C2×D3)⋊C4—34no—
374(C2×D3)⋊C4—94no—
375(C2×D3)⋊C4—94no—
376(C2×D3)⋊C4—94no—
377(C2×D3)⋊C4—94no—
378(C2×D3)⋊C4—94no—
379(C2×D3)⋊C4—91no—
380(C2×D3)⋊C4—94no—
381(C2×D3)⋊C4—94no—
382(C2×D3)⋊C4—94no—
383(C2×D3)⋊C4—94no—
384(C2×D3)⋊C4—91no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—91no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—91no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4—91no—
392(C2×D3)⋊C4—184no—
393(C2×D3)⋊C4—184no—
394(C2×D3)⋊C4—184no—
395(C2×D3)⋊C4—184no—
396(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
397C4⋊Dic3—94no—
398C4⋊Dic3—91no—
399Dic3⋊C4—34no—
400Dic3⋊C4—94no—
401Dic3⋊C4—94no—
402Dic3⋊C4—94no—
403Dic3⋊C4—91no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
407C4×Dic3—34no—
408C4×Dic3C2×C3⋊D311yescharacteristic, complemented
409C22×C32—28no—
410C22×C32—28no—
411C22×C32—24no—
412C22×C32—21no—
413C22×C32—24no—
414C22×C32—21no—
415C22×C32—24no—
416C22×C32—28no—
417C22×C32—61no—
418C22×C32—61no—
419C22×C32—61no—
420C22×C32#23518yes—
421C22×C32#23512yes—
422C22×C32C23×D314yes—
423C22×C32C23×D311yescharacteristic
424C2×C3⋊D3—21no—
425C2×C3⋊D3—21no—
426C2×C3⋊D3—21no—
427C2×C3⋊D3—68no—
428C2×C3⋊D3—68no—
429C2×C3⋊D3—64no—
430C2×C3⋊D3—64no—
431C2×C3⋊D3—61no—
432C2×C3⋊D3—61no—
433C2×C3⋊D3—61no—
434C2×C3⋊D3—61no—
435C2×C3⋊D3—61no—
436C2×C3⋊D3—61no—
437C2×C3⋊D3—64no—
438C2×C3⋊D3—64no—
439C2×C3⋊D3—64no—
440C2×C3⋊D3—64no—
441C2×C3⋊D3—124no—
442C2×C3⋊D3—124no—
443C2×C3⋊D3—124no—
444C2×C3⋊D3—124no—
445C2×C3⋊D3—1232no—
446C2×C3⋊D3—1216no—
447C2×C3⋊D3—124no—
448C2×C3×D3—24no—
449C2×C3×D3—24no—
450C2×C3×D3—24no—
451C2×C3×D3—64no—
452C2×C3×D3—64no—
453C2×C3×D3—64no—
454C32×C4—21no—
455C32×C4—21no—
456C32×C4—24no—
457C32×C4—24no—
458C32×C4—44no—
459C32×C4—44no—
460C32×C4—61no—
461C32×C4—61no—
462C32×C4—61no—
463C3⋊Dic3—21no—
464C3⋊Dic3—21no—
465C3⋊Dic3—21no—
466C3⋊Dic3—61no—
467C3⋊Dic3—61no—
468C3⋊Dic3—64no—
469C3⋊Dic3—64no—
470C3⋊Dic3—124no—
471C3⋊Dic3—124no—
472C3×Dic3—24no—
473C3×Dic3—24no—
474C3×Dic3—24no—
475C3×Dic3—64no—
476C3×Dic3—64no—
477C3×Dic3—64no—
478#126—271no—
479#126—271no—
480#124—271no—
481#124—271no—
482#123—271no—
483#123—271no—
484C22⋊Q8—271no—
485#121—271no—
486#121—271no—
487#121—271no—
488#120—271no—
489#120—271no—
490C4×D4—31no—
491C4×D4—91no—
492C2×C22⋊C4—271no—
493C33#53811yescharacteristic, complemented, Sylow
494C23×C3—24no—
495C23×C3—34no—
496C23×C3—91no—
497C23×C3C2×D3214yes—
498C23×C3C22×C3⋊D311yescharacteristic
499C22×D3—34no—
500C22×D3—94no—
501C22×D3—94no—
502C22×D3—91no—
503C22×D3—91no—
504C22×D3—184no—
505C22×D3—184no—
506C22×D3—1816no—
507C22×D3—188no—
508C22×D3—182no—
509C22×D3—364no—
510C22×D3—364no—
511C22×D3—361no—
512C22×D3—361no—
513C22×D3—368no—
514C22×D3—368no—
515C22×D3C22×C3⋊D311yescharacteristic
516C3×D4—68no—
517C3×D4—182no—
518C2×C3×C4—24no—
519C2×C3×C4—24no—
520C2×C3×C4—34no—
521C2×C3×C4—34no—
522C2×C3×C4—34no—
523C2×C3×C4—44no—
524C2×C3×C4—41no—
525C2×C3×C4—48no—
526C2×C3×C4—91no—
527C2×C3×C4—91no—
528C2×C3×C4—91no—
529C2×C3×C4—124no—
530C2×C3×C4—361no—
531C2×C3×C4C2×D3214yes—
532C2×C3×C4C2×D3214yes—
533C2×C3×C4C22×C3⋊D311yescharacteristic
534C2×C3×C4C22×C3⋊D311yescharacteristic
535#67—22no—
536#67—68no—
537#67—361no—
538#67—361no—
539#67—364no—
540#67—364no—
541#67—361no—
542#67—364no—
543C2×Dic3—34no—
544C2×Dic3—34no—
545C2×Dic3—34no—
546C2×Dic3—94no—
547C2×Dic3—94no—
548C2×Dic3—91no—
549C2×Dic3—91no—
550C2×Dic3—184no—
551C2×Dic3—184no—
552C2×Dic3—364no—
553C2×Dic3—361no—
554C2×Dic3—368no—
555C2×Dic3C22×C3⋊D311yescharacteristic
556C2×Dic3C22×C3⋊D311yescharacteristic
557C2×Dic3C22×C3⋊D311yescharacteristic
558D12—364no—
559D12—364no—
560D12—361no—
561D12—361no—
562C4×D3—41no—
563C4×D3—124no—
564Dic6—361no—
565Dic6—364no—
566C2×C32—216no—
567C2×C32—28no—
568C2×C32—22no—
569C2×C32—24no—
570C2×C32—24no—
571C2×C32—24no—
572C2×C32—121no—
573C2×C32C2×#23514yes—
574C2×C32C2×#23511yescharacteristic
575C2×C32#100414yes—
576C2×C32#100411yescharacteristic
577C2×C32#100914yes—
578C2×C32#100911yescharacteristic
579C3⋊D3—41no—
580C3⋊D3—128no—
581C3⋊D3—128no—
582C3⋊D3—124no—
583C3⋊D3—124no—
584C3⋊D3—121no—
585C3⋊D3—121no—
586C3×D3—44no—
587C3×D3—124no—
588C24—271no—
589C2×Q8—271no—
590C2×D4—31no—
591C2×D4—91no—
592C2×D4—271no—
593C2×D4—271no—
594C2×D4—271no—
595C2×D4—271no—
596C2×D4—271no—
597C22×C4—31no—
598C22×C4—91no—
599C22×C4—271no—
600C22×C4D3×C3⋊D311yescharacteristic
601C4⋊C4—31no—
602C4⋊C4—91no—
603C4⋊C4—271no—
604C4⋊C4—271no—
605C4⋊C4—271no—
606C4⋊C4—271no—
607C22⋊C4—31no—
608C22⋊C4—31no—
609C22⋊C4—91no—
610C22⋊C4—91no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C22⋊C4—271no—
614C22⋊C4—271no—
615C22⋊C4—271no—
616C22⋊C4—271no—
617C22⋊C4—271no—
618C22⋊C4—271no—
619C22⋊C4—271no—
620C22⋊C4—271no—
621C42—31no—
622C42—91no—
623C22×C3—28no—
624C22×C3—28no—
625C22×C3—24no—
626C22×C3—24no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—24no—
630C22×C3—28no—
631C22×C3—64no—
632C22×C3—64no—
633C22×C3—64no—
634C22×C3—181no—
635C22×C3—181no—
636C22×C3—181no—
637C22×C3#379818yes—
638C22×C3#382812yes—
639C22×C3C22×D3214yes—
640C22×C3C23×C3⋊D311yescharacteristic
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—64no—
645C2×D3—64no—
646C2×D3—64no—
647C2×D3—188no—
648C2×D3—188no—
649C2×D3—184no—
650C2×D3—184no—
651C2×D3—184no—
652C2×D3—184no—
653C2×D3—184no—
654C2×D3—184no—
655C2×D3—181no—
656C2×D3—181no—
657C2×D3—181no—
658C2×D3—181no—
659C2×D3—181no—
660C2×D3—181no—
661C2×D3—364no—
662C2×D3—364no—
663C2×D3—364no—
664C2×D3—364no—
665C2×D3—3632no—
666C2×D3—364no—
667C2×D3—3616no—
668C3×C4—24no—
669C3×C4—24no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—44no—
673C3×C4—44no—
674C3×C4—64no—
675C3×C4—64no—
676C3×C4—64no—
677C3×C4—181no—
678C3×C4—181no—
679C3×C4—181no—
680Dic3—21no—
681Dic3—21no—
682Dic3—21no—
683Dic3—64no—
684Dic3—64no—
685Dic3—64no—
686Dic3—184no—
687Dic3—184no—
688Dic3—181no—
689Dic3—181no—
690Dic3—364no—
691Dic3—364no—
692C32—24no—
693C32#556014yescomplemented
694C32#556011yescharacteristic, complemented
695C23—31no—
696C23—91no—
697C23—271no—
698C23—271no—
699C23—542no—
700C23—1081no—
701C23—1081no—
702C23C2×D3×C3⋊D311yescharacteristic
703Q8—1081no—
704D4—62no—
705D4—182no—
706D4—1081no—
707D4—1081no—
708D4—1081no—
709D4—1081no—
710D4—1081no—
711C2×C4—31no—
712C2×C4—31no—
713C2×C4—31no—
714C2×C4—41no—
715C2×C4—91no—
716C2×C4—91no—
717C2×C4—91no—
718C2×C4—121no—
719C2×C4—271no—
720C2×C4—271no—
721C2×C4—361no—
722C2×C4—1081no—
723C2×C4C2×D3×C3⋊D311yescharacteristic
724C2×C4C2×D3×C3⋊D311yescharacteristic
725C2×C3—216no—
726C2×C3—22no—
727C2×C3—28no—
728C2×C3—24no—
729C2×C3—24no—
730C2×C3—24no—
731C2×C3—124no—
732C2×C3—361no—
733C2×C3C2×#379814yes—
734C2×C3#6430814yes—
735C2×C3#6433014yes—
736C2×C3C2×#382811yescharacteristic
737C2×C3#6436111yescharacteristic
738C2×C3#6436611yescharacteristic
739D3—41no—
740D3—124no—
741D3—368no—
742D3—368no—
743D3—361no—
744D3—361no—
745D3—364no—
746D3—364no—
747C22—21no—
748C22—21no—
749C22—61no—
750C22—61no—
751C22—61no—
752C22—181no—
753C22—181no—
754C22—181no—
755C22—541no—
756C22—541no—
757C22—541no—
758C22—541no—
759C22—541no—
760C22—541no—
761C22—1084no—
762C22#8902012yes—
763C22C22×D3×C3⋊D311yescharacteristic
764C4—21no—
765C4—21no—
766C4—61no—
767C4—61no—
768C4—61no—
769C4—181no—
770C4—181no—
771C4—181no—
772C4—541no—
773C4—541no—
774C3—24no—
775C3#1059503914yescomplemented
776C3#1059603111yescharacteristic, complemented
777C2—22no—
778C2—121no—
779C2—361no—
780C2—1081no—
781C2—1081no—
782C2C2×#8902011yescharacteristic
783C2#1172458111yescharacteristic
784C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC22×C33×C4C22
hypercenterC22×C4D3×C3⋊D3
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#88859C2semidirect
2. C3×C4×#638C2semidirect
3. C32×C4×#67C2semidirect
4. #11723642C2semidirect
5. #11723639C2semidirect
6. #11723638C2semidirect
7. #11723637C2semidirect
8. #11723520C2semidirect
9. #11723514C2semidirect
10. #11723453C2semidirect
11. #11723446C2semidirect
12. #11723419C2semidirect
13. #11723417C2semidirect
14. #11723416C2semidirect
15. #11723414C2semidirect
22. C2×C3×C4×C3⋊D3C22semidirect
24. C2×C32×C4×D3C22semidirect
25. C2×#6293C22semidirect
30. C2×#6290C22semidirect
36. C3×#3752C22semidirect
37. C3×#3750C22semidirect
38. C3×C4×C3⋊Dic3C22semidirect
40. C32×(C2×D3)⋊C4C22semidirect
41. C32×Dic3⋊C4C22semidirect
42. C32×C4×Dic3C22semidirect
43. #88807C22semidirect
44. #88806C22semidirect
45. #88806C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
51. #88803C22semidirect
52. (C2×D3)⋊(C3⋊Dic3)C22semidirect
58. C4×#638D3semidirect
71. C3×C4×#67D3semidirect
133. C2×C4×C3⋊D3C2×D3semidirect
138. C2×C3×C4×D3C2×D3semidirect
168. #3752C2×D3semidirect
173. #3750C2×D3semidirect
174. C4×C3⋊Dic3C2×D3semidirect
178. C3×(C2×D3)⋊C4C2×D3semidirect
180. C3×Dic3⋊C4C2×D3semidirect
182. C3×C4×Dic3C2×D3semidirect
231. C4×#67C3⋊D3semidirect
358. C2×C4×D3C2×C3⋊D3semidirect
396. (C2×D3)⋊C4C2×C3⋊D3semidirect
406. Dic3⋊C4C2×C3⋊D3semidirect
408. C4×Dic3C2×C3⋊D3semidirect
493. C33#538semidirect
693. C32#5560semidirect
694. C32#5560semidirect
775. C3#10595039semidirect
776. C3#10596031semidirect

Maximal subgroups

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

subgroupindex
C2×#888592
C3×C4×#6382
C32×C4×#672
#117236422
#117236392
#117236382
#117236372
#117235202
#117235142
#117234532
#117234462
#117234192
#117234172
#117234162
#117234142
#105960313
#105950393