Finite Group Databasebeta

← #13175844

Subgroups — #13175844

Order 1728.

2020 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723923C211yesmaximal, characteristic, complemented
2C3×#64087C211yesmaximal, characteristic, complemented
3C32×#67⋊C4C211yesmaximal, characteristic, complemented
4#11723638C211yesmaximal, characteristic, complemented
5#11723635C211yesmaximal, characteristic, complemented
6#11723618C211yesmaximal, characteristic, complemented
7C2×#88804C211yesmaximal, characteristic, complemented
8#11723525C211yesmaximal, characteristic, complemented
9#11723521C211yesmaximal, characteristic, complemented
10#11723516C211yesmaximal, characteristic, complemented
11#11723498C211yesmaximal, characteristic, complemented
12#11723453C211yesmaximal, characteristic, complemented
13#11723441C211yesmaximal, characteristic, complemented
14#11723414C211yesmaximal, characteristic, complemented
15#11723403C211yesmaximal, characteristic, complemented
16#10596031—31nomaximal
17#10594243—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C2×#6312C2211yescharacteristic
20C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
21C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C2×C3×#634C2211yescharacteristic, complemented
24C2×C32×#67C2211yescharacteristic
25C22×C32×Dic3C2211yescharacteristic
26C2×C32×C4×D3C2211yescharacteristic, complemented
27C2×#6291C2211yescharacteristic
28C2×#6291C2211yescharacteristic
29C2×#6291C2211yescharacteristic, complemented
30C2×#6289C2211yescharacteristic, complemented
31C33×C22⋊C4C2211yescharacteristic
32#88859C2211yescharacteristic
33#88859C2211yescharacteristic
34C3×#3757C2211yescharacteristic
35C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
36C3×#3750C2211yescharacteristic, complemented
37C3×#3750C2211yescharacteristic, complemented
38C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
39C32×Dic3⋊C4C2211yescharacteristic, complemented
40C32×C4×Dic3C2211yescharacteristic, complemented
41#88807C2211yescharacteristic, complemented
42#88806C2211yescharacteristic, complemented
43#88804C2211yescharacteristic
44#88804C2211yescharacteristic
45#88804C2211yescharacteristic
46#88804C2211yescharacteristic
47#88804C2211yescharacteristic
48#88804C2211yescharacteristic
49#88804C2211yescharacteristic, complemented
50#88804C2211yescharacteristic, complemented
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×C4×D4—31no—
54#64148—31no—
55#64146—31no—
56#64139—31no—
57#64138—31no—
58C4×#638—31no—
59C2×#3752—31no—
60#64107—31no—
61#64103—31no—
62#64094—31no—
63#64093—31no—
64#64091—31no—
65#64091—34no—
66#64091—64no—
67#64087D311yescharacteristic, complemented
68#64085—31no—
69#64084—31no—
70C3×#67⋊C4D314yescomplemented
71C3×#878—34no—
72#63981—34no—
73#63978—34no—
74C2×#3722—34no—
75#63952—34no—
76#63910—34no—
77#63909—34no—
78#63907—34no—
79#63897—34no—
80#63868—34no—
81#63864—34no—
82#63850—34no—
83#63848—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⋊D3)C2311yescharacteristic
91C22×C32×D3C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94#6312—22no—
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C4⋊(C3⋊(C3⋊D3))—41no—
97C4⋊(C3⋊(C3⋊D3))—41no—
98C2×C3×C3⋊Dic3—41no—
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C3×#634—41no—
104C32×#67—22no—
105C2×C32×Dic3—41no—
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C2×C32×Dic3C2311yescharacteristic
109C32×C4×D3—41no—
110#6291—41no—
111#6291—41no—
112#6291—41no—
113#6289—41no—
114#5644—91no—
115#5560—94no—
116C23×C3⋊D3—31no—
117C23×C3⋊D3—34no—
118C23×C3⋊D3—64no—
119C2×C32×D4—31no—
120C22×C32×C4—31no—
121C22×C32×C4—31no—
122C2×#638—31no—
123C2×#638—34no—
124C2×#638—31no—
125C2×#638—31no—
126C2×#638—31no—
127C2×#638—64no—
128C22×C3⋊Dic3C2×D311yescharacteristic
129C2×C4⋊(C3⋊D3)—31no—
130C2×C4⋊(C3⋊D3)—31no—
131C2×C4⋊(C3⋊D3)—34no—
132C2×C4⋊(C3⋊D3)—34no—
133C2×C4⋊(C3⋊D3)—64no—
134C2×C4⋊(C3⋊D3)—64no—
135C2×C4×C3⋊D3—31no—
136C2×#634C2×D311yescharacteristic, complemented
137C2×C3×#67C2×D314yes—
138C22×C3×Dic3—34no—
139C22×C3×Dic3C2×D314yes—
140C2×C3×C4×D3C2×D314yescomplemented
141C2×C3×Dic6—34no—
142C2×#626—34no—
143C2×#626—34no—
144C2×#626—34no—
145C2×#624—34no—
146C32×C4⋊C4—31no—
147C32×C22⋊C4—24no—
148C32×C22⋊C4—31no—
149C32×C22⋊C4C2×D314yes—
150C32×C22⋊C4C2×D311yescharacteristic
151C32×C42—31no—
152#3757—31no—
153#3757C2×D311yescharacteristic
154#3752—31no—
155#3752—31no—
156#3752—34no—
157#3752—34no—
158#3752—31no—
159#3752—31no—
160#3752—31no—
161#3752—31no—
162#3752—31no—
163#3752—31no—
164#3752—31no—
165#3752—31no—
166#3752—64no—
167#3752—64no—
168C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
169#3750—31no—
170#3750—31no—
171#3750C2×D311yescharacteristic, complemented
172#3750C2×D311yescharacteristic, complemented
173C4×C3⋊Dic3—31no—
174C3×#217—34no—
175C3×(C2×D3)⋊C4C2×D314yescomplemented
176C3×C4⋊Dic3—34no—
177C3×Dic3⋊C4—34no—
178C3×Dic3⋊C4—34no—
179C3×Dic3⋊C4C2×D314yescomplemented
180C3×C4×Dic3C2×D314yescomplemented
181#3724—34no—
182Dic3⋊Dic3—34no—
183#3722—34no—
184#3722—34no—
185#3722—34no—
186#3722—34no—
187#3722—34no—
188#3722—34no—
189#3722—34no—
190#3722—34no—
191(C2×D3)⋊Dic3—34no—
192Dic32—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)—21no—
204C2×C3⋊(C3⋊D3)—21no—
205C2×C3⋊(C3⋊D3)—21no—
206C2×C3⋊(C3⋊D3)—44no—
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×C22⋊Q8—91no—
221C3×C4×D4—34no—
222#947—91no—
223#947—91no—
224#939—94no—
225#937—94no—
226#930—94no—
227#930—91no—
228#929—94no—
229C4×#67—94no—
230C2×(C2×D3)⋊C4—94no—
231C2×(C2×D3)⋊C4—91no—
232#898—94no—
233#898—91no—
234#898—91no—
235#895—91no—
236#895—91no—
237#894—94no—
238#894—91no—
239#894—91no—
240#885—94no—
241#884—94no—
242#882—91no—
243#882—94no—
244#882—91no—
245#882—184no—
246#67⋊C4—91no—
247#67⋊C4C3⋊D311yescharacteristic, complemented
248#878—34no—
249#876—94no—
250#875—94no—
251C23×C32—24no—
252C23×C32—31no—
253C23×C32C22×D314yes—
254C23×C32C22×D311yescharacteristic
255C22×C3⋊D3—31no—
256C22×C3⋊D3—31no—
257C22×C3⋊D3—31no—
258C22×C3⋊D3—34no—
259C22×C3⋊D3—34no—
260C22×C3⋊D3—34no—
261C22×C3⋊D3—64no—
262C22×C3⋊D3—64no—
263C22×C3⋊D3—64no—
264C22×C3⋊D3—62no—
265C22×C3⋊D3—68no—
266C22×C3⋊D3—128no—
267C22×C3⋊D3—121no—
268C22×C3⋊D3—121no—
269C22×C3⋊D3—124no—
270C22×C3⋊D3—124no—
271C22×C3⋊D3—128no—
272C22×C3⋊D3—128no—
273C22×C3×D3C22×D314yes—
274C32×D4—62no—
275C2×C32×C4—24no—
276C2×C32×C4—24no—
277C2×C32×C4—31no—
278C2×C32×C4—31no—
279C2×C32×C4—31no—
280C2×C32×C4—121no—
281C2×C32×C4—121no—
282C2×C32×C4C22×D314yes—
283C2×C32×C4C22×D314yes—
284C2×C32×C4C22×D311yescharacteristic
285C2×C32×C4C22×D311yescharacteristic
286#638—62no—
287#638—68no—
288#638—128no—
289#638—121no—
290#638—121no—
291#638—121no—
292C2×C3⋊Dic3—31no—
293C2×C3⋊Dic3—34no—
294C2×C3⋊Dic3—41no—
295C2×C3⋊Dic3—64no—
296C2×C3⋊Dic3C22×D311yescharacteristic
297C2×C3⋊Dic3C22×D311yescharacteristic
298C2×C3⋊Dic3C22×D311yescharacteristic
299C2×C3⋊Dic3C22×D311yescharacteristic
300C4⋊(C3⋊D3)—121no—
301C4⋊(C3⋊D3)—121no—
302C4⋊(C3⋊D3)—124no—
303C4⋊(C3⋊D3)—124no—
304C4⋊(C3⋊D3)—128no—
305C4⋊(C3⋊D3)—128no—
306C4×C3⋊D3—121no—
307#634—41no—
308C3×#67—28no—
309C2×C3×Dic3—34no—
310C2×C3×Dic3—34no—
311C2×C3×Dic3—34no—
312C2×C3×Dic3—34no—
313C2×C3×Dic3—44no—
314C2×C3×Dic3—124no—
315C2×C3×Dic3C22×D314yes—
316C2×C3×Dic3C22×D314yes—
317C2×C3×Dic3C22×D314yes—
318C3×C4×D3—44no—
319C3×Dic6—124no—
320#626—124no—
321#626—124no—
322#626—124no—
323#624—124no—
324#538—271noSylow
325C2×C33—22no—
326C2×C33C2×#4111yescharacteristic
327C2×C33H(5,𝔽2)11yescharacteristic
328C2×C33H(5,𝔽2)11yescharacteristic
329C3⋊(C3⋊D3)—41no—
330C3⋊(C3⋊D3)—41no—
331C3⋊(C3⋊D3)—41no—
332C32×D3—41no—
333C23×D3—94no—
334C23×D3—91no—
335C23×D3—184no—
336C2×C3×Q8—91no—
337C2×C3×D4—34no—
338C22×C3×C4—34no—
339C22×C3×C4—34no—
340C22×C3×C4—91no—
341C2×#67—94no—
342C2×#67—94no—
343C2×#67—94no—
344C2×#67—94no—
345C2×#67—91no—
346C2×#67—184no—
347C2×#67C2×C3⋊D311yescharacteristic
348C22×Dic3—34no—
349C22×Dic3C2×C3⋊D311yescharacteristic
350C2×D12—91no—
351C2×D12—91no—
352C2×D12—91no—
353C2×D12—94no—
354C2×D12—94no—
355C2×D12—91no—
356C2×D12—91no—
357C2×D12—184no—
358C2×D12—184no—
359C2×C4×D3—94no—
360C2×C4×D3—91no—
361C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
362C2×Dic6—34no—
363C3×C4⋊C4—34no—
364C3×C4⋊C4—91no—
365C3×C4⋊C4—91no—
366C3×C4⋊C4—91no—
367C3×C22⋊C4—24no—
368C3×C22⋊C4—34no—
369C3×C22⋊C4—91no—
370C3×C22⋊C4D3214yes—
371C3×C22⋊C4C2×C3⋊D311yescharacteristic
372C3×C42—34no—
373#217—34no—
374#217—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—94no—
380(C2×D3)⋊C4—94no—
381(C2×D3)⋊C4—94no—
382(C2×D3)⋊C4—94no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—94no—
385(C2×D3)⋊C4—94no—
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—91no—
393(C2×D3)⋊C4—91no—
394(C2×D3)⋊C4—91no—
395(C2×D3)⋊C4—91no—
396(C2×D3)⋊C4—184no—
397(C2×D3)⋊C4—184no—
398(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
399C4⋊Dic3—34no—
400C4⋊Dic3—91no—
401Dic3⋊C4—34no—
402Dic3⋊C4—34no—
403Dic3⋊C4—94no—
404Dic3⋊C4—94no—
405Dic3⋊C4—91no—
406Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
407C4×Dic3—94no—
408C4×Dic3—91no—
409C4×Dic3C2×C3⋊D311yescharacteristic, complemented
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—24no—
413C22×C32—28no—
414C22×C32—24no—
415C22×C32—24no—
416C22×C32—44no—
417C22×C32—44no—
418C22×C32—61no—
419C22×C32—61no—
420C22×C32—61no—
421C22×C32#23518yes—
422C22×C32#23912yes—
423C22×C32C23×D314yes—
424C22×C32C23×D311yescharacteristic
425C2×C3⋊D3—68no—
426C2×C3⋊D3—68no—
427C2×C3⋊D3—61no—
428C2×C3⋊D3—64no—
429C2×C3⋊D3—61no—
430C2×C3⋊D3—61no—
431C2×C3⋊D3—61no—
432C2×C3⋊D3—61no—
433C2×C3⋊D3—61no—
434C2×C3⋊D3—61no—
435C2×C3⋊D3—64no—
436C2×C3⋊D3—61no—
437C2×C3⋊D3—61no—
438C2×C3⋊D3—64no—
439C2×C3⋊D3—64no—
440C2×C3⋊D3—64no—
441C2×C3⋊D3—64no—
442C2×C3⋊D3—64no—
443C2×C3⋊D3—64no—
444C2×C3⋊D3—64no—
445C2×C3⋊D3—124no—
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—124no—
453C2×C3⋊D3—1216no—
454C2×C3⋊D3—1232no—
455C2×C3×D3—24no—
456C2×C3×D3—24no—
457C2×C3×D3—24no—
458C32×C4—21no—
459C32×C4—21no—
460C32×C4—24no—
461C32×C4—24no—
462C32×C4—44no—
463C32×C4—44no—
464C32×C4—61no—
465C32×C4—61no—
466C32×C4—61no—
467C3⋊Dic3—21no—
468C3⋊Dic3—21no—
469C3⋊Dic3—21no—
470C3⋊Dic3—21no—
471C3⋊Dic3—61no—
472C3⋊Dic3—64no—
473C3⋊Dic3—124no—
474C3×Dic3—24no—
475C3×Dic3—24no—
476C3×Dic3—24no—
477C3×Dic3—64no—
478C3×Dic3—64no—
479C3×Dic3—64no—
480C3×Dic3—64no—
481#126—271no—
482#126—271no—
483#124—271no—
484#124—271no—
485#123—271no—
486#123—271no—
487C22⋊Q8—91no—
488#121—271no—
489#121—271no—
490#121—271no—
491#120—271no—
492#120—271no—
493C4×D4—31no—
494C4×D4—271no—
495C2×C22⋊C4—271no—
496C33#53811yescharacteristic, complemented, Sylow
497C23×C3—24no—
498C23×C3—34no—
499C23×C3C2×D3214yes—
500C23×C3C22×C3⋊D311yescharacteristic
501C22×D3—94no—
502C22×D3—94no—
503C22×D3—94no—
504C22×D3—91no—
505C22×D3—91no—
506C22×D3—91no—
507C22×D3—184no—
508C22×D3—184no—
509C22×D3—184no—
510C22×D3—188no—
511C22×D3—182no—
512C22×D3—368no—
513C22×D3—364no—
514C22×D3—364no—
515C22×D3—361no—
516C22×D3—361no—
517C22×D3—368no—
518C22×D3—368no—
519C22×D3C22×C3⋊D311yescharacteristic
520C3×Q8—361no—
521C3×D4—68no—
522C2×C3×C4—24no—
523C2×C3×C4—24no—
524C2×C3×C4—34no—
525C2×C3×C4—34no—
526C2×C3×C4—34no—
527C2×C3×C4—91no—
528C2×C3×C4—91no—
529C2×C3×C4—91no—
530C2×C3×C4—91no—
531C2×C3×C4—124no—
532C2×C3×C4—124no—
533C2×C3×C4—361no—
534C2×C3×C4C2×D3214yes—
535C2×C3×C4C2×D3214yes—
536C2×C3×C4C22×C3⋊D311yescharacteristic
537C2×C3×C4C22×C3⋊D311yescharacteristic
538#67—22no—
539#67—188no—
540#67—182no—
541#67—368no—
542#67—364no—
543#67—364no—
544#67—364no—
545C2×Dic3—34no—
546C2×Dic3—34no—
547C2×Dic3—34no—
548C2×Dic3—34no—
549C2×Dic3—41no—
550C2×Dic3—94no—
551C2×Dic3—91no—
552C2×Dic3—124no—
553C2×Dic3—184no—
554C2×Dic3C22×C3⋊D311yescharacteristic
555C2×Dic3C22×C3⋊D311yescharacteristic
556C2×Dic3C22×C3⋊D311yescharacteristic
557D12—364no—
558D12—364no—
559D12—361no—
560D12—361no—
561D12—368no—
562D12—368no—
563D12—361no—
564D12—361no—
565D12—361no—
566C4×D3—41no—
567C4×D3—361no—
568C4×D3—364no—
569Dic6—124no—
570C2×C32—22no—
571C2×C32—24no—
572C2×C32—24no—
573C2×C32—24no—
574C2×C32—28no—
575C2×C32—48no—
576C2×C32—121no—
577C2×C32C2×#23514yes—
578C2×C32#100414yes—
579C2×C32#100411yescharacteristic
580C2×C32C2×#23911yescharacteristic
581C2×C32#100914yes—
582C2×C32#100911yescharacteristic
583C3⋊D3—128no—
584C3⋊D3—128no—
585C3⋊D3—121no—
586C3⋊D3—121no—
587C3⋊D3—121no—
588C3⋊D3—124no—
589C3⋊D3—124no—
590C3⋊D3—124no—
591C3⋊D3—244no—
592C3×D3—44no—
593C24—271no—
594C2×Q8—91no—
595C2×D4—31no—
596C2×D4—271no—
597C2×D4—271no—
598C2×D4—271no—
599C2×D4—271no—
600C2×D4—271no—
601C2×D4—271no—
602C22×C4—31no—
603C22×C4—31no—
604C22×C4—91no—
605C22×C4—271no—
606C4⋊C4—31no—
607C4⋊C4—91no—
608C4⋊C4—91no—
609C4⋊C4—91no—
610C4⋊C4—271no—
611C4⋊C4—271no—
612C22⋊C4—31no—
613C22⋊C4—91no—
614C22⋊C4—271no—
615C22⋊C4—271no—
616C22⋊C4—271no—
617C22⋊C4—271no—
618C22⋊C4—271no—
619C22⋊C4—271no—
620C22⋊C4—271no—
621C22⋊C4—271no—
622C22⋊C4—271no—
623C22⋊C4—271no—
624C22⋊C4—271no—
625C22⋊C4D3×C3⋊D311yescharacteristic
626C42—31no—
627C42—271no—
628C22×C3—24no—
629C22×C3—24no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—24no—
633C22×C3—28no—
634C22×C3—44no—
635C22×C3—44no—
636C22×C3—64no—
637C22×C3—64no—
638C22×C3—64no—
639C22×C3#379918yes—
640C22×C3#382812yes—
641C22×C3C22×D3214yes—
642C22×C3C23×C3⋊D311yescharacteristic
643C2×D3—21no—
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—188no—
647C2×D3—188no—
648C2×D3—184no—
649C2×D3—184no—
650C2×D3—184no—
651C2×D3—184no—
652C2×D3—184no—
653C2×D3—184no—
654C2×D3—184no—
655C2×D3—184no—
656C2×D3—184no—
657C2×D3—181no—
658C2×D3—181no—
659C2×D3—181no—
660C2×D3—181no—
661C2×D3—181no—
662C2×D3—181no—
663C2×D3—181no—
664C2×D3—181no—
665C2×D3—181no—
666C2×D3—364no—
667C2×D3—364no—
668C2×D3—364no—
669C2×D3—364no—
670C2×D3—364no—
671C2×D3—364no—
672C2×D3—364no—
673C2×D3—364no—
674C2×D3—3616no—
675C2×D3—3632no—
676C3×C4—24no—
677C3×C4—24no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—44no—
681C3×C4—44no—
682C3×C4—64no—
683C3×C4—64no—
684C3×C4—64no—
685C3×C4—181no—
686C3×C4—181no—
687C3×C4—181no—
688C3×C4—181no—
689Dic3—21no—
690Dic3—21no—
691Dic3—21no—
692Dic3—64no—
693Dic3—64no—
694Dic3—64no—
695Dic3—64no—
696Dic3—184no—
697Dic3—181no—
698Dic3—364no—
699C32—24no—
700C32#556014yescomplemented
701C32#564411yescharacteristic, complemented
702C23—31no—
703C23—271no—
704C23—271no—
705C23—271no—
706C23—542no—
707C23—1081no—
708C23—1081no—
709C23C2×D3×C3⋊D311yescharacteristic
710Q8—361no—
711D4—62no—
712D4—542no—
713D4—1081no—
714D4—1081no—
715D4—1081no—
716D4—1081no—
717D4—1081no—
718C2×C4—31no—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—91no—
722C2×C4—91no—
723C2×C4—91no—
724C2×C4—91no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—271no—
728C2×C4—361no—
729C2×C4—1081no—
730C2×C4C2×D3×C3⋊D311yescharacteristic
731C2×C4C2×D3×C3⋊D311yescharacteristic
732C2×C3—22no—
733C2×C3—28no—
734C2×C3—24no—
735C2×C3—24no—
736C2×C3—24no—
737C2×C3—48no—
738C2×C3—124no—
739C2×C3C2×#379914yes—
740C2×C3#6431414yes—
741C2×C3#6431414yes—
742C2×C3C2×#382811yescharacteristic
743C2×C3#6436111yescharacteristic
744C2×C3#6436611yescharacteristic
745D3—41no—
746D3—368no—
747D3—368no—
748D3—361no—
749D3—361no—
750D3—361no—
751D3—364no—
752D3—364no—
753D3—364no—
754D3—724no—
755C22—21no—
756C22—21no—
757C22—61no—
758C22—61no—
759C22—61no—
760C22—541no—
761C22—541no—
762C22—541no—
763C22—541no—
764C22—541no—
765C22—541no—
766C22—541no—
767C22—541no—
768C22—541no—
769C22—1084no—
770C22#8902212yes—
771C22C22×D3×C3⋊D311yescharacteristic
772C4—21no—
773C4—21no—
774C4—61no—
775C4—61no—
776C4—61no—
777C4—181no—
778C4—181no—
779C4—181no—
780C4—181no—
781C4—541no—
782C3—24no—
783C3#1059424314yescomplemented
784C3#1059603111yescharacteristic, complemented
785C2—22no—
786C2—121no—
787C2—1081no—
788C2—1081no—
789C2—1081no—
790C2C2×#8902211yescharacteristic
791C2#1172458811yescharacteristic
792C2#1172458911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊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. #11723923C2semidirect
2. C3×#64087C2semidirect
3. C32×#67⋊C4C2semidirect
4. #11723638C2semidirect
5. #11723635C2semidirect
6. #11723618C2semidirect
7. C2×#88804C2semidirect
8. #11723525C2semidirect
9. #11723521C2semidirect
10. #11723516C2semidirect
11. #11723498C2semidirect
12. #11723453C2semidirect
13. #11723441C2semidirect
14. #11723414C2semidirect
15. #11723403C2semidirect
23. C2×C3×#634C22semidirect
26. C2×C32×C4×D3C22semidirect
29. C2×#6291C22semidirect
30. C2×#6289C22semidirect
35. C3×C4⋊(C3⋊Dic3)C22semidirect
36. C3×#3750C22semidirect
37. C3×#3750C22semidirect
38. C32×(C2×D3)⋊C4C22semidirect
39. C32×Dic3⋊C4C22semidirect
40. C32×C4×Dic3C22semidirect
41. #88807C22semidirect
42. #88806C22semidirect
49. #88804C22semidirect
50. #88804C22semidirect
51. (C2×D3)⋊(C3⋊Dic3)C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
67. #64087D3semidirect
70. C3×#67⋊C4D3semidirect
136. C2×#634C2×D3semidirect
140. C2×C3×C4×D3C2×D3semidirect
168. C4⋊(C3⋊Dic3)C2×D3semidirect
171. #3750C2×D3semidirect
172. #3750C2×D3semidirect
175. C3×(C2×D3)⋊C4C2×D3semidirect
179. C3×Dic3⋊C4C2×D3semidirect
180. C3×C4×Dic3C2×D3semidirect
247. #67⋊C4C3⋊D3semidirect
361. C2×C4×D3C2×C3⋊D3semidirect
398. (C2×D3)⋊C4C2×C3⋊D3semidirect
406. Dic3⋊C4C2×C3⋊D3semidirect
409. C4×Dic3C2×C3⋊D3semidirect
496. C33#538semidirect
700. C32#5560semidirect
701. C32#5644semidirect
783. C3#10594243semidirect
784. C3#10596031semidirect

Maximal subgroups

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

subgroupindex
#117239232
C3×#640872
C32×#67⋊C42
#117236382
#117236352
#117236182
C2×#888042
#117235252
#117235212
#117235162
#117234982
#117234532
#117234412
#117234142
#117234032
#105960313
#105942433