Finite Group Databasebeta

← #13148447

Subgroups — #13148447

Order 1728.

844 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721730C211yesmaximal, characteristic, complemented
2C9×#886C211yesmaximal, characteristic, complemented
3C3×#63447C211yesmaximal, characteristic, complemented
4#11721292C211yesmaximal, characteristic, complemented
5#11721277C211yesmaximal, characteristic, complemented
6#11721262C211yesmaximal, characteristic, complemented
7#11721240C211yesmaximal, characteristic, complemented
8#11721051C211yesmaximal, characteristic, complemented
9#11721048C211yesmaximal, characteristic, complemented
10#11721035C211yesmaximal, characteristic, complemented
11#11720992C211yesmaximal, characteristic, complemented
12#11720963C211yesmaximal, characteristic, complemented
13#11720946C211yesmaximal, characteristic, complemented
14#11720942C211yesmaximal, characteristic, complemented
15#11720936C211yesmaximal, characteristic, complemented
16#10594307—31nomaximal
17#10589759—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×#6233C2211yescharacteristic, complemented
21C2×C4⋊(C3⋊D9)C2211yescharacteristic
22C2×C4×C3⋊D9C2211yescharacteristic
23C2×C9×#67C2211yescharacteristic
24C2×C3×#611C2211yescharacteristic
25C22×C9×Dic3C2211yescharacteristic, complemented
26C2×C3×Dic18C2211yescharacteristic, complemented
27C2×#6195C2211yescharacteristic
28C2×#6192C2211yescharacteristic
29C2×(C3⋊D9)⋊C4C2211yescharacteristic
30C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
31C3×C9×C22⋊C4C2211yescharacteristic, complemented
32#88536C2211yescharacteristic, complemented
33#88534C2211yescharacteristic, complemented
34C3×#3676C2211yescharacteristic, complemented
35C9×(C2×D3)⋊C4C2211yescharacteristic
36C9×(C2×D3)⋊C4C2211yescharacteristic
37C3×(C2×D9)⋊C4C2211yescharacteristic
38C3×(C2×D9)⋊C4C2211yescharacteristic
39C9×C4⋊Dic3C2211yescharacteristic, complemented
40C9×C4⋊Dic3C2211yescharacteristic, complemented
41C3×C4×Dic9C2211yescharacteristic, complemented
42(C2×D3)⋊Dic9C2211yescharacteristic
43(C2×D3)⋊Dic9C2211yescharacteristic
44#88445C2211yescharacteristic
45#88445C2211yescharacteristic
46#88445C2211yescharacteristic, complemented
47(C2×D9)⋊Dic3C2211yescharacteristic
48(C2×D9)⋊Dic3C2211yescharacteristic
49Dic3⋊Dic9C2211yescharacteristic, complemented
50Dic3⋊Dic9C2211yescharacteristic, complemented
51#88442C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64093—31no—
54C3×#886D311yescharacteristic
55C3×#885—31no—
56#63983—31no—
57#63978—31no—
58#63958—31no—
59#63952—31no—
60#63923—31no—
61#63921—31no—
62#63907—31no—
63#63894—31no—
64#63871—31no—
65#63859—31no—
66#63858—31no—
67#63854—31no—
68C9×#123—31no—
69#63500—31no—
70#63499—31no—
71#63492—31no—
72C4×#611—31no—
73#63460—31no—
74#63459—31no—
75#63456—31no—
76#63455—31no—
77#63447—31no—
78#63447D311yescharacteristic, complemented
79#63446—31no—
80#63446—61no—
81#63444—31no—
82C22⋊C4×D9—31no—
83#63441—31no—
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C22×C3⋊D9C2311yescharacteristic
87C22×D3×C9C2311yescharacteristic
88C22×C3×D9C2311yescharacteristic
89C2×D3×D9—22no—
90C2×D3×D9—41no—
91C2×D3×D9—41no—
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94#6233—22no—
95#6233—41no—
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C4⋊(C3⋊D9)—22no—
99C4×C3⋊D9—41no—
100C9×#67—41no—
101C3×#611—41no—
102C2×C9×Dic3—41no—
103C2×C9×Dic3C2311yescharacteristic
104C2×C9×Dic3C2311yescharacteristic
105C2×C9×Dic3C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C3×Dic18—41no—
110#6195—41no—
111#6192—41no—
112(C3⋊D9)⋊C4—41no—
113(C3⋊D9)⋊C4—41no—
114#5678—91no—
115#5657—91no—
116C22×D32—31no—
117C2×#638—31no—
118C2×#638—31no—
119C2×C4⋊(C3⋊D3)—31no—
120C2×C4×C3⋊D3—31no—
121C2×C3×#67—31no—
122C2×C3×#67C2×D311yescharacteristic
123C22×C3×Dic3C2×D311yescharacteristic
124C2×C3×Dic6—31no—
125C2×#626—31no—
126C2×#626—31no—
127C2×#624—31no—
128C2×#624—31no—
129C23×D9—31no—
130C32×C22⋊C4C2×D311yescharacteristic
131#3752—31no—
132#3750—31no—
133C3×#217—31no—
134C3×(C2×D3)⋊C4—31no—
135C3×(C2×D3)⋊C4—31no—
136C3×(C2×D3)⋊C4C2×D311yescharacteristic
137C3×(C2×D3)⋊C4C2×D311yescharacteristic
138C3×C4⋊Dic3C2×D311yescharacteristic
139C3×C4⋊Dic3C2×D311yescharacteristic
140C3×C4×Dic3—31no—
141#3724—31no—
142Dic3⋊Dic3—31no—
143Dic3⋊Dic3—31no—
144#3722—31no—
145#3722—31no—
146#3722—31no—
147(C2×D3)⋊Dic3—31no—
148(C2×D3)⋊Dic3—31no—
149(C2×D3)⋊Dic3—31no—
150(C2×D3)⋊Dic3—31no—
151Dic32—31no—
152C2×D4×C9—31no—
153C22×C4×C9—31no—
154C2×#611—31no—
155C2×#611—31no—
156C2×#611—31no—
157C2×#611—61no—
158C2×#611—61no—
159C2×#611C2×D311yescharacteristic
160C2×D36—31no—
161C2×D36—31no—
162C2×D36—61no—
163C2×C4×D9—31no—
164C2×C4×D9—31no—
165C2×C4×D9—31no—
166C2×C4×D9—61no—
167C2×Dic18C2×D311yescharacteristic, complemented
168C9×C4⋊C4—31no—
169C9×C4⋊C4—31no—
170C9×C22⋊C4—21no—
171C9×C22⋊C4—31no—
172C9×C22⋊C4—31no—
173C9×C22⋊C4C2×D311yescharacteristic, complemented
174#3676—31no—
175#3676—31no—
176#3676C2×D311yescharacteristic, complemented
177(C2×D9)⋊C4—31no—
178(C2×D9)⋊C4—31no—
179(C2×D9)⋊C4—31no—
180(C2×D9)⋊C4—31no—
181(C2×D9)⋊C4—31no—
182(C2×D9)⋊C4—31no—
183(C2×D9)⋊C4—61no—
184(C2×D9)⋊C4C2×D311yescharacteristic
185(C2×D9)⋊C4C2×D311yescharacteristic
186C4⋊Dic9—31no—
187C4⋊Dic9—31no—
188Dic9⋊C4—31no—
189Dic9⋊C4—31no—
190Dic9⋊C4—61no—
191C4×Dic9—31no—
192C4×Dic9C2×D311yescharacteristic, complemented
193C22×C3×C9—21no—
194C22×C3×C9—21no—
195C22×C3×C9—21no—
196C22×C3×C9C2411yescharacteristic
197C2×C3⋊D9—21no—
198C2×C3⋊D9—21no—
199C2×C3⋊D9—21no—
200C2×C3⋊D9—21no—
201C2×C3⋊D9—21no—
202C2×C3⋊D9#4112yes—
203C2×D3×C9—21no—
204C2×D3×C9—21no—
205C2×D3×C9—21no—
206C2×C3×D9—21no—
207C2×C3×D9—21no—
208C2×C3×D9—21no—
209D3×D9—44no—
210C3×C4×C9—21no—
211C3×C4×C9—21no—
212C3⋊Dic9—21no—
213C3⋊Dic9—21no—
214C9×Dic3—21no—
215C9×Dic3—21no—
216C9×Dic3—21no—
217C3×Dic9—21no—
218C3×Dic9—21no—
219C3×Dic9—21no—
220C3×#124—91no—
221C3×#123—31no—
222#947—91no—
223#946—91no—
224#939—91no—
225#938—91no—
226#937—91no—
227#937—91no—
228#930—91no—
229C4×#67—91no—
230#898—91no—
231#897—91no—
232#894—91no—
233#893—91no—
234#886D911yescharacteristic, complemented
235#885—31no—
236#885—91no—
237#884—91no—
238#884—91no—
239#884—91no—
240#884—181no—
241#883—91no—
242#882—91no—
243#882—91no—
244#67⋊C4—91no—
245D3×C22⋊C4—91no—
246D3×C22⋊C4—91no—
247#879—91no—
248#879—91no—
249#876—91no—
250C4×D12—91no—
251C23×C32C22×D311yescharacteristic
252C22×C3⋊D3—31no—
253C22×C3⋊D3—31no—
254C22×C3×D3—31no—
255C22×C3×D3C22×D311yescharacteristic
256C2×D32—62no—
257C2×D32—121no—
258C2×D32—121no—
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261#638—62no—
262#638—121no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265C4⋊(C3⋊D3)—62no—
266C4×C3⋊D3—121no—
267C3×#67—41no—
268C3×#67—121no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—41no—
273C2×C3×Dic3C22×D311yescharacteristic
274C2×C3×Dic3C22×D311yescharacteristic
275C2×C3×Dic3C22×D311yescharacteristic
276C3×Dic6—121no—
277#626—121no—
278#626—121no—
279#624—121no—
280#624—121no—
281C23×C9—21no—
282C23×C9—31no—
283C23×C9C22×D311yescharacteristic
284C22×D9—31no—
285C22×D9—31no—
286C22×D9—61no—
287C22×D9—61no—
288C22×D9—62no—
289C22×D9—121no—
290C22×D9—121no—
291C22×D9C22×D311yescharacteristic
292D4×C9—121no—
293C2×C4×C9—21no—
294C2×C4×C9—21no—
295C2×C4×C9—31no—
296C2×C4×C9—31no—
297C2×C4×C9—31no—
298C2×C4×C9—121no—
299C2×C4×C9C22×D311yescharacteristic
300C2×C4×C9C22×D311yescharacteristic
301#611—41no—
302#611—62no—
303#611—122no—
304#611—121no—
305#611—121no—
306#611—122no—
307C2×Dic9—31no—
308C2×Dic9—31no—
309C2×Dic9—61no—
310C2×Dic9—61no—
311C2×Dic9C22×D311yescharacteristic
312C2×Dic9C22×D311yescharacteristic
313C2×Dic9C22×D311yescharacteristic
314D36—62no—
315D36—122no—
316D36—121no—
317C4×D9—121no—
318C4×D9—121no—
319C4×D9—121no—
320C4×D9—122no—
321Dic18—41no—
322#538—271noSylow
323C2×C3×C9—41no—
324C2×C3×C9C2×#4111yescharacteristic
325C2×C3×C9H(5,𝔽2)11yescharacteristic
326C2×C3×C9H(5,𝔽2)11yescharacteristic
327C3⋊D9—22no—
328C3⋊D9—41no—
329D3×C9—41no—
330C3×D9—41no—
331C23×D3—91no—
332C23×D3—91no—
333C2×C3×Q8—91no—
334C2×C3×D4—31no—
335C2×C3×D4—91no—
336C22×C3×C4—31no—
337C2×#67—31no—
338C2×#67—91no—
339C2×#67—91no—
340C2×#67—91no—
341C2×#67—91no—
342C2×#67—91no—
343C2×#67—91no—
344C2×#67—181no—
345C2×#67—181no—
346C2×#67C2×D911yescharacteristic
347C22×Dic3C2×D911yescharacteristic, complemented
348C2×D12—91no—
349C2×D12—91no—
350C2×D12—91no—
351C2×D12—91no—
352C2×D12—181no—
353C2×C4×D3—91no—
354C2×C4×D3—91no—
355C2×C4×D3—91no—
356C2×C4×D3—91no—
357C2×C4×D3—91no—
358C2×C4×D3—91no—
359C2×C4×D3—181no—
360C2×Dic6—31no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—31no—
365C3×C22⋊C4—31no—
366C3×C22⋊C4—91no—
367C3×C22⋊C4—91no—
368C3×C22⋊C4—91no—
369C3×C22⋊C4C2×D911yescharacteristic, complemented
370C3×C22⋊C4D3211yescharacteristic
371C3×C42—91no—
372#217—31no—
373#217—91no—
374#217—91no—
375#217—91no—
376#217—91no—
377(C2×D3)⋊C4—31no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—91no—
380(C2×D3)⋊C4—91no—
381(C2×D3)⋊C4—91no—
382(C2×D3)⋊C4—91no—
383(C2×D3)⋊C4—91no—
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—181no—
392(C2×D3)⋊C4C2×D911yescharacteristic
393(C2×D3)⋊C4C2×D911yescharacteristic
394C4⋊Dic3—91no—
395C4⋊Dic3—91no—
396C4⋊Dic3C2×D911yescharacteristic, complemented
397C4⋊Dic3C2×D911yescharacteristic, complemented
398Dic3⋊C4—91no—
399Dic3⋊C4—91no—
400Dic3⋊C4—91no—
401Dic3⋊C4—91no—
402Dic3⋊C4—91no—
403Dic3⋊C4—91no—
404Dic3⋊C4—181no—
405C4×Dic3—31no—
406C4×Dic3—91no—
407C4×Dic3—91no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32C23×D311yescharacteristic
412C2×C3⋊D3—32no—
413C2×C3⋊D3—61no—
414C2×C3⋊D3—61no—
415C2×C3⋊D3—61no—
416C2×C3⋊D3—61no—
417C2×C3⋊D3—61no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—61no—
422C2×C3×D3—61no—
423C2×C3×D3—61no—
424D32—124no—
425C32×C4—21no—
426C32×C4—21no—
427C3⋊Dic3—61no—
428C3⋊Dic3—61no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—61no—
433C3×Dic3—61no—
434C3×Dic3—61no—
435C22×C9—21no—
436C22×C9—21no—
437C22×C9—21no—
438C22×C9—21no—
439C22×C9—41no—
440C22×C9—41no—
441C22×C9—41no—
442C22×C9—61no—
443C22×C9—61no—
444C22×C9—61no—
445C22×C9C23×D311yescharacteristic
446C2×D9—21no—
447C2×D9—21no—
448C2×D9—21no—
449C2×D9—32no—
450C2×D9—62no—
451C2×D9—61no—
452C2×D9—61no—
453C2×D9—61no—
454C2×D9—61no—
455C2×D9—61no—
456C2×D9—121no—
457C2×D9—121no—
458C2×D9—121no—
459C2×D9—121no—
460C2×D9—121no—
461C2×D9—124no—
462C4×C9—21no—
463C4×C9—21no—
464C4×C9—41no—
465C4×C9—41no—
466C4×C9—61no—
467C4×C9—61no—
468C4×C9—61no—
469Dic9—21no—
470Dic9—21no—
471Dic9—21no—
472Dic9—62no—
473Dic9—61no—
474Dic9—61no—
475Dic9—121no—
476#126—271no—
477#126—271no—
478#124—91no—
479#124—271no—
480#123—31no—
481#123—271no—
482C22⋊Q8—271no—
483#121—271no—
484#121—271no—
485#121—271no—
486#120—271no—
487#120—271no—
488C4×D4—271no—
489C4×D4—271no—
490C2×C22⋊C4—271no—
491C3×C9#53811yescharacteristic, complemented, Sylow
492C23×C3—21no—
493C23×C3—31no—
494C23×C3—91no—
495C23×C3C22×D911yescharacteristic
496C23×C3C2×D3211yescharacteristic
497C22×D3—31no—
498C22×D3—91no—
499C22×D3—91no—
500C22×D3—91no—
501C22×D3—91no—
502C22×D3—181no—
503C22×D3—181no—
504C22×D3—182no—
505C22×D3—182no—
506C22×D3—361no—
507C22×D3—361no—
508C22×D3—361no—
509C22×D3—361no—
510C22×D3C22×D911yescharacteristic
511C3×Q8—361no—
512C3×D4—121no—
513C3×D4—361no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—91no—
520C2×C3×C4—91no—
521C2×C3×C4—91no—
522C2×C3×C4—121no—
523C2×C3×C4C22×D911yescharacteristic
524C2×C3×C4C22×D911yescharacteristic
525C2×C3×C4C2×D3211yescharacteristic
526C2×C3×C4C2×D3211yescharacteristic
527#67—41no—
528#67—121no—
529#67—182no—
530#67—182no—
531#67—362no—
532#67—361no—
533#67—361no—
534#67—361no—
535#67—361no—
536#67—362no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—41no—
541C2×Dic3—91no—
542C2×Dic3—91no—
543C2×Dic3—91no—
544C2×Dic3—91no—
545C2×Dic3—181no—
546C2×Dic3—181no—
547C2×Dic3C22×D911yescharacteristic
548C2×Dic3C22×D911yescharacteristic
549C2×Dic3C22×D911yescharacteristic
550D12—182no—
551D12—182no—
552D12—362no—
553D12—361no—
554D12—361no—
555C4×D3—361no—
556C4×D3—361no—
557C4×D3—361no—
558C4×D3—361no—
559C4×D3—361no—
560C4×D3—361no—
561C4×D3—362no—
562Dic6—121no—
563C2×C32—41no—
564C2×C32#100411yescharacteristic
565C2×C32D3×#4111yescharacteristic
566C2×C32#100911yescharacteristic
567C3⋊D3—62no—
568C3⋊D3—121no—
569C3×D3—41no—
570C3×D3—121no—
571C2×C9—21no—
572C2×C9—21no—
573C2×C9—21no—
574C2×C9—41no—
575C2×C9—81no—
576C2×C9—121no—
577C2×C9#100411yescharacteristic
578C2×C9D3×#4111yescharacteristic
579C2×C9#100911yescharacteristic
580D9—41no—
581D9—62no—
582D9—122no—
583D9—121no—
584D9—241no—
585C24—271no—
586C2×Q8—91no—
587C2×D4—31no—
588C2×D4—91no—
589C2×D4—271no—
590C2×D4—271no—
591C2×D4—271no—
592C2×D4—271no—
593C2×D4—271no—
594C22×C4—31no—
595C22×C4—271no—
596C22×C4—271no—
597C22×C4—271no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—271no—
601C4⋊C4—271no—
602C4⋊C4—271no—
603C4⋊C4—271no—
604C22⋊C4—31no—
605C22⋊C4—31no—
606C22⋊C4—91no—
607C22⋊C4—91no—
608C22⋊C4—91no—
609C22⋊C4—271no—
610C22⋊C4—271no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C22⋊C4—271no—
614C22⋊C4—271no—
615C22⋊C4—271no—
616C22⋊C4—271no—
617C22⋊C4D3×D911yescharacteristic, complemented
618C42—91no—
619C42—271no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—181no—
634C22×C3—181no—
635C22×C3—181no—
636C22×C3C23×D911yescharacteristic
637C22×C3C22×D3211yescharacteristic
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—61no—
644C2×D3—92no—
645C2×D3—92no—
646C2×D3—182no—
647C2×D3—181no—
648C2×D3—181no—
649C2×D3—181no—
650C2×D3—181no—
651C2×D3—181no—
652C2×D3—181no—
653C2×D3—181no—
654C2×D3—181no—
655C2×D3—181no—
656C2×D3—181no—
657C2×D3—361no—
658C2×D3—361no—
659C2×D3—361no—
660C2×D3—361no—
661C2×D3—361no—
662C2×D3—364no—
663C2×D3—364no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—61no—
671C3×C4—61no—
672C3×C4—61no—
673C3×C4—181no—
674C3×C4—181no—
675C3×C4—181no—
676Dic3—21no—
677Dic3—21no—
678Dic3—21no—
679Dic3—61no—
680Dic3—61no—
681Dic3—61no—
682Dic3—182no—
683Dic3—181no—
684Dic3—181no—
685Dic3—181no—
686Dic3—181no—
687Dic3—361no—
688C32#565711yescharacteristic
689C9—21no—
690C9#567811yescharacteristic, complemented
691C23—31no—
692C23—91no—
693C23—271no—
694C23—271no—
695C23—542no—
696C23—1081no—
697C23—1081no—
698C23C2×D3×D911yescharacteristic
699Q8—361no—
700D4—121no—
701D4—361no—
702D4—542no—
703D4—542no—
704D4—1081no—
705D4—1081no—
706D4—1081no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—31no—
710C2×C4—91no—
711C2×C4—91no—
712C2×C4—91no—
713C2×C4—121no—
714C2×C4—271no—
715C2×C4—271no—
716C2×C4—1081no—
717C2×C4—1081no—
718C2×C4—1081no—
719C2×C4C2×D3×D911yescharacteristic
720C2×C4C2×D3×D911yescharacteristic
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—41no—
725C2×C3—41no—
726C2×C3—81no—
727C2×C3—121no—
728C2×C3—361no—
729C2×C3#6371011yescharacteristic
730C2×C3#41×D911yescharacteristic
731C2×C3#6371511yescharacteristic
732C2×C3#6430711yescharacteristic
733C2×C3#6431211yescharacteristic
734C2×C3#6431411yescharacteristic
735D3—41no—
736D3—121no—
737D3—182no—
738D3—182no—
739D3—362no—
740D3—361no—
741D3—361no—
742D3—721no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—61no—
747C22—61no—
748C22—61no—
749C22—181no—
750C22—181no—
751C22—181no—
752C22—272no—
753C22—541no—
754C22—541no—
755C22—541no—
756C22—541no—
757C22—541no—
758C22—1084no—
759C22C22×D3×D911yescharacteristic
760C4—21no—
761C4—21no—
762C4—61no—
763C4—61no—
764C4—61no—
765C4—181no—
766C4—181no—
767C4—181no—
768C4—541no—
769C4—541no—
770C3—21no—
771C3#1058975911yescharacteristic, complemented
772C3#1059430711yescharacteristic
773C2—41no—
774C2—121no—
775C2—361no—
776C2—542no—
777C2—1081no—
778C2#1172247611yescharacteristic
779C2#1172249811yescharacteristic
780C2#1172250111yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#538
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #11721730C2semidirect
2. C9×#886C2semidirect
3. C3×#63447C2semidirect
4. #11721292C2semidirect
5. #11721277C2semidirect
6. #11721262C2semidirect
7. #11721240C2semidirect
8. #11721051C2semidirect
9. #11721048C2semidirect
10. #11721035C2semidirect
11. #11720992C2semidirect
12. #11720963C2semidirect
13. #11720946C2semidirect
14. #11720942C2semidirect
15. #11720936C2semidirect
20. C2×#6233C22semidirect
25. C22×C9×Dic3C22semidirect
26. C2×C3×Dic18C22semidirect
30. C2×(C3⋊D9)⋊C4C22semidirect
31. C3×C9×C22⋊C4C22semidirect
32. #88536C22semidirect
33. #88534C22semidirect
34. C3×#3676C22semidirect
39. C9×C4⋊Dic3C22semidirect
40. C9×C4⋊Dic3C22semidirect
41. C3×C4×Dic9C22semidirect
46. #88445C22semidirect
49. Dic3⋊Dic9C22semidirect
50. Dic3⋊Dic9C22semidirect
51. #88442C22semidirect
52. Dic3×Dic9C22semidirect
78. #63447D3semidirect
167. C2×Dic18C2×D3semidirect
173. C9×C22⋊C4C2×D3semidirect
176. #3676C2×D3semidirect
192. C4×Dic9C2×D3semidirect
234. #886D9semidirect
347. C22×Dic3C2×D9semidirect
369. C3×C22⋊C4C2×D9semidirect
396. C4⋊Dic3C2×D9semidirect
397. C4⋊Dic3C2×D9semidirect
491. C3×C9#538semidirect
617. C22⋊C4D3×D9semidirect
690. C9#5678semidirect
771. C3#10589759semidirect

Maximal subgroups

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

subgroupindex
#117217302
C9×#8862
C3×#634472
#117212922
#117212772
#117212622
#117212402
#117210512
#117210482
#117210352
#117209922
#117209632
#117209462
#117209422
#117209362
#105943073
#105897593