Finite Group Databasebeta

← #13148187

Subgroups — #13148187

Order 1728.

880 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#11721728C211yesmaximal, characteristic, complemented
2C3×#611⋊C4C211yesmaximal, characteristic, complemented
3C9×#878C211yesmaximal, characteristic, complemented
4#11721278C211yesmaximal, characteristic, complemented
5#11721277C211yesmaximal, characteristic, complemented
6C2×#88445C211yesmaximal, characteristic, complemented
7#11721241C211yesmaximal, characteristic, complemented
8#11721005C211yesmaximal, characteristic, complemented
9#11721004C211yesmaximal, characteristic, complemented
10#11721003C211yesmaximal, characteristic, complemented
11#11720997C211yesmaximal, characteristic, complemented
12#11720953C211yesmaximal, characteristic, complemented
13#11720938C211yesmaximal, characteristic, complemented
14#11720934C211yesmaximal, characteristic, complemented
15#11720920C211yesmaximal, characteristic, complemented
16#10594243—31nomaximal
17#10589746—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×C4⋊(C3⋊D9)C2211yescharacteristic
21C2×C4⋊(C3⋊D9)C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C22×C9×Dic3C2211yescharacteristic
24C22×C3×Dic9C2211yescharacteristic
25C2×C3×C4×D9C2211yescharacteristic, complemented
26C2×C9×Dic6C2211yescharacteristic, complemented
27C2×#6192C2211yescharacteristic
28C2×#6192C2211yescharacteristic
29C2×#6192C2211yescharacteristic, complemented
30C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
31C3×C9×C22⋊C4C2211yescharacteristic
32#88536C2211yescharacteristic
33#88536C2211yescharacteristic
34C9×#217C2211yescharacteristic
35C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
36C9×C4⋊Dic3C2211yescharacteristic, complemented
37C9×Dic3⋊C4C2211yescharacteristic, complemented
38C9×Dic3⋊C4C2211yescharacteristic, complemented
39C3×Dic9⋊C4C2211yescharacteristic, complemented
40C3×C4×Dic9C2211yescharacteristic, complemented
41#88445C2211yescharacteristic
42#88445C2211yescharacteristic
43#88445C2211yescharacteristic
44#88445C2211yescharacteristic
45#88445C2211yescharacteristic
46#88445C2211yescharacteristic
47#88445C2211yescharacteristic, complemented
48#88445C2211yescharacteristic, complemented
49(C2×D9)⋊Dic3C2211yescharacteristic, complemented
50Dic3⋊Dic9C2211yescharacteristic, complemented
51#88442C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64091—31no—
54C3×#67⋊C4—31no—
55C3×#878D311yescharacteristic
56#63981—31no—
57#63978—31no—
58C2×#3722—31no—
59#63952—31no—
60#63910—31no—
61#63909—31no—
62#63907—31no—
63#63897—31no—
64#63868—31no—
65#63864—31no—
66#63850—31no—
67#63848—31no—
68C9×C22⋊Q8—31no—
69#63509—31no—
70#63509—31no—
71#63492—31no—
72C2×(C2×D9)⋊C4—31no—
73#63460—31no—
74#63460—31no—
75#63457—31no—
76#63457—31no—
77#63456—31no—
78#63456—31no—
79#63444—31no—
80#63444—31no—
81#63444—61no—
82#611⋊C4—31no—
83#611⋊C4D311yescharacteristic, complemented
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9—22no—
86C22×C3⋊D9—41no—
87C22×C3⋊D9—41no—
88C22×C3⋊D9C2311yescharacteristic
89C22×C3⋊D9C2311yescharacteristic
90C22×C3⋊D9C2311yescharacteristic
91C22×C3×D9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94#6233—22no—
95C2×C3⋊Dic9C2311yescharacteristic
96C4⋊(C3⋊D9)—41no—
97C4⋊(C3⋊D9)—41no—
98C3×#611—22no—
99C2×C9×Dic3—41no—
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C3×Dic9—41no—
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108C3×C4×D9—41no—
109C9×Dic6—41no—
110#6192—41no—
111#6192—41no—
112#6192—41no—
113(C3⋊D9)⋊C4—41no—
114#5644—91no—
115#5560—91no—
116C23×C3⋊D3—31no—
117C2×#638—31no—
118C2×C4⋊(C3⋊D3)—31no—
119C2×C4⋊(C3⋊D3)—31no—
120C2×C3×#67—31no—
121C22×C3×Dic3—31no—
122C22×C3×Dic3C2×D311yescharacteristic
123C2×C3×C4×D3—31no—
124C2×C3×Dic6C2×D311yescharacteristic
125C2×#626—31no—
126C2×#626—31no—
127C2×#626—31no—
128C2×#624—31no—
129C23×D9—31no—
130C23×D9—61no—
131C32×C22⋊C4C2×D311yescharacteristic
132#3752—31no—
133#3752—31no—
134C3×#217C2×D311yescharacteristic
135C3×(C2×D3)⋊C4—31no—
136C3×C4⋊Dic3C2×D311yescharacteristic
137C3×Dic3⋊C4—31no—
138C3×Dic3⋊C4C2×D311yescharacteristic
139C3×Dic3⋊C4C2×D311yescharacteristic
140C3×C4×Dic3—31no—
141#3724—31no—
142Dic3⋊Dic3—31no—
143#3722—31no—
144#3722—31no—
145#3722—31no—
146#3722—31no—
147#3722—31no—
148#3722—31no—
149#3722—31no—
150#3722—31no—
151(C2×D3)⋊Dic3—31no—
152Dic32—31no—
153C2×Q8×C9—31no—
154C22×C4×C9—31no—
155C2×#611—31no—
156C2×#611—61no—
157C2×#611C2×D311yescharacteristic
158C22×Dic9C2×D311yescharacteristic
159C2×D36—31no—
160C2×D36—31no—
161C2×D36—31no—
162C2×D36—31no—
163C2×D36—31no—
164C2×D36—61no—
165C2×D36—61no—
166C2×C4×D9—31no—
167C2×C4×D9C2×D311yescharacteristic, complemented
168C9×C4⋊C4—31no—
169C9×C4⋊C4—31no—
170C9×C4⋊C4—31no—
171C9×C22⋊C4—21no—
172C9×C22⋊C4—31no—
173C9×C22⋊C4C2×D311yescharacteristic
174(C2×D9)⋊C4—31no—
175(C2×D9)⋊C4—31no—
176(C2×D9)⋊C4—31no—
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—31no—
184(C2×D9)⋊C4—31no—
185(C2×D9)⋊C4—61no—
186(C2×D9)⋊C4—61no—
187(C2×D9)⋊C4C2×D311yescharacteristic, complemented
188C4⋊Dic9—31no—
189Dic9⋊C4—31no—
190Dic9⋊C4C2×D311yescharacteristic, complemented
191C4×Dic9—31no—
192C4×Dic9C2×D311yescharacteristic, complemented
193C22×C3×C9—21no—
194C22×C3×C9—21no—
195C22×C3×C9#4112yes—
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—21no—
203C2×C3⋊D9—21no—
204C2×C3⋊D9—21no—
205C2×C3⋊D9—21no—
206C2×C3⋊D9—44no—
207C2×C3×D9—21no—
208C2×C3×D9—21no—
209C2×C3×D9—21no—
210C3×C4×C9—21no—
211C3×C4×C9—21no—
212C3⋊Dic9—21no—
213C9×Dic3—21no—
214C9×Dic3—21no—
215C9×Dic3—21no—
216C9×Dic3—21no—
217C3×Dic9—21no—
218C3×Dic9—21no—
219C3×Dic9—21no—
220C3×C22⋊Q8—31no—
221C3×C4×D4—91no—
222#947—91no—
223#947—91no—
224#939—91no—
225#937—91no—
226#930—91no—
227#930—91no—
228#929—91no—
229C4×#67—91no—
230C2×(C2×D3)⋊C4—91no—
231C2×(C2×D3)⋊C4—91no—
232#898—91no—
233#898—91no—
234#898—91no—
235#895—91no—
236#895—91no—
237#894—91no—
238#894—91no—
239#894—91no—
240#885—91no—
241#884—91no—
242#882—91no—
243#882—91no—
244#882—91no—
245#882—181no—
246#67⋊C4—31no—
247#67⋊C4—91no—
248#878D911yescharacteristic, complemented
249#876—91no—
250#875—91no—
251C23×C32C22×D311yescharacteristic
252C22×C3⋊D3—31no—
253C22×C3⋊D3—31no—
254C22×C3⋊D3—31no—
255C22×C3⋊D3—62no—
256C22×C3⋊D3—121no—
257C22×C3⋊D3—121no—
258C22×C3×D3—31no—
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261#638—62no—
262C2×C3⋊Dic3—31no—
263C4⋊(C3⋊D3)—121no—
264C4⋊(C3⋊D3)—121no—
265C3×#67—62no—
266C2×C3×Dic3—31no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—41no—
270C2×C3×Dic3—121no—
271C2×C3×Dic3C22×D311yescharacteristic
272C2×C3×Dic3C22×D311yescharacteristic
273C2×C3×Dic3C22×D311yescharacteristic
274C2×C3×Dic3C22×D311yescharacteristic
275C3×C4×D3—121no—
276C3×Dic6—41no—
277#626—121no—
278#626—121no—
279#626—121no—
280#624—121no—
281C23×C9—21no—
282C23×C9C22×D311yescharacteristic
283C22×D9—31no—
284C22×D9—31no—
285C22×D9—31no—
286C22×D9—61no—
287C22×D9—61no—
288C22×D9—61no—
289C22×D9—62no—
290C22×D9—122no—
291C22×D9—121no—
292C22×D9—121no—
293C22×D9—122no—
294C22×D9—122no—
295C22×D9C22×D311yescharacteristic
296Q8×C9—121no—
297C2×C4×C9—21no—
298C2×C4×C9—21no—
299C2×C4×C9—31no—
300C2×C4×C9—31no—
301C2×C4×C9—31no—
302C2×C4×C9—31no—
303C2×C4×C9—121no—
304C2×C4×C9C22×D311yescharacteristic
305C2×C4×C9C22×D311yescharacteristic
306#611—22no—
307#611—62no—
308#611—122no—
309C2×Dic9—31no—
310C2×Dic9—41no—
311C2×Dic9—61no—
312C2×Dic9C22×D311yescharacteristic
313C2×Dic9C22×D311yescharacteristic
314C2×Dic9C22×D311yescharacteristic
315D36—121no—
316D36—121no—
317D36—122no—
318D36—122no—
319D36—121no—
320D36—121no—
321D36—121no—
322C4×D9—41no—
323C4×D9—121no—
324#538—271noSylow
325C2×C3×C9—22no—
326C2×C3×C9C2×#4111yescharacteristic
327C2×C3×C9H(5,𝔽2)11yescharacteristic
328C2×C3×C9H(5,𝔽2)11yescharacteristic
329C3⋊D9—41no—
330C3⋊D9—41no—
331C3⋊D9—41no—
332C3×D9—41no—
333C23×D3—91no—
334C23×D3—91no—
335C23×D3—181no—
336C2×C3×Q8—31no—
337C2×C3×D4—91no—
338C22×C3×C4—31no—
339C22×C3×C4—91no—
340C22×C3×C4—91no—
341C2×#67—31no—
342C2×#67—91no—
343C2×#67—91no—
344C2×#67—91no—
345C2×#67—91no—
346C2×#67—91no—
347C2×#67—181no—
348C22×Dic3—31no—
349C22×Dic3C2×D911yescharacteristic
350C2×D12—91no—
351C2×D12—91no—
352C2×D12—91no—
353C2×D12—91no—
354C2×D12—91no—
355C2×D12—91no—
356C2×D12—91no—
357C2×D12—181no—
358C2×D12—181no—
359C2×C4×D3—31no—
360C2×C4×D3—91no—
361C2×C4×D3—91no—
362C2×Dic6C2×D911yescharacteristic, complemented
363C3×C4⋊C4—31no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—31no—
366C3×C4⋊C4—91no—
367C3×C22⋊C4—21no—
368C3×C22⋊C4—31no—
369C3×C22⋊C4—91no—
370C3×C22⋊C4C2×D911yescharacteristic
371C3×C22⋊C4D3211yescharacteristic
372C3×C42—91no—
373#217—91no—
374#217C2×D911yescharacteristic
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—91no—
377(C2×D3)⋊C4—91no—
378(C2×D3)⋊C4—91no—
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—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—91no—
397(C2×D3)⋊C4—181no—
398(C2×D3)⋊C4—181no—
399C4⋊Dic3—91no—
400C4⋊Dic3C2×D911yescharacteristic, complemented
401Dic3⋊C4—31no—
402Dic3⋊C4—91no—
403Dic3⋊C4—91no—
404Dic3⋊C4—91no—
405Dic3⋊C4C2×D911yescharacteristic, complemented
406Dic3⋊C4C2×D911yescharacteristic, complemented
407C4×Dic3—31no—
408C4×Dic3—91no—
409C4×Dic3—91no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32#23912yes—
413C22×C32C23×D311yescharacteristic
414C2×C3⋊D3—61no—
415C2×C3⋊D3—61no—
416C2×C3⋊D3—61no—
417C2×C3⋊D3—61no—
418C2×C3⋊D3—61no—
419C2×C3⋊D3—61no—
420C2×C3⋊D3—61no—
421C2×C3⋊D3—61no—
422C2×C3⋊D3—61no—
423C2×C3⋊D3—124no—
424C2×C3×D3—61no—
425C2×C3×D3—61no—
426C2×C3×D3—61no—
427C32×C4—21no—
428C32×C4—21no—
429C3⋊Dic3—61no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—61no—
435C3×Dic3—61no—
436C3×Dic3—61no—
437C22×C9—21no—
438C22×C9—21no—
439C22×C9—21no—
440C22×C9—22no—
441C22×C9—41no—
442C22×C9—41no—
443C22×C9#23512yes—
444C22×C9C23×D311yescharacteristic
445C2×D9—21no—
446C2×D9—21no—
447C2×D9—21no—
448C2×D9—62no—
449C2×D9—62no—
450C2×D9—61no—
451C2×D9—61no—
452C2×D9—61no—
453C2×D9—61no—
454C2×D9—61no—
455C2×D9—61no—
456C2×D9—61no—
457C2×D9—61no—
458C2×D9—61no—
459C2×D9—121no—
460C2×D9—121no—
461C2×D9—121no—
462C2×D9—121no—
463C2×D9—121no—
464C2×D9—121no—
465C2×D9—121no—
466C2×D9—124no—
467C2×D9—128no—
468C4×C9—21no—
469C4×C9—21no—
470C4×C9—41no—
471C4×C9—41no—
472C4×C9—61no—
473C4×C9—61no—
474C4×C9—61no—
475C4×C9—61no—
476Dic9—21no—
477Dic9—21no—
478Dic9—21no—
479Dic9—61no—
480Dic9—121no—
481#126—271no—
482#126—271no—
483#124—271no—
484#124—271no—
485#123—271no—
486#123—271no—
487C22⋊Q8—31no—
488#121—271no—
489#121—271no—
490#121—271no—
491#120—271no—
492#120—271no—
493C4×D4—91no—
494C4×D4—271no—
495C2×C22⋊C4—271no—
496C3×C9#53811yescharacteristic, complemented, Sylow
497C23×C3—21no—
498C23×C3—91no—
499C23×C3C22×D911yescharacteristic
500C23×C3C2×D3211yescharacteristic
501C22×D3—31no—
502C22×D3—91no—
503C22×D3—91no—
504C22×D3—91no—
505C22×D3—91no—
506C22×D3—91no—
507C22×D3—91no—
508C22×D3—181no—
509C22×D3—181no—
510C22×D3—181no—
511C22×D3—182no—
512C22×D3—182no—
513C22×D3—362no—
514C22×D3—361no—
515C22×D3—361no—
516C22×D3—361no—
517C22×D3—361no—
518C22×D3—362no—
519C22×D3—362no—
520C3×Q8—121no—
521C3×D4—182no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
527C2×C3×C4—31no—
528C2×C3×C4—91no—
529C2×C3×C4—91no—
530C2×C3×C4—91no—
531C2×C3×C4—121no—
532C2×C3×C4—361no—
533C2×C3×C4—361no—
534C2×C3×C4C22×D911yescharacteristic
535C2×C3×C4C22×D911yescharacteristic
536C2×C3×C4C2×D3211yescharacteristic
537C2×C3×C4C2×D3211yescharacteristic
538#67—62no—
539#67—182no—
540#67—182no—
541#67—362no—
542#67—361no—
543#67—361no—
544#67—361no—
545C2×Dic3—31no—
546C2×Dic3—31no—
547C2×Dic3—31no—
548C2×Dic3—41no—
549C2×Dic3—91no—
550C2×Dic3—91no—
551C2×Dic3—121no—
552C2×Dic3—181no—
553C2×Dic3C22×D911yescharacteristic
554C2×Dic3C22×D911yescharacteristic
555C2×Dic3C22×D911yescharacteristic
556C2×Dic3C22×D911yescharacteristic
557D12—361no—
558D12—361no—
559D12—361no—
560D12—361no—
561D12—362no—
562D12—362no—
563D12—361no—
564D12—361no—
565D12—361no—
566C4×D3—121no—
567C4×D3—361no—
568C4×D3—361no—
569Dic6—41no—
570C2×C32—22no—
571C2×C32#100411yescharacteristic
572C2×C32C2×#23911yescharacteristic
573C2×C32#100911yescharacteristic
574C3⋊D3—121no—
575C3⋊D3—121no—
576C3⋊D3—121no—
577C3×D3—121no—
578C2×C9—22no—
579C2×C9—21no—
580C2×C9—21no—
581C2×C9—21no—
582C2×C9—42no—
583C2×C9C2×#23511yescharacteristic
584C2×C9#100411yescharacteristic
585C2×C9#100911yescharacteristic
586D9—41no—
587D9—122no—
588D9—122no—
589D9—121no—
590D9—121no—
591D9—121no—
592D9—241no—
593C24—271no—
594C2×Q8—31no—
595C2×D4—91no—
596C2×D4—271no—
597C2×D4—271no—
598C2×D4—271no—
599C2×D4—271no—
600C2×D4—271no—
601C2×D4—271no—
602C22×C4—31no—
603C22×C4—91no—
604C22×C4—91no—
605C22×C4—271no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—31no—
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×D911yescharacteristic
626C42—91no—
627C42—271no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—22no—
633C22×C3—21no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—181no—
637C22×C3—181no—
638C22×C3—181no—
639C22×C3#370112yes—
640C22×C3C23×D911yescharacteristic
641C22×C3#379912yes—
642C22×C3C22×D3211yescharacteristic
643C2×D3—61no—
644C2×D3—61no—
645C2×D3—61no—
646C2×D3—182no—
647C2×D3—182no—
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—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—361no—
667C2×D3—361no—
668C2×D3—361no—
669C2×D3—361no—
670C2×D3—361no—
671C2×D3—361no—
672C2×D3—361no—
673C2×D3—364no—
674C2×D3—364no—
675C2×D3—368no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—61no—
683C3×C4—61no—
684C3×C4—61no—
685C3×C4—61no—
686C3×C4—181no—
687C3×C4—181no—
688C3×C4—181no—
689Dic3—21no—
690Dic3—21no—
691Dic3—21no—
692Dic3—21no—
693Dic3—61no—
694Dic3—61no—
695Dic3—61no—
696Dic3—181no—
697Dic3—181no—
698Dic3—361no—
699C32#564411yescharacteristic
700C9—21no—
701C9#556011yescharacteristic, complemented
702C23—91no—
703C23—271no—
704C23—271no—
705C23—271no—
706C23—542no—
707C23—1081no—
708C23—1081no—
709C23C2×D3×D911yescharacteristic
710Q8—121no—
711D4—182no—
712D4—542no—
713D4—1081no—
714D4—1081no—
715D4—1081no—
716D4—1081no—
717D4—1081no—
718C2×C4—31no—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—91no—
723C2×C4—91no—
724C2×C4—91no—
725C2×C4—121no—
726C2×C4—271no—
727C2×C4—361no—
728C2×C4—361no—
729C2×C4—1081no—
730C2×C4C2×D3×D911yescharacteristic
731C2×C4C2×D3×D911yescharacteristic
732C2×C3—22no—
733C2×C3—22no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—42no—
738C2×C3—361no—
739C2×C3#6371011yescharacteristic
740C2×C3C2×#370111yescharacteristic
741C2×C3#6371511yescharacteristic
742C2×C3C2×#379911yescharacteristic
743C2×C3#6431411yescharacteristic
744C2×C3#6431411yescharacteristic
745D3—121no—
746D3—362no—
747D3—362no—
748D3—361no—
749D3—361no—
750D3—361no—
751D3—361no—
752D3—361no—
753D3—361no—
754D3—721no—
755C22—21no—
756C22—21no—
757C22—181no—
758C22—181no—
759C22—181no—
760C22—541no—
761C22—541no—
762C22—541no—
763C22—541no—
764C22—541no—
765C22—541no—
766C22—541no—
767C22—541no—
768C22—541no—
769C22—1084no—
770C22#8863512yes—
771C22C22×D3×D911yescharacteristic
772C4—21no—
773C4—21no—
774C4—61no—
775C4—61no—
776C4—61no—
777C4—61no—
778C4—181no—
779C4—181no—
780C4—181no—
781C4—541no—
782C3—21no—
783C3#1058974611yescharacteristic, complemented
784C3#1059424311yescharacteristic
785C2—22no—
786C2—361no—
787C2—1081no—
788C2—1081no—
789C2—1081no—
790C2C2×#8863511yescharacteristic
791C2#1172250011yescharacteristic
792C2#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. #11721728C2semidirect
2. C3×#611⋊C4C2semidirect
3. C9×#878C2semidirect
4. #11721278C2semidirect
5. #11721277C2semidirect
6. C2×#88445C2semidirect
7. #11721241C2semidirect
8. #11721005C2semidirect
9. #11721004C2semidirect
10. #11721003C2semidirect
11. #11720997C2semidirect
12. #11720953C2semidirect
13. #11720938C2semidirect
14. #11720934C2semidirect
15. #11720920C2semidirect
25. C2×C3×C4×D9C22semidirect
26. C2×C9×Dic6C22semidirect
29. C2×#6192C22semidirect
30. C2×(C3⋊D9)⋊C4C22semidirect
35. C3×(C2×D9)⋊C4C22semidirect
36. C9×C4⋊Dic3C22semidirect
37. C9×Dic3⋊C4C22semidirect
38. C9×Dic3⋊C4C22semidirect
39. C3×Dic9⋊C4C22semidirect
40. C3×C4×Dic9C22semidirect
47. #88445C22semidirect
48. #88445C22semidirect
49. (C2×D9)⋊Dic3C22semidirect
50. Dic3⋊Dic9C22semidirect
51. #88442C22semidirect
52. Dic3×Dic9C22semidirect
83. #611⋊C4D3semidirect
167. C2×C4×D9C2×D3semidirect
187. (C2×D9)⋊C4C2×D3semidirect
190. Dic9⋊C4C2×D3semidirect
192. C4×Dic9C2×D3semidirect
248. #878D9semidirect
362. C2×Dic6C2×D9semidirect
400. C4⋊Dic3C2×D9semidirect
405. Dic3⋊C4C2×D9semidirect
406. Dic3⋊C4C2×D9semidirect
496. C3×C9#538semidirect
701. C9#5560semidirect
783. C3#10589746semidirect

Maximal subgroups

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

subgroupindex
#117217282
C3×#611⋊C42
C9×#8782
#117212782
#117212772
C2×#884452
#117212412
#117210052
#117210042
#117210032
#117209972
#117209532
#117209382
#117209342
#117209202
#105942433
#105897463