Finite Group Databasebeta

← #13148169

Subgroups — #13148169

Order 1728.

882 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
1C22⋊C4×C3⋊D9C211yesmaximal, characteristic, complemented
2C3×#63446C211yesmaximal, characteristic, complemented
3C9×#879C211yesmaximal, characteristic, complemented
4#11721278C211yesmaximal, characteristic, complemented
5#11721278C211yesmaximal, characteristic, complemented
6#11721269C211yesmaximal, characteristic, complemented
7#11721257C211yesmaximal, characteristic, complemented
8#11721007C211yesmaximal, characteristic, complemented
9C4×#6192C211yesmaximal, characteristic, complemented
10#11720983C211yesmaximal, characteristic, complemented
11#11720978C211yesmaximal, characteristic, complemented
12#11720940C211yesmaximal, characteristic, complemented
13#11720938C211yesmaximal, characteristic, complemented
14#11720923C211yesmaximal, characteristic, complemented
15#11720920C211yesmaximal, characteristic, complemented
16#10594226—31nomaximal
17#10589806—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C2×C4×C3⋊D9C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic
21C2×C3×#611C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C2×C3×D36C2211yescharacteristic, complemented
24C2×C3×C4×D9C2211yescharacteristic, complemented
25C2×#6192C2211yescharacteristic
26C2×#6192C2211yescharacteristic
27C2×#6192C2211yescharacteristic
28C2×#6192C2211yescharacteristic
29C2×Dic3×D9C2211yescharacteristic, complemented
30C2×#6189C2211yescharacteristic, complemented
31C3×C9×C22⋊C4C2211yescharacteristic
32#88551C2211yescharacteristic
33#88536C2211yescharacteristic
34#88536C2211yescharacteristic
35C9×#217C2211yescharacteristic
36C9×#217C2211yescharacteristic
37C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
38C9×C4⋊Dic3C2211yescharacteristic, complemented
39C9×Dic3⋊C4C2211yescharacteristic, complemented
40C9×Dic3⋊C4C2211yescharacteristic, complemented
41C4×C9×Dic3C2211yescharacteristic, complemented
42C3×Dic9⋊C4C2211yescharacteristic, complemented
43#88445C2211yescharacteristic
44#88445C2211yescharacteristic
45#88445C2211yescharacteristic
46#88445C2211yescharacteristic
47(C2×D9)⋊Dic3C2211yescharacteristic, complemented
48(C2×D9)⋊Dic3C2211yescharacteristic, complemented
49(C2×D9)⋊Dic3C2211yescharacteristic, complemented
50Dic3⋊Dic9C2211yescharacteristic, complemented
51#88442C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53C22⋊C4×C3⋊D3—31no—
54C3×#884—31no—
55C3×#879D311yescharacteristic
56#63981—31no—
57#63981—31no—
58#63969—31no—
59#63959—31no—
60#63916—31no—
61C4×#626—31no—
62#63886—31no—
63#63881—31no—
64#63865—31no—
65#63852—31no—
66#63850—31no—
67#63848—31no—
68C9×#126—31no—
69#63460—31no—
70#63458—31no—
71#63457—31no—
72#63457—31no—
73#63456—31no—
74#63455—31no—
75#63447—31no—
76#63446D311yescharacteristic, complemented
77#63445—31no—
78#63444—31no—
79#63444—31no—
80C22⋊C4×D9—31no—
81C22⋊C4×D9—61no—
82#63437—31no—
83C4×D36—31no—
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
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C4×C3⋊D9—41no—
97C4×C3⋊D9—41no—
98C3×#611—41no—
99C3×#611—41no—
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C3×D36—41no—
107C3×C4×D9—41no—
108#6192—22no—
109#6192—22no—
110#6192—41no—
111#6192—41no—
112Dic3×D9—41no—
113#6189—41no—
114#5704—91no—
115#5613—91no—
116C23×C3⋊D3—31no—
117C2×C4×C3⋊D3—31no—
118C2×C4×C3⋊D3—31no—
119C2×C3×#67—31no—
120C2×C3×#67—31no—
121C2×C3×D12—31no—
122C2×C3×C4×D3—31no—
123C2×#627—31no—
124C2×#626—31no—
125C2×#626—31no—
126C2×#626—31no—
127C2×#626—31no—
128C2×D3×Dic3—31no—
129C23×D9—31no—
130C23×D9—61no—
131C32×C22⋊C4C2×D311yescharacteristic
132#3757—31no—
133#3752—31no—
134#3752—31no—
135C3×#217C2×D311yescharacteristic
136C3×#217C2×D311yescharacteristic
137C3×(C2×D3)⋊C4—31no—
138C3×C4⋊Dic3C2×D311yescharacteristic
139C3×Dic3⋊C4—31no—
140C3×Dic3⋊C4C2×D311yescharacteristic
141C3×Dic3⋊C4C2×D311yescharacteristic
142C3×C4×Dic3C2×D311yescharacteristic
143#3724—31no—
144Dic3⋊Dic3—31no—
145#3722—31no—
146#3722—31no—
147#3722—31no—
148#3722—31no—
149(C2×D3)⋊Dic3—31no—
150(C2×D3)⋊Dic3—31no—
151(C2×D3)⋊Dic3—31no—
152Dic32—31no—
153C2×#611C2×D311yescharacteristic
154C2×#611C2×D311yescharacteristic
155C2×D36—31no—
156C2×D36—31no—
157C2×D36—31no—
158C2×D36—31no—
159C2×D36C2×D311yescharacteristic, complemented
160C2×C4×D9—31no—
161C2×C4×D9—31no—
162C2×C4×D9—31no—
163C2×C4×D9—61no—
164C2×C4×D9—61no—
165C2×C4×D9C2×D311yescharacteristic, complemented
166C2×Dic18—31no—
167C9×C4⋊C4—31no—
168C9×C4⋊C4—31no—
169C9×C4⋊C4—31no—
170C9×C22⋊C4—21no—
171C9×C22⋊C4—31no—
172C9×C22⋊C4—31no—
173C9×C22⋊C4C2×D311yescharacteristic
174C42×C9—31no—
175#3676—31no—
176#3676—61no—
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—31no—
186(C2×D9)⋊C4—61no—
187(C2×D9)⋊C4—61no—
188(C2×D9)⋊C4C2×D311yescharacteristic, complemented
189C4⋊Dic9—31no—
190Dic9⋊C4—31no—
191Dic9⋊C4C2×D311yescharacteristic, complemented
192C4×Dic9—31no—
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—44no—
203C2×C3⋊D9#4112yes—
204C2×C3×D9—21no—
205C2×C3×D9—21no—
206C2×C3×D9—21no—
207C2×C3×D9—21no—
208C2×C3×D9—21no—
209C2×C3×D9—21no—
210C3×C4×C9—21no—
211C3×C4×C9—21no—
212C3⋊Dic9—21no—
213C3⋊Dic9—21no—
214C9×Dic3—21no—
215C9×Dic3—21no—
216C9×Dic3—21no—
217C9×Dic3—21no—
218C3×Dic9—21no—
219C3×Dic9—21no—
220C3×#126—31no—
221C3×#121—91no—
222#939—91no—
223#938—91no—
224#937—91no—
225#937—91no—
226#936—91no—
227#935—91no—
228#929—91no—
229C4×#67—91no—
230#898—91no—
231#898—91no—
232#896—91no—
233#896—91no—
234#895—91no—
235#895—91no—
236#894—91no—
237#893—91no—
238#885—91no—
239#885—91no—
240#884—31no—
241#883—91no—
242#882—91no—
243#882—91no—
244#67⋊C4—91no—
245D3×C22⋊C4—91no—
246D3×C22⋊C4—91no—
247D3×C22⋊C4—181no—
248#879D911yescharacteristic, complemented
249#875—91no—
250C4×D12—91no—
251C23×C32C22×D311yescharacteristic
252C22×C3⋊D3—31no—
253C22×C3⋊D3—31no—
254C22×C3⋊D3—62no—
255C22×C3⋊D3—121no—
256C22×C3⋊D3—121no—
257C22×C3×D3—31no—
258C22×C3×D3—31no—
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261C2×C3⋊Dic3—31no—
262C2×C3⋊Dic3—31no—
263C4×C3⋊D3—121no—
264C4×C3⋊D3—121no—
265C3×#67—121no—
266C3×#67—121no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3C22×D311yescharacteristic
270C2×C3×Dic3C22×D311yescharacteristic
271C2×C3×Dic3C22×D311yescharacteristic
272C2×C3×Dic3C22×D311yescharacteristic
273C3×D12—121no—
274C3×C4×D3—121no—
275#627—121no—
276#626—62no—
277#626—62no—
278#626—121no—
279#626—121no—
280D3×Dic3—121no—
281C23×C9—21no—
282C23×C9C22×D311yescharacteristic
283C22×D9—31no—
284C22×D9—31no—
285C22×D9—61no—
286C22×D9—61no—
287C22×D9—62no—
288C22×D9—64no—
289C22×D9—121no—
290C22×D9—121no—
291C22×D9—122no—
292C22×D9—122no—
293C22×D9C22×D311yescharacteristic
294C22×D9C22×D311yescharacteristic
295C2×C4×C9—21no—
296C2×C4×C9—21no—
297C2×C4×C9—31no—
298C2×C4×C9—31no—
299C2×C4×C9—31no—
300C2×C4×C9—31no—
301C2×C4×C9C22×D311yescharacteristic
302C2×C4×C9C22×D311yescharacteristic
303#611—41no—
304#611—41no—
305C2×Dic9—31no—
306C2×Dic9—31no—
307C2×Dic9—61no—
308C2×Dic9—61no—
309C2×Dic9C22×D311yescharacteristic
310C2×Dic9C22×D311yescharacteristic
311D36—41no—
312D36—62no—
313D36—62no—
314D36—121no—
315D36—121no—
316C4×D9—41no—
317C4×D9—121no—
318C4×D9—121no—
319C4×D9—121no—
320C4×D9—122no—
321C4×D9—122no—
322Dic18—121no—
323#538—271noSylow
324C2×C3×C9—41no—
325C2×C3×C9C2×#4111yescharacteristic
326C2×C3×C9H(5,𝔽2)11yescharacteristic
327C2×C3×C9H(5,𝔽2)11yescharacteristic
328C3⋊D9—22no—
329C3⋊D9—41no—
330C3×D9—41no—
331C3×D9—41no—
332C23×D3—91no—
333C23×D3—91no—
334C23×D3—181no—
335C2×C3×D4—91no—
336C2×C3×D4—91no—
337C2×C3×D4—91no—
338C22×C3×C4—91no—
339C2×#67—31no—
340C2×#67—31no—
341C2×#67—91no—
342C2×#67—91no—
343C2×#67—91no—
344C2×#67—91no—
345C22×Dic3—91no—
346C2×D12—31no—
347C2×D12—91no—
348C2×D12—91no—
349C2×D12—91no—
350C2×D12—91no—
351C2×C4×D3—31no—
352C2×C4×D3—91no—
353C2×C4×D3—91no—
354C2×C4×D3—91no—
355C2×C4×D3—91no—
356C2×C4×D3—91no—
357C2×C4×D3—181no—
358C2×C4×D3—181no—
359C2×Dic6—91no—
360C2×Dic6—91no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—91no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—31no—
367C3×C22⋊C4—31no—
368C3×C22⋊C4—91no—
369C3×C22⋊C4C2×D911yescharacteristic
370C3×C22⋊C4D3211yescharacteristic
371C3×C42—31no—
372#217—91no—
373#217—91no—
374#217—91no—
375#217—91no—
376#217—91no—
377#217—181no—
378#217C2×D911yescharacteristic
379#217C2×D911yescharacteristic
380(C2×D3)⋊C4—31no—
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—181no—
397(C2×D3)⋊C4—181no—
398C4⋊Dic3—91no—
399C4⋊Dic3C2×D911yescharacteristic, complemented
400Dic3⋊C4—31no—
401Dic3⋊C4—91no—
402Dic3⋊C4—91no—
403Dic3⋊C4—91no—
404Dic3⋊C4C2×D911yescharacteristic, complemented
405Dic3⋊C4C2×D911yescharacteristic, complemented
406C4×Dic3—91no—
407C4×Dic3—91no—
408C4×Dic3C2×D911yescharacteristic, complemented
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32C23×D311yescharacteristic
413C2×C3⋊D3—32no—
414C2×C3⋊D3—61no—
415C2×C3⋊D3—61no—
416C2×C3⋊D3—61no—
417C2×C3⋊D3—61no—
418C2×C3⋊D3—61no—
419C2×C3⋊D3—124no—
420C2×C3×D3—61no—
421C2×C3×D3—61no—
422C2×C3×D3—61no—
423C2×C3×D3—61no—
424C2×C3×D3—61no—
425C2×C3×D3—61no—
426C32×C4—21no—
427C32×C4—21no—
428C3⋊Dic3—61no—
429C3⋊Dic3—61no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—61no—
435C3×Dic3—61no—
436C22×C9—22no—
437C22×C9—21no—
438C22×C9—21no—
439C22×C9—21no—
440C22×C9—21no—
441C22×C9—41no—
442C22×C9—41no—
443C22×C9C23×D311yescharacteristic
444C2×D9—21no—
445C2×D9—21no—
446C2×D9—21no—
447C2×D9—21no—
448C2×D9—21no—
449C2×D9—21no—
450C2×D9—32no—
451C2×D9—62no—
452C2×D9—62no—
453C2×D9—62no—
454C2×D9—61no—
455C2×D9—61no—
456C2×D9—62no—
457C2×D9—61no—
458C2×D9—61no—
459C2×D9—61no—
460C2×D9—121no—
461C2×D9—121no—
462C2×D9—128no—
463C2×D9—124no—
464C4×C9—21no—
465C4×C9—21no—
466C4×C9—41no—
467C4×C9—41no—
468C4×C9—61no—
469C4×C9—61no—
470C4×C9—61no—
471C4×C9—61no—
472Dic9—21no—
473Dic9—21no—
474Dic9—61no—
475Dic9—61no—
476Dic9—121no—
477Dic9—121no—
478#126—31no—
479#126—271no—
480#124—271no—
481#124—271no—
482#123—271no—
483#123—271no—
484C22⋊Q8—271no—
485#121—91no—
486#121—271no—
487#121—271no—
488#120—271no—
489#120—271no—
490C4×D4—271no—
491C4×D4—271no—
492C2×C22⋊C4—271no—
493C3×C9#53811yescharacteristic, complemented, Sylow
494C23×C3—21no—
495C23×C3—91no—
496C23×C3—91no—
497C23×C3C22×D911yescharacteristic
498C23×C3C2×D3211yescharacteristic
499C22×D3—31no—
500C22×D3—31no—
501C22×D3—91no—
502C22×D3—91no—
503C22×D3—91no—
504C22×D3—91no—
505C22×D3—181no—
506C22×D3—181no—
507C22×D3—182no—
508C22×D3—182no—
509C22×D3—184no—
510C22×D3—361no—
511C22×D3—361no—
512C22×D3—361no—
513C22×D3—361no—
514C22×D3—362no—
515C22×D3—362no—
516C3×D4—361no—
517C3×D4—361no—
518C3×D4—361no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—91no—
526C2×C3×C4—91no—
527C2×C3×C4—361no—
528C2×C3×C4C22×D911yescharacteristic
529C2×C3×C4C22×D911yescharacteristic
530C2×C3×C4C2×D3211yescharacteristic
531C2×C3×C4C2×D3211yescharacteristic
532#67—121no—
533#67—121no—
534#67—182no—
535#67—182no—
536#67—361no—
537#67—361no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—91no—
541C2×Dic3—91no—
542C2×Dic3—91no—
543C2×Dic3—91no—
544C2×Dic3—181no—
545C2×Dic3—181no—
546C2×Dic3—361no—
547C2×Dic3C22×D911yescharacteristic
548C2×Dic3C22×D911yescharacteristic
549C2×Dic3C22×D911yescharacteristic
550C2×Dic3C22×D911yescharacteristic
551D12—121no—
552D12—182no—
553D12—182no—
554D12—361no—
555D12—361no—
556C4×D3—121no—
557C4×D3—361no—
558C4×D3—361no—
559C4×D3—361no—
560C4×D3—361no—
561C4×D3—361no—
562C4×D3—362no—
563C4×D3—362no—
564Dic6—361no—
565Dic6—361no—
566C2×C32—41no—
567C2×C32D3×#4111yescharacteristic
568C2×C32#100911yescharacteristic
569C2×C32#100911yescharacteristic
570C3⋊D3—62no—
571C3⋊D3—121no—
572C3×D3—121no—
573C3×D3—121no—
574C2×C9—21no—
575C2×C9—21no—
576C2×C9—21no—
577C2×C9—42no—
578C2×C9—41no—
579C2×C9#100411yescharacteristic
580C2×C9#100411yescharacteristic
581C2×C9D3×#4111yescharacteristic
582D9—41no—
583D9—41no—
584D9—64no—
585D9—62no—
586D9—122no—
587D9—121no—
588C24—271no—
589C2×Q8—271no—
590C2×D4—91no—
591C2×D4—91no—
592C2×D4—91no—
593C2×D4—271no—
594C2×D4—271no—
595C2×D4—271no—
596C2×D4—271no—
597C22×C4—91no—
598C22×C4—271no—
599C22×C4—271no—
600C22×C4—271no—
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—31no—
604C4⋊C4—91no—
605C4⋊C4—271no—
606C4⋊C4—271no—
607C22⋊C4—31no—
608C22⋊C4—31no—
609C22⋊C4—91no—
610C22⋊C4—271no—
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⋊C4D3×D911yescharacteristic
621C42—31no—
622C42—271no—
623C22×C3—22no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—181no—
634C22×C3—181no—
635C22×C3—181no—
636C22×C3—181no—
637C22×C3—181no—
638C22×C3—181no—
639C22×C3C23×D911yescharacteristic
640C22×C3C22×D3211yescharacteristic
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—61no—
644C2×D3—61no—
645C2×D3—61no—
646C2×D3—61no—
647C2×D3—92no—
648C2×D3—92no—
649C2×D3—182no—
650C2×D3—182no—
651C2×D3—182no—
652C2×D3—181no—
653C2×D3—181no—
654C2×D3—181no—
655C2×D3—181no—
656C2×D3—182no—
657C2×D3—181no—
658C2×D3—181no—
659C2×D3—181no—
660C2×D3—181no—
661C2×D3—181no—
662C2×D3—181no—
663C2×D3—361no—
664C2×D3—361no—
665C2×D3—364no—
666C2×D3—368no—
667C2×D3—364no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—61no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—61no—
678C3×C4—181no—
679C3×C4—181no—
680Dic3—21no—
681Dic3—21no—
682Dic3—21no—
683Dic3—21no—
684Dic3—61no—
685Dic3—61no—
686Dic3—181no—
687Dic3—181no—
688Dic3—181no—
689Dic3—181no—
690Dic3—361no—
691Dic3—361no—
692C32#570411yescharacteristic
693C9—21no—
694C9#561311yescharacteristic, complemented
695C23—91no—
696C23—91no—
697C23—271no—
698C23—271no—
699C23—542no—
700C23—1081no—
701C23—1081no—
702C23C2×D3×D911yescharacteristic
703Q8—1081no—
704D4—361no—
705D4—361no—
706D4—361no—
707D4—542no—
708D4—542no—
709D4—1081no—
710D4—1081no—
711C2×C4—31no—
712C2×C4—31no—
713C2×C4—31no—
714C2×C4—31no—
715C2×C4—91no—
716C2×C4—91no—
717C2×C4—271no—
718C2×C4—271no—
719C2×C4—361no—
720C2×C4—1081no—
721C2×C4—1081no—
722C2×C4—1081no—
723C2×C4C2×D3×D911yescharacteristic
724C2×C4C2×D3×D911yescharacteristic
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—42no—
729C2×C3—41no—
730C2×C3—41no—
731C2×C3—361no—
732C2×C3—361no—
733C2×C3#41×D911yescharacteristic
734C2×C3#6371511yescharacteristic
735C2×C3#6371511yescharacteristic
736C2×C3#6430611yescharacteristic
737C2×C3#6431411yescharacteristic
738C2×C3#6431411yescharacteristic
739D3—121no—
740D3—121no—
741D3—184no—
742D3—182no—
743D3—182no—
744D3—362no—
745D3—361no—
746D3—361no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—181no—
751C22—181no—
752C22—181no—
753C22—181no—
754C22—181no—
755C22—181no—
756C22—272no—
757C22—541no—
758C22—541no—
759C22—541no—
760C22—541no—
761C22—541no—
762C22—1084no—
763C22C22×D3×D911yescharacteristic
764C4—21no—
765C4—21no—
766C4—61no—
767C4—61no—
768C4—61no—
769C4—61no—
770C4—181no—
771C4—181no—
772C4—541no—
773C4—541no—
774C3—21no—
775C3#1058980611yescharacteristic, complemented
776C3#1059422611yescharacteristic
777C2—41no—
778C2—361no—
779C2—361no—
780C2—542no—
781C2—1081no—
782C2#1172247511yescharacteristic
783C2#1172250111yescharacteristic
784C2#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. C22⋊C4×C3⋊D9C2semidirect
2. C3×#63446C2semidirect
3. C9×#879C2semidirect
4. #11721278C2semidirect
5. #11721278C2semidirect
6. #11721269C2semidirect
7. #11721257C2semidirect
8. #11721007C2semidirect
9. C4×#6192C2semidirect
10. #11720983C2semidirect
11. #11720978C2semidirect
12. #11720940C2semidirect
13. #11720938C2semidirect
14. #11720923C2semidirect
15. #11720920C2semidirect
23. C2×C3×D36C22semidirect
24. C2×C3×C4×D9C22semidirect
29. C2×Dic3×D9C22semidirect
30. C2×#6189C22semidirect
37. C3×(C2×D9)⋊C4C22semidirect
38. C9×C4⋊Dic3C22semidirect
39. C9×Dic3⋊C4C22semidirect
40. C9×Dic3⋊C4C22semidirect
41. C4×C9×Dic3C22semidirect
42. C3×Dic9⋊C4C22semidirect
47. (C2×D9)⋊Dic3C22semidirect
48. (C2×D9)⋊Dic3C22semidirect
49. (C2×D9)⋊Dic3C22semidirect
50. Dic3⋊Dic9C22semidirect
51. #88442C22semidirect
52. Dic3×Dic9C22semidirect
76. #63446D3semidirect
159. C2×D36C2×D3semidirect
165. C2×C4×D9C2×D3semidirect
188. (C2×D9)⋊C4C2×D3semidirect
191. Dic9⋊C4C2×D3semidirect
248. #879D9semidirect
399. C4⋊Dic3C2×D9semidirect
404. Dic3⋊C4C2×D9semidirect
405. Dic3⋊C4C2×D9semidirect
408. C4×Dic3C2×D9semidirect
493. C3×C9#538semidirect
694. C9#5613semidirect
775. C3#10589806semidirect

Maximal subgroups

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

subgroupindex
C22⋊C4×C3⋊D92
C3×#634462
C9×#8792
#117212782
#117212692
#117212572
#117210072
C4×#61922
#117209832
#117209782
#117209402
#117209382
#117209232
#117209202
#105942263
#105898063