Finite Group Databasebeta

← #13149370

Subgroups — #13149370

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#11721751C211yesmaximal, characteristic, complemented
2C9×#898C211yesmaximal, characteristic, complemented
3C3×#63460C211yesmaximal, characteristic, complemented
4#11721051C211yesmaximal, characteristic, complemented
5#11721051C211yesmaximal, characteristic, complemented
6#11721048C211yesmaximal, characteristic, complemented
7#11721039C211yesmaximal, characteristic, complemented
8#11721005C211yesmaximal, characteristic, complemented
9#11720993C211yesmaximal, characteristic, complemented
10#11720992C211yesmaximal, characteristic, complemented
11#11720958C211yesmaximal, characteristic, complemented
12#11720956C211yesmaximal, characteristic, complemented
13#11720942C211yesmaximal, characteristic, complemented
14#11720940C211yesmaximal, characteristic, complemented
15#11720923C211yesmaximal, characteristic, complemented
16#10594658—31nomaximal
17#10589806—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×C4⋊(C3⋊D9)C2211yescharacteristic
20C2×C4⋊(C3⋊D9)C2211yescharacteristic
21C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
22C2×C4×C3⋊D9C2211yescharacteristic
23C2×#6195C2211yescharacteristic
24C2×#6195C2211yescharacteristic
25C2×#6192C2211yescharacteristic
26C2×#6192C2211yescharacteristic
27C2×(C3⋊D9)⋊C4C2211yescharacteristic
28C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
29C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
30C2×#6189C2211yescharacteristic, complemented
31C3×C9×C4⋊C4C2211yescharacteristic, complemented
32#88536C2211yescharacteristic, complemented
33#88536C2211yescharacteristic, complemented
34C9×(C2×D3)⋊C4C2211yescharacteristic
35C9×(C2×D3)⋊C4C2211yescharacteristic
36C9×(C2×D3)⋊C4C2211yescharacteristic
37C3×(C2×D9)⋊C4C2211yescharacteristic
38C3×(C2×D9)⋊C4C2211yescharacteristic
39C3×(C2×D9)⋊C4C2211yescharacteristic
40C9×C4⋊Dic3C2211yescharacteristic, complemented
41C9×Dic3⋊C4C2211yescharacteristic, complemented
42C4×C9×Dic3C2211yescharacteristic, complemented
43C3×C4⋊Dic9C2211yescharacteristic, complemented
44C3×Dic9⋊C4C2211yescharacteristic, complemented
45C3×C4×Dic9C2211yescharacteristic, complemented
46(C2×D3)⋊Dic9C2211yescharacteristic
47#88445C2211yescharacteristic
48#88445C2211yescharacteristic
49#88445C2211yescharacteristic, complemented
50#88445C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic
52#88442C2211yescharacteristic, complemented
53#64104—31no—
54C3×#898—31no—
55C3×#898D311yescharacteristic
56#63923—31no—
57#63923—31no—
58#63921—31no—
59#63910—31no—
60#63910—31no—
61#63894—31no—
62#63894—31no—
63#63865—31no—
64#63854—31no—
65#63854—31no—
66#63852—31no—
67#63852—31no—
68C9×#126—31no—
69#63460D311yescharacteristic, complemented
70#63458—31no—
71#63457—31no—
72#63457—31no—
73#63457—61no—
74#63456—31no—
75#63455—31no—
76#63447—31no—
77#63446—31no—
78#63445—31no—
79#63444—31no—
80#63444—31no—
81C22⋊C4×D9—31no—
82#63437—31no—
83C4×D36—31no—
84C22×C3⋊D9C2311yescharacteristic
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
94C2×C3×C4×C9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C4⋊(C3⋊D9)—22no—
97C4⋊(C3⋊D9)—22no—
98C4⋊(C3⋊D9)—41no—
99C4×C3⋊D9—41no—
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106#6195—41no—
107#6195—41no—
108#6192—41no—
109#6192—41no—
110(C3⋊D9)⋊C4—41no—
111(C3⋊D9)⋊C4—41no—
112(C3⋊D9)⋊C4—41no—
113#6189—41no—
114#5704—91no—
115#5704—91no—
116C22×D32—31no—
117C2×C4⋊(C3⋊D3)—31no—
118C2×C4⋊(C3⋊D3)—31no—
119C2×C4⋊(C3⋊D3)—31no—
120C2×C4×C3⋊D3—31no—
121C2×#627—31no—
122C2×#626—31no—
123C2×#626—31no—
124C2×#626—31no—
125C2×#626—31no—
126C2×#624—31no—
127C2×#624—31no—
128C2×#624—31no—
129C23×D9—31no—
130C32×C4⋊C4C2×D311yescharacteristic
131#3752—31no—
132#3752—31no—
133C3×(C2×D3)⋊C4—31no—
134C3×(C2×D3)⋊C4—31no—
135C3×(C2×D3)⋊C4—31no—
136C3×(C2×D3)⋊C4C2×D311yescharacteristic
137C3×(C2×D3)⋊C4C2×D311yescharacteristic
138C3×(C2×D3)⋊C4C2×D311yescharacteristic
139C3×C4⋊Dic3—31no—
140C3×C4⋊Dic3C2×D311yescharacteristic
141C3×Dic3⋊C4—31no—
142C3×Dic3⋊C4C2×D311yescharacteristic
143C3×C4×Dic3—31no—
144C3×C4×Dic3C2×D311yescharacteristic
145#3724—31no—
146#3722—31no—
147#3722—31no—
148#3722—31no—
149#3722—31no—
150(C2×D3)⋊Dic3—31no—
151(C2×D3)⋊Dic3—31no—
152C2×#611—31no—
153C2×#611—31no—
154C2×D36—31no—
155C2×D36—31no—
156C2×D36—31no—
157C2×D36—31no—
158C2×D36—31no—
159C2×D36—61no—
160C2×D36—61no—
161C2×D36—61no—
162C2×C4×D9—31no—
163C2×C4×D9—31no—
164C2×C4×D9—31no—
165C2×C4×D9—31no—
166C2×C4×D9—61no—
167C2×Dic18—31no—
168C9×C4⋊C4—21no—
169C9×C4⋊C4—31no—
170C9×C4⋊C4—31no—
171C9×C4⋊C4C2×D311yescharacteristic, complemented
172C9×C22⋊C4—31no—
173C9×C22⋊C4—31no—
174C9×C22⋊C4—31no—
175C42×C9—31no—
176#3676—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—61no—
185(C2×D9)⋊C4—61no—
186(C2×D9)⋊C4C2×D311yescharacteristic
187(C2×D9)⋊C4C2×D311yescharacteristic
188(C2×D9)⋊C4C2×D311yescharacteristic
189C4⋊Dic9C2×D311yescharacteristic, complemented
190Dic9⋊C4—31no—
191Dic9⋊C4C2×D311yescharacteristic, complemented
192C4×Dic9C2×D311yescharacteristic, complemented
193C22×C3×C9C2411yescharacteristic
194C2×C3⋊D9—21no—
195C2×C3⋊D9—21no—
196C2×C3⋊D9—21no—
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×C4×C9—21no—
213C3⋊Dic9—21no—
214C9×Dic3—21no—
215C9×Dic3—21no—
216C9×Dic3—21no—
217C3×Dic9—21no—
218C3×Dic9—21no—
219C3×Dic9—21no—
220C3×#126—31no—
221C3×#126—91no—
222#898—31no—
223#898D911yescharacteristic, complemented
224#896—91no—
225#896—91no—
226#895—91no—
227#895—91no—
228#895—91no—
229#895—91no—
230#895—181no—
231#894—91no—
232#894—91no—
233#893—91no—
234#893—91no—
235#885—91no—
236#885—91no—
237#884—91no—
238#884—91no—
239#883—91no—
240#883—91no—
241#882—91no—
242#882—91no—
243#882—91no—
244#882—91no—
245D3×C22⋊C4—91no—
246D3×C22⋊C4—91no—
247#875—91no—
248#875—91no—
249C4×D12—91no—
250C4×D12—91no—
251C22×C3⋊D3—31no—
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
261C2×C32×C4C22×D311yescharacteristic
262C2×C3⋊Dic3—31no—
263C4⋊(C3⋊D3)—62no—
264C4⋊(C3⋊D3)—62no—
265C4⋊(C3⋊D3)—121no—
266C4×C3⋊D3—121no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3C22×D311yescharacteristic
271C2×C3×Dic3C22×D311yescharacteristic
272C2×C3×Dic3C22×D311yescharacteristic
273#627—121no—
274#626—121no—
275#626—121no—
276#626—121no—
277#626—121no—
278#624—121no—
279#624—121no—
280#624—121no—
281C23×C9—31no—
282C22×D9—31no—
283C22×D9—31no—
284C22×D9—31no—
285C22×D9—61no—
286C22×D9—61no—
287C22×D9—61no—
288C22×D9—62no—
289C22×D9—121no—
290C22×D9—121no—
291C22×D9C22×D311yescharacteristic
292C2×C4×C9—21no—
293C2×C4×C9—21no—
294C2×C4×C9—21no—
295C2×C4×C9—31no—
296C2×C4×C9—31no—
297C2×C4×C9—31no—
298C2×C4×C9C22×D311yescharacteristic
299C2×C4×C9C22×D311yescharacteristic
300C2×C4×C9C22×D311yescharacteristic
301#611—121no—
302#611—121no—
303C2×Dic9—31no—
304C2×Dic9—61no—
305C2×Dic9C22×D311yescharacteristic
306C2×Dic9C22×D311yescharacteristic
307C2×Dic9C22×D311yescharacteristic
308D36—62no—
309D36—62no—
310D36—122no—
311D36—122no—
312D36—121no—
313D36—122no—
314D36—121no—
315D36—121no—
316C4×D9—121no—
317C4×D9—121no—
318C4×D9—121no—
319C4×D9—121no—
320C4×D9—122no—
321Dic18—121no—
322#538—271noSylow
323C2×C3×C9C2×#4111yescharacteristic
324C2×C3×C9H(5,𝔽2)11yescharacteristic
325C2×C3×C9H(5,𝔽2)11yescharacteristic
326C3⋊D9—22no—
327C3⋊D9—41no—
328C3⋊D9—41no—
329D3×C9—41no—
330C3×D9—41no—
331C23×D3—91no—
332C23×D3—91no—
333C2×#67—91no—
334C2×#67—91no—
335C2×#67—91no—
336C2×#67—91no—
337C2×D12—91no—
338C2×D12—91no—
339C2×D12—91no—
340C2×D12—91no—
341C2×D12—91no—
342C2×D12—91no—
343C2×D12—91no—
344C2×D12—91no—
345C2×D12—91no—
346C2×D12—91no—
347C2×D12—181no—
348C2×D12—181no—
349C2×D12—181no—
350C2×C4×D3—91no—
351C2×C4×D3—91no—
352C2×C4×D3—91no—
353C2×C4×D3—91no—
354C2×C4×D3—91no—
355C2×C4×D3—91no—
356C2×C4×D3—91no—
357C2×C4×D3—91no—
358C2×C4×D3—181no—
359C2×Dic6—91no—
360C2×Dic6—91no—
361C3×C4⋊C4—21no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—91no—
365C3×C4⋊C4—91no—
366C3×C4⋊C4C2×D911yescharacteristic, complemented
367C3×C4⋊C4D3211yescharacteristic
368C3×C22⋊C4—31no—
369C3×C22⋊C4—31no—
370C3×C22⋊C4—31no—
371C3×C22⋊C4—91no—
372C3×C22⋊C4—91no—
373C3×C22⋊C4—91no—
374C3×C42—31no—
375C3×C42—91no—
376#217—91no—
377#217—91no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—31no—
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—181no—
396(C2×D3)⋊C4—181no—
397(C2×D3)⋊C4C2×D911yescharacteristic
398(C2×D3)⋊C4C2×D911yescharacteristic
399(C2×D3)⋊C4C2×D911yescharacteristic
400C4⋊Dic3—31no—
401C4⋊Dic3C2×D911yescharacteristic, complemented
402Dic3⋊C4—31no—
403Dic3⋊C4—91no—
404Dic3⋊C4—91no—
405Dic3⋊C4C2×D911yescharacteristic, complemented
406C4×Dic3—31no—
407C4×Dic3C2×D911yescharacteristic, complemented
408C22×C32C23×D311yescharacteristic
409C2×C3⋊D3—32no—
410C2×C3⋊D3—61no—
411C2×C3⋊D3—61no—
412C2×C3⋊D3—61no—
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—
427C32×C4—21no—
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—61no—
437C22×C9—61no—
438C22×C9—61no—
439C22×C9C23×D311yescharacteristic
440C2×D9—21no—
441C2×D9—21no—
442C2×D9—21no—
443C2×D9—32no—
444C2×D9—62no—
445C2×D9—61no—
446C2×D9—61no—
447C2×D9—61no—
448C2×D9—61no—
449C2×D9—61no—
450C2×D9—61no—
451C2×D9—61no—
452C2×D9—61no—
453C2×D9—121no—
454C2×D9—121no—
455C2×D9—121no—
456C2×D9—121no—
457C2×D9—121no—
458C2×D9—121no—
459C2×D9—121no—
460C2×D9—121no—
461C2×D9—124no—
462C4×C9—22no—
463C4×C9—21no—
464C4×C9—21no—
465C4×C9—21no—
466C4×C9—41no—
467C4×C9—41no—
468C4×C9—61no—
469C4×C9—61no—
470C4×C9—61no—
471Dic9—21no—
472Dic9—21no—
473Dic9—21no—
474Dic9—61no—
475Dic9—121no—
476#126—31no—
477#126—91no—
478#124—271no—
479#124—271no—
480#123—271no—
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—31no—
493C23×C3—91no—
494C22×D3—31no—
495C22×D3—91no—
496C22×D3—91no—
497C22×D3—91no—
498C22×D3—91no—
499C22×D3—91no—
500C22×D3—91no—
501C22×D3—181no—
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
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—91no—
518C2×C3×C4—91no—
519C2×C3×C4—91no—
520C2×C3×C4C22×D911yescharacteristic
521C2×C3×C4C22×D911yescharacteristic
522C2×C3×C4C22×D911yescharacteristic
523C2×C3×C4C2×D3211yescharacteristic
524C2×C3×C4C2×D3211yescharacteristic
525C2×C3×C4C2×D3211yescharacteristic
526#67—361no—
527#67—361no—
528#67—361no—
529#67—361no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—91no—
534C2×Dic3—91no—
535C2×Dic3—181no—
536C2×Dic3C22×D911yescharacteristic
537C2×Dic3C22×D911yescharacteristic
538C2×Dic3C22×D911yescharacteristic
539D12—182no—
540D12—182no—
541D12—182no—
542D12—182no—
543D12—362no—
544D12—362no—
545D12—361no—
546D12—361no—
547D12—362no—
548D12—361no—
549D12—361no—
550D12—361no—
551D12—361no—
552C4×D3—361no—
553C4×D3—361no—
554C4×D3—361no—
555C4×D3—361no—
556C4×D3—361no—
557C4×D3—361no—
558C4×D3—361no—
559C4×D3—361no—
560C4×D3—362no—
561Dic6—361no—
562Dic6—361no—
563C2×C32D3×#4111yescharacteristic
564C2×C32#100911yescharacteristic
565C2×C32#100911yescharacteristic
566C3⋊D3—62no—
567C3⋊D3—121no—
568C3⋊D3—121no—
569C3×D3—41no—
570C3×D3—121no—
571C2×C9—21no—
572C2×C9—21no—
573C2×C9—21no—
574C2×C9—121no—
575C2×C9D3×#4111yescharacteristic
576C2×C9#100911yescharacteristic
577C2×C9#100911yescharacteristic
578D9—41no—
579D9—62no—
580D9—122no—
581D9—121no—
582D9—121no—
583D9—241no—
584D9—241no—
585C24—271no—
586C2×Q8—271no—
587C2×D4—271no—
588C2×D4—271no—
589C2×D4—271no—
590C2×D4—271no—
591C2×D4—271no—
592C2×D4—271no—
593C2×D4—271no—
594C22×C4—271no—
595C22×C4—271no—
596C22×C4—271no—
597C22×C4—271no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—91no—
601C4⋊C4—91no—
602C4⋊C4—271no—
603C4⋊C4D3×D911yescharacteristic, complemented
604C22⋊C4—31no—
605C22⋊C4—31no—
606C22⋊C4—31no—
607C22⋊C4—91no—
608C22⋊C4—91no—
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—
618C42—31no—
619C42—91no—
620C22×C3—21no—
621C22×C3—61no—
622C22×C3—61no—
623C22×C3—61no—
624C22×C3—181no—
625C22×C3—181no—
626C22×C3—181no—
627C22×C3C23×D911yescharacteristic
628C22×C3C22×D3211yescharacteristic
629C2×D3—21no—
630C2×D3—21no—
631C2×D3—21no—
632C2×D3—61no—
633C2×D3—61no—
634C2×D3—61no—
635C2×D3—92no—
636C2×D3—92no—
637C2×D3—182no—
638C2×D3—181no—
639C2×D3—181no—
640C2×D3—181no—
641C2×D3—181no—
642C2×D3—181no—
643C2×D3—181no—
644C2×D3—181no—
645C2×D3—181no—
646C2×D3—181no—
647C2×D3—181no—
648C2×D3—181no—
649C2×D3—181no—
650C2×D3—181no—
651C2×D3—181no—
652C2×D3—181no—
653C2×D3—181no—
654C2×D3—361no—
655C2×D3—361no—
656C2×D3—361no—
657C2×D3—361no—
658C2×D3—361no—
659C2×D3—361no—
660C2×D3—361no—
661C2×D3—361no—
662C2×D3—364no—
663C2×D3—364no—
664C3×C4—22no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—61no—
676C3×C4—181no—
677C3×C4—181no—
678C3×C4—181no—
679Dic3—21no—
680Dic3—21no—
681Dic3—21no—
682Dic3—61no—
683Dic3—61no—
684Dic3—61no—
685Dic3—181no—
686Dic3—181no—
687Dic3—361no—
688C32#570411yescharacteristic
689C9—21no—
690C9#570411yescharacteristic, complemented
691C23—31no—
692C23—91no—
693C23—271no—
694C23—271no—
695C23—271no—
696C23—542no—
697C23—1081no—
698C23—1081no—
699Q8—1081no—
700D4—542no—
701D4—542no—
702D4—1081no—
703D4—1081no—
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—271no—
714C2×C4—1081no—
715C2×C4—1081no—
716C2×C4—1081no—
717C2×C4—1081no—
718C2×C4C2×D3×D911yescharacteristic
719C2×C4C2×D3×D911yescharacteristic
720C2×C4C2×D3×D911yescharacteristic
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—121no—
725C2×C3—361no—
726C2×C3#41×D911yescharacteristic
727C2×C3#6371511yescharacteristic
728C2×C3#6371511yescharacteristic
729C2×C3#6430811yescharacteristic
730C2×C3#6431211yescharacteristic
731C2×C3#6432011yescharacteristic
732D3—41no—
733D3—121no—
734D3—182no—
735D3—182no—
736D3—362no—
737D3—361no—
738D3—361no—
739D3—361no—
740D3—361no—
741D3—721no—
742D3—721no—
743C22—61no—
744C22—61no—
745C22—61no—
746C22—181no—
747C22—181no—
748C22—181no—
749C22—272no—
750C22—541no—
751C22—541no—
752C22—541no—
753C22—541no—
754C22—541no—
755C22—541no—
756C22—541no—
757C22—541no—
758C22—1084no—
759C22C22×D3×D911yescharacteristic
760C4—21no—
761C4—21no—
762C4—21no—
763C4—61no—
764C4—61no—
765C4—61no—
766C4—181no—
767C4—181no—
768C4—181no—
769C4—541no—
770C3—21no—
771C3#1058980611yescharacteristic, complemented
772C3#1059465811yescharacteristic
773C2—121no—
774C2—361no—
775C2—542no—
776C2—1081no—
777C2—1081no—
778C2#1172247811yescharacteristic
779C2#1172249811yescharacteristic
780C2#1172251511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
hypercenterC4⋊C4D3×D9
hypocenterC3×C9#538
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #11721751C2semidirect
2. C9×#898C2semidirect
3. C3×#63460C2semidirect
4. #11721051C2semidirect
5. #11721051C2semidirect
6. #11721048C2semidirect
7. #11721039C2semidirect
8. #11721005C2semidirect
9. #11720993C2semidirect
10. #11720992C2semidirect
11. #11720958C2semidirect
12. #11720956C2semidirect
13. #11720942C2semidirect
14. #11720940C2semidirect
15. #11720923C2semidirect
21. C2×C4⋊(C3⋊D9)C22semidirect
28. C2×(C3⋊D9)⋊C4C22semidirect
29. C2×(C3⋊D9)⋊C4C22semidirect
30. C2×#6189C22semidirect
31. C3×C9×C4⋊C4C22semidirect
32. #88536C22semidirect
33. #88536C22semidirect
40. C9×C4⋊Dic3C22semidirect
41. C9×Dic3⋊C4C22semidirect
42. C4×C9×Dic3C22semidirect
43. C3×C4⋊Dic9C22semidirect
44. C3×Dic9⋊C4C22semidirect
45. C3×C4×Dic9C22semidirect
49. #88445C22semidirect
50. #88445C22semidirect
52. #88442C22semidirect
69. #63460D3semidirect
171. C9×C4⋊C4C2×D3semidirect
189. C4⋊Dic9C2×D3semidirect
191. Dic9⋊C4C2×D3semidirect
192. C4×Dic9C2×D3semidirect
223. #898D9semidirect
366. C3×C4⋊C4C2×D9semidirect
401. C4⋊Dic3C2×D9semidirect
405. Dic3⋊C4C2×D9semidirect
407. C4×Dic3C2×D9semidirect
491. C3×C9#538semidirect
603. C4⋊C4D3×D9semidirect
690. C9#5704semidirect
771. C3#10589806semidirect

Maximal subgroups

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

subgroupindex
#117217512
C9×#8982
C3×#634602
#117210512
#117210482
#117210392
#117210052
#117209932
#117209922
#117209582
#117209562
#117209422
#117209402
#117209232
#105946583
#105898063