Finite Group Databasebeta

← #13147739

Subgroups — #13147739

Order 1728.

838 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C4⋊(C3⋊D9)C211yesmaximal, characteristic, complemented
2C9×#876C211yesmaximal, characteristic, complemented
3C3×#63434C211yesmaximal, characteristic, complemented
4#11721051C211yesmaximal, characteristic
5#11721048C211yesmaximal, characteristic, complemented
6D9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7#11720997C211yesmaximal, characteristic, complemented
8#11720991C211yesmaximal, characteristic, complemented
9#11720978C211yesmaximal, characteristic, complemented
10#11720965C211yesmaximal, characteristic, complemented
11#11720957C211yesmaximal, characteristic, complemented
12#11720956C211yesmaximal, characteristic, complemented
13#11720938C211yesmaximal, characteristic, complemented
14#11720923C211yesmaximal, characteristic, complemented
15#11720899C211yesmaximal, characteristic, complemented
16#10594017—31nomaximal
17#10589807—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×C4⋊(C3⋊D9)C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic
21C2×C4×C3⋊D9C2211yescharacteristic, complemented
22C2×C3×C4×D9C2211yescharacteristic
23C2×#6195C2211yescharacteristic
24C2×#6192C2211yescharacteristic
25C2×(C3⋊D9)⋊C4C2211yescharacteristic
26C2×Dic3×D9C2211yescharacteristic
27C2×#6189C2211yescharacteristic, complemented
28C3×C42×C9C2211yescharacteristic, complemented
29#88536C2211yescharacteristic
30#88536C2211yescharacteristic, complemented
31C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
32C9×(C2×D3)⋊C4C2211yescharacteristic
33C9×(C2×D3)⋊C4C2211yescharacteristic
34C9×(C2×D3)⋊C4C2211yescharacteristic
35C3×(C2×D9)⋊C4C2211yescharacteristic
36C3×(C2×D9)⋊C4C2211yescharacteristic
37C9×Dic3⋊C4C2211yescharacteristic, complemented
38C9×Dic3⋊C4C2211yescharacteristic, complemented
39C9×Dic3⋊C4C2211yescharacteristic, complemented
40C3×Dic9⋊C4C2211yescharacteristic, complemented
41C3×Dic9⋊C4C2211yescharacteristic, complemented
42C3×C4×Dic9C2211yescharacteristic, complemented
43(C2×D3)⋊Dic9C2211yescharacteristic
44(C2×D3)⋊Dic9C2211yescharacteristic
45#88445C2211yescharacteristic
46#88445C2211yescharacteristic
47#88445C2211yescharacteristic, complemented
48#88445C2211yescharacteristic, complemented
49(C2×D9)⋊Dic3C2211yescharacteristic
50Dic3⋊Dic9C2211yescharacteristic, complemented
51#88442C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53C4×C4⋊(C3⋊D3)—31no—
54C3×#876D311yescharacteristic
55C3×#872—31no—
56#63923—31no—
57#63921—31no—
58D3×(C2×D3)⋊C4—31no—
59#63897—31no—
60#63893—31no—
61#63881—31no—
62#63865—31no—
63#63861—31no—
64#63853—31no—
65#63852—31no—
66#63850—31no—
67#63836—31no—
68C9×#126—31no—
69#63459—31no—
70#63458—31no—
71#63456—31no—
72#63456—31no—
73#63455—31no—
74#63454—31no—
75#63447—31no—
76#63445—31no—
77#63444—31no—
78C22⋊C4×D9—31no—
79C22⋊C4×D9—31no—
80#63441—31no—
81C4×D36—31no—
82C4×D36—61no—
83#63434D311yescharacteristic, complemented
84C22×C3⋊D9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C22×D3×C9C2311yescharacteristic
87C22×C3×D9C2311yescharacteristic
88C2×D3×D9—22no—
89C2×D3×D9—22no—
90C2×D3×D9—41no—
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C4⋊(C3⋊D9)—22no—
97C4×C3⋊D9—41no—
98C4×C3⋊D9—41no—
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C3×C4×D9—22no—
106#6195—41no—
107#6192—22no—
108(C3⋊D9)⋊C4—22no—
109Dic3×D9—41no—
110#6189—41no—
111#5705—91no—
112#5527—91no—
113C22×D32—31no—
114C2×C4⋊(C3⋊D3)—31no—
115C2×C4×C3⋊D3—31no—
116C2×C4×C3⋊D3—31no—
117C2×C3×C4×D3—31no—
118C2×#627—31no—
119C2×#626—31no—
120C2×#626—31no—
121C2×#624—31no—
122C2×D3×Dic3—31no—
123C23×D9—31no—
124C32×C42C2×D311yescharacteristic
125#3752—31no—
126#3752—31no—
127C4⋊(C3⋊Dic3)—31no—
128C3×(C2×D3)⋊C4—31no—
129C3×(C2×D3)⋊C4—31no—
130C3×(C2×D3)⋊C4C2×D311yescharacteristic
131C3×(C2×D3)⋊C4C2×D311yescharacteristic
132C3×(C2×D3)⋊C4C2×D311yescharacteristic
133C3×Dic3⋊C4—31no—
134C3×Dic3⋊C4—31no—
135C3×Dic3⋊C4C2×D311yescharacteristic
136C3×Dic3⋊C4C2×D311yescharacteristic
137C3×Dic3⋊C4C2×D311yescharacteristic
138C3×C4×Dic3—31no—
139#3724—31no—
140Dic3⋊Dic3—31no—
141#3722—31no—
142#3722—31no—
143#3722—31no—
144#3722—31no—
145(C2×D3)⋊Dic3—31no—
146(C2×D3)⋊Dic3—31no—
147(C2×D3)⋊Dic3—31no—
148Dic32—31no—
149C2×#611—31no—
150C2×D36—31no—
151C2×D36—31no—
152C2×D36—61no—
153C2×C4×D9—31no—
154C2×C4×D9—31no—
155C2×C4×D9—31no—
156C2×C4×D9—31no—
157C2×C4×D9—61no—
158C2×C4×D9—61no—
159C2×C4×D9C2×D311yescharacteristic
160C2×Dic18—31no—
161C9×C4⋊C4—31no—
162C9×C4⋊C4—31no—
163C9×C4⋊C4—31no—
164C9×C22⋊C4—31no—
165C9×C22⋊C4—31no—
166C9×C22⋊C4—31no—
167C42×C9—21no—
168C42×C9C2×D311yescharacteristic, complemented
169#3676—31no—
170#3676—31no—
171(C2×D9)⋊C4—31no—
172(C2×D9)⋊C4—31no—
173(C2×D9)⋊C4—31no—
174(C2×D9)⋊C4—31no—
175(C2×D9)⋊C4—31no—
176(C2×D9)⋊C4—31no—
177(C2×D9)⋊C4—31no—
178(C2×D9)⋊C4—61no—
179(C2×D9)⋊C4—61no—
180(C2×D9)⋊C4C2×D311yescharacteristic
181(C2×D9)⋊C4C2×D311yescharacteristic
182C4⋊Dic9—31no—
183C4⋊Dic9—31no—
184C4⋊Dic9—61no—
185Dic9⋊C4—31no—
186Dic9⋊C4C2×D311yescharacteristic, complemented
187Dic9⋊C4C2×D311yescharacteristic, complemented
188C4×Dic9—31no—
189C4×Dic9C2×D311yescharacteristic, complemented
190C22×C3×C9C2411yescharacteristic
191C2×C3⋊D9—21no—
192C2×C3⋊D9—21no—
193C2×C3⋊D9—21no—
194C2×C3⋊D9—21no—
195C2×C3⋊D9—21no—
196C2×C3⋊D9#4112yes—
197C2×D3×C9—21no—
198C2×D3×C9—21no—
199C2×D3×C9—21no—
200C2×C3×D9—21no—
201C2×C3×D9—21no—
202C2×C3×D9#4112yes—
203D3×D9—44no—
204C3×C4×C9—21no—
205C3×C4×C9—21no—
206C3×C4×C9—21no—
207C3⋊Dic9—21no—
208C3⋊Dic9—21no—
209C9×Dic3—21no—
210C9×Dic3—21no—
211C9×Dic3—21no—
212C3×Dic9—21no—
213C3×Dic9—21no—
214C3×Dic9—21no—
215C3×#126—31no—
216C3×#117—91no—
217#929—91no—
218C2×(C2×D3)⋊C4—91no—
219#898—91no—
220#897—91no—
221#896—91no—
222#896—91no—
223#894—91no—
224#894—91no—
225#894—91no—
226#894—91no—
227#893—91no—
228#892—91no—
229#885—91no—
230#883—91no—
231#882—91no—
232#882—91no—
233#67⋊C4—91no—
234D3×C22⋊C4—91no—
235D3×C22⋊C4—91no—
236D3×C22⋊C4—91no—
237#879—91no—
238#878—91no—
239#876D911yescharacteristic, complemented
240#875—91no—
241C4×D12—91no—
242C4×D12—91no—
243C4×D12—181no—
244#872—31no—
245#872—91no—
246C22×C3⋊D3—31no—
247C22×C3⋊D3—31no—
248C22×C3×D3—31no—
249C22×C3×D3C22×D311yescharacteristic
250C2×D32—62no—
251C2×D32—62no—
252C2×D32—121no—
253C2×C32×C4C22×D311yescharacteristic
254C2×C32×C4C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256C2×C3⋊Dic3—31no—
257C2×C3⋊Dic3—31no—
258C4⋊(C3⋊D3)—62no—
259C4×C3⋊D3—121no—
260C4×C3⋊D3—121no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3C22×D311yescharacteristic
265C2×C3×Dic3C22×D311yescharacteristic
266C2×C3×Dic3C22×D311yescharacteristic
267C3×C4×D3—62no—
268#627—121no—
269#626—62no—
270#626—121no—
271#624—62no—
272D3×Dic3—121no—
273C23×C9—31no—
274C22×D9—31no—
275C22×D9—31no—
276C22×D9—61no—
277C22×D9—61no—
278C22×D9—62no—
279C22×D9—62no—
280C22×D9—121no—
281C22×D9C22×D311yescharacteristic
282C2×C4×C9—21no—
283C2×C4×C9—21no—
284C2×C4×C9—21no—
285C2×C4×C9—31no—
286C2×C4×C9—31no—
287C2×C4×C9—31no—
288C2×C4×C9C22×D311yescharacteristic
289C2×C4×C9C22×D311yescharacteristic
290C2×C4×C9C22×D311yescharacteristic
291#611—121no—
292C2×Dic9—31no—
293C2×Dic9—31no—
294C2×Dic9—61no—
295C2×Dic9—61no—
296C2×Dic9C22×D311yescharacteristic
297C2×Dic9C22×D311yescharacteristic
298C2×Dic9C22×D311yescharacteristic
299D36—62no—
300D36—64no—
301D36—62no—
302C4×D9—22no—
303C4×D9—62no—
304C4×D9—121no—
305C4×D9—121no—
306C4×D9—121no—
307C4×D9—122no—
308C4×D9—122no—
309Dic18—121no—
310#551—271noSylow
311C2×C3×C9C2×#4111yescharacteristic
312C2×C3×C9C2×#4111yescharacteristic
313C2×C3×C9H(5,𝔽2)11yescharacteristic
314C3⋊D9—22no—
315C3⋊D9—41no—
316D3×C9—41no—
317C3×D9—22no—
318C23×D3—91no—
319C23×D3—91no—
320C22×C3×C4—91no—
321C2×#67—91no—
322C2×#67—91no—
323C22×Dic3—91no—
324C2×D12—91no—
325C2×D12—91no—
326C2×D12—91no—
327C2×D12—91no—
328C2×D12—181no—
329C2×C4×D3—31no—
330C2×C4×D3—91no—
331C2×C4×D3—91no—
332C2×C4×D3—91no—
333C2×C4×D3—91no—
334C2×C4×D3—91no—
335C2×C4×D3—91no—
336C2×C4×D3—91no—
337C2×C4×D3—181no—
338C2×C4×D3—181no—
339C2×Dic6—91no—
340C2×Dic6—91no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—91no—
345C3×C4⋊C4—91no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—31no—
349C3×C22⋊C4—91no—
350C3×C22⋊C4—91no—
351C3×C42—21no—
352C3×C42—91no—
353C3×C42C2×D911yescharacteristic, complemented
354C3×C42D3211yescharacteristic
355#217—91no—
356#217—91no—
357#217—91no—
358(C2×D3)⋊C4—31no—
359(C2×D3)⋊C4—31no—
360(C2×D3)⋊C4—91no—
361(C2×D3)⋊C4—91no—
362(C2×D3)⋊C4—91no—
363(C2×D3)⋊C4—91no—
364(C2×D3)⋊C4—91no—
365(C2×D3)⋊C4—91no—
366(C2×D3)⋊C4—91no—
367(C2×D3)⋊C4—91no—
368(C2×D3)⋊C4—91no—
369(C2×D3)⋊C4—91no—
370(C2×D3)⋊C4—91no—
371(C2×D3)⋊C4—91no—
372(C2×D3)⋊C4—91no—
373(C2×D3)⋊C4—91no—
374(C2×D3)⋊C4—91no—
375(C2×D3)⋊C4—181no—
376(C2×D3)⋊C4—181no—
377(C2×D3)⋊C4C2×D911yescharacteristic
378(C2×D3)⋊C4C2×D911yescharacteristic
379(C2×D3)⋊C4C2×D911yescharacteristic
380C4⋊Dic3—91no—
381C4⋊Dic3—91no—
382C4⋊Dic3—91no—
383C4⋊Dic3—181no—
384Dic3⋊C4—31no—
385Dic3⋊C4—31no—
386Dic3⋊C4—91no—
387Dic3⋊C4—91no—
388Dic3⋊C4—91no—
389Dic3⋊C4C2×D911yescharacteristic, complemented
390Dic3⋊C4C2×D911yescharacteristic, complemented
391Dic3⋊C4C2×D911yescharacteristic, complemented
392C4×Dic3—31no—
393C4×Dic3—91no—
394C4×Dic3—91no—
395C22×C32C23×D311yescharacteristic
396C2×C3⋊D3—32no—
397C2×C3⋊D3—61no—
398C2×C3⋊D3—61no—
399C2×C3⋊D3—61no—
400C2×C3⋊D3—61no—
401C2×C3⋊D3—61no—
402C2×C3×D3—21no—
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—32no—
406C2×C3×D3—61no—
407C2×C3×D3—61no—
408D32—124no—
409C32×C4—21no—
410C32×C4—21no—
411C32×C4—21no—
412C3⋊Dic3—61no—
413C3⋊Dic3—61no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—61no—
418C3×Dic3—61no—
419C3×Dic3—61no—
420C22×C9—21no—
421C22×C9—61no—
422C22×C9—61no—
423C22×C9—61no—
424C22×C9C23×D311yescharacteristic
425C2×D9—21no—
426C2×D9—21no—
427C2×D9—32no—
428C2×D9—62no—
429C2×D9—61no—
430C2×D9—61no—
431C2×D9—62no—
432C2×D9—61no—
433C2×D9—61no—
434C2×D9—61no—
435C2×D9—121no—
436C2×D9—121no—
437C2×D9—121no—
438C2×D9—121no—
439C2×D9—124no—
440C2×D9#23512yes—
441C4×C9—22no—
442C4×C9—22no—
443C4×C9—21no—
444C4×C9—21no—
445C4×C9—21no—
446C4×C9—41no—
447C4×C9—61no—
448C4×C9—61no—
449C4×C9—61no—
450Dic9—21no—
451Dic9—21no—
452Dic9—21no—
453Dic9—61no—
454Dic9—61no—
455Dic9—121no—
456Dic9—121no—
457#126—31no—
458#126—271no—
459#124—271no—
460#123—271no—
461#123—271no—
462#123—271no—
463C22⋊Q8—271no—
464C22⋊Q8—271no—
465#120—271no—
466C4×D4—271no—
467C4×D4—271no—
468#117—91no—
469#117—271no—
470C2×C22⋊C4—271no—
471C2×C22⋊C4—271no—
472C3×C9#55111yescharacteristic, complemented, Sylow
473C23×C3—31no—
474C23×C3—91no—
475C22×D3—31no—
476C22×D3—91no—
477C22×D3—91no—
478C22×D3—91no—
479C22×D3—91no—
480C22×D3—181no—
481C22×D3—181no—
482C22×D3—182no—
483C22×D3—182no—
484C22×D3—182no—
485C22×D3—182no—
486C22×D3—361no—
487C22×D3—361no—
488C22×D3C22×D911yescharacteristic
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—91no—
496C2×C3×C4—91no—
497C2×C3×C4—91no—
498C2×C3×C4—182no—
499C2×C3×C4C22×D911yescharacteristic
500C2×C3×C4C22×D911yescharacteristic
501C2×C3×C4C22×D911yescharacteristic
502C2×C3×C4C2×D3211yescharacteristic
503C2×C3×C4C2×D3211yescharacteristic
504C2×C3×C4C2×D3211yescharacteristic
505#67—182no—
506#67—361no—
507C2×Dic3—31no—
508C2×Dic3—31no—
509C2×Dic3—31no—
510C2×Dic3—91no—
511C2×Dic3—91no—
512C2×Dic3—91no—
513C2×Dic3—91no—
514C2×Dic3—181no—
515C2×Dic3—181no—
516C2×Dic3—361no—
517C2×Dic3C22×D911yescharacteristic
518C2×Dic3C22×D911yescharacteristic
519C2×Dic3C22×D911yescharacteristic
520D12—182no—
521D12—182no—
522D12—184no—
523D12—182no—
524D12—361no—
525C4×D3—62no—
526C4×D3—182no—
527C4×D3—182no—
528C4×D3—361no—
529C4×D3—361no—
530C4×D3—361no—
531C4×D3—361no—
532C4×D3—361no—
533C4×D3—362no—
534C4×D3—362no—
535Dic6—361no—
536Dic6—361no—
537C2×C32D3×#4111yescharacteristic
538C2×C32D3×#4111yescharacteristic
539C2×C32#100911yescharacteristic
540C3⋊D3—62no—
541C3⋊D3—121no—
542C3×D3—41no—
543C3×D3—62no—
544C2×C9—21no—
545C2×C9—21no—
546C2×C9—21no—
547C2×C9—121no—
548C2×C9C2×#23511yescharacteristic
549C2×C9D3×#4111yescharacteristic
550C2×C9#100911yescharacteristic
551D9—22no—
552D9—62no—
553D9—122no—
554D9—122no—
555D9—121no—
556C24—271no—
557C2×Q8—271no—
558C2×D4—271no—
559C2×D4—271no—
560C2×D4—271no—
561C22×C4—91no—
562C22×C4—271no—
563C22×C4—271no—
564C22×C4—271no—
565C22×C4—271no—
566C4⋊C4—31no—
567C4⋊C4—31no—
568C4⋊C4—31no—
569C4⋊C4—91no—
570C4⋊C4—91no—
571C4⋊C4—271no—
572C4⋊C4—271no—
573C4⋊C4—271no—
574C22⋊C4—31no—
575C22⋊C4—31no—
576C22⋊C4—31no—
577C22⋊C4—91no—
578C22⋊C4—91no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22⋊C4—271no—
583C22⋊C4—271no—
584C22⋊C4—271no—
585C22⋊C4—271no—
586C22⋊C4—271no—
587C22⋊C4—271no—
588C42—91no—
589C42—271no—
590C42D3×D911yescharacteristic, complemented
591C22×C3—21no—
592C22×C3—61no—
593C22×C3—61no—
594C22×C3—61no—
595C22×C3—92no—
596C22×C3—181no—
597C22×C3—181no—
598C22×C3C23×D911yescharacteristic
599C22×C3C22×D3211yescharacteristic
600C2×D3—21no—
601C2×D3—21no—
602C2×D3—21no—
603C2×D3—32no—
604C2×D3—61no—
605C2×D3—61no—
606C2×D3—92no—
607C2×D3—92no—
608C2×D3—182no—
609C2×D3—181no—
610C2×D3—181no—
611C2×D3—181no—
612C2×D3—181no—
613C2×D3—182no—
614C2×D3—181no—
615C2×D3—181no—
616C2×D3—181no—
617C2×D3—181no—
618C2×D3—181no—
619C2×D3—181no—
620C2×D3—361no—
621C2×D3—361no—
622C2×D3—361no—
623C2×D3—361no—
624C2×D3—364no—
625C2×D3—364no—
626C3×C4—22no—
627C3×C4—22no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—41no—
635C3×C4—61no—
636C3×C4—61no—
637C3×C4—61no—
638C3×C4—181no—
639C3×C4—181no—
640C3×C4—181no—
641Dic3—21no—
642Dic3—21no—
643Dic3—21no—
644Dic3—61no—
645Dic3—61no—
646Dic3—61no—
647Dic3—181no—
648Dic3—181no—
649Dic3—181no—
650Dic3—181no—
651Dic3—361no—
652Dic3—361no—
653C32#570511yescharacteristic
654C9—21no—
655C9#552711yescharacteristic, complemented
656C23—31no—
657C23—91no—
658C23—271no—
659C23—271no—
660C23—542no—
661C23—542no—
662C23—1081no—
663Q8—1081no—
664D4—542no—
665D4—542no—
666D4—1081no—
667C2×C4—31no—
668C2×C4—31no—
669C2×C4—31no—
670C2×C4—91no—
671C2×C4—91no—
672C2×C4—91no—
673C2×C4—182no—
674C2×C4—271no—
675C2×C4—271no—
676C2×C4—542no—
677C2×C4—1081no—
678C2×C4—1081no—
679C2×C4—1081no—
680C2×C4C2×D3×D911yescharacteristic
681C2×C4C2×D3×D911yescharacteristic
682C2×C4C2×D3×D911yescharacteristic
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—121no—
687C2×C3—182no—
688C2×C3#41×D911yescharacteristic
689C2×C3#41×D911yescharacteristic
690C2×C3#6371511yescharacteristic
691C2×C3D3×#23511yescharacteristic
692C2×C3#6430611yescharacteristic
693C2×C3#6430811yescharacteristic
694D3—41no—
695D3—62no—
696D3—182no—
697D3—182no—
698D3—362no—
699D3—362no—
700D3—361no—
701D3—361no—
702C22—61no—
703C22—61no—
704C22—61no—
705C22—92no—
706C22—181no—
707C22—181no—
708C22—272no—
709C22—541no—
710C22—541no—
711C22—541no—
712C22—541no—
713C22—541no—
714C22—1084no—
715C22C22×D3×D911yescharacteristic
716C4—21no—
717C4—21no—
718C4—21no—
719C4—61no—
720C4—61no—
721C4—61no—
722C4—181no—
723C4—181no—
724C4—181no—
725C4—541no—
726C4—541no—
727C3—21no—
728C3#1058980711yescharacteristic, complemented
729C3#1059401711yescharacteristic
730C2—121no—
731C2—182no—
732C2—542no—
733C2—1081no—
734C2D9×#23511yescharacteristic
735C2#1172247511yescharacteristic
736C2#1172247811yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C42×C9C22
socleC22×C32C23×D3
prime radical#11721051C2
hypercenterC42D3×D9
hypocenterC3×C9#551
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C4×C4⋊(C3⋊D9)C2semidirect
2. C9×#876C2semidirect
3. C3×#63434C2semidirect
5. #11721048C2semidirect
6. D9×(C2×D3)⋊C4C2semidirect
7. #11720997C2semidirect
8. #11720991C2semidirect
9. #11720978C2semidirect
10. #11720965C2semidirect
11. #11720957C2semidirect
12. #11720956C2semidirect
13. #11720938C2semidirect
14. #11720923C2semidirect
15. #11720899C2semidirect
21. C2×C4×C3⋊D9C22semidirect
27. C2×#6189C22semidirect
28. C3×C42×C9C22semidirect
30. #88536C22semidirect
31. C4⋊(C3⋊Dic9)C22semidirect
37. C9×Dic3⋊C4C22semidirect
38. C9×Dic3⋊C4C22semidirect
39. C9×Dic3⋊C4C22semidirect
40. C3×Dic9⋊C4C22semidirect
41. C3×Dic9⋊C4C22semidirect
42. C3×C4×Dic9C22semidirect
47. #88445C22semidirect
48. #88445C22semidirect
50. Dic3⋊Dic9C22semidirect
51. #88442C22semidirect
52. Dic3×Dic9C22semidirect
83. #63434D3semidirect
168. C42×C9C2×D3semidirect
186. Dic9⋊C4C2×D3semidirect
187. Dic9⋊C4C2×D3semidirect
189. C4×Dic9C2×D3semidirect
239. #876D9semidirect
353. C3×C42C2×D9semidirect
389. Dic3⋊C4C2×D9semidirect
390. Dic3⋊C4C2×D9semidirect
391. Dic3⋊C4C2×D9semidirect
472. C3×C9#551semidirect
590. C42D3×D9semidirect
655. C9#5527semidirect
728. C3#10589807semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊(C3⋊D9)2
C9×#8762
C3×#634342
#117210512
#117210482
D9×(C2×D3)⋊C42
#117209972
#117209912
#117209782
#117209652
#117209572
#117209562
#117209382
#117209232
#117208992
#105940173
#105898073