Finite Group Databasebeta

← #13149330

Subgroups — #13149330

Order 1728.

800 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721752C211yesmaximal, characteristic, complemented
2C9×#896C211yesmaximal, characteristic, complemented
3C3×#63459C211yesmaximal, characteristic, complemented
4#11721048C211yesmaximal, characteristic
5D3×(C2×D9)⋊C4C211yesmaximal, characteristic
6D9×(C2×D3)⋊C4C211yesmaximal, characteristic
7#11721026C211yesmaximal, characteristic, complemented
8#11721018C211yesmaximal, characteristic, complemented
9#11720996C211yesmaximal, characteristic, complemented
10#11720995C211yesmaximal, characteristic, complemented
11#11720985C211yesmaximal, characteristic, complemented
12#11720984C211yesmaximal, characteristic, complemented
13#11720961C211yesmaximal, characteristic, complemented
14#11720939C211yesmaximal, characteristic, complemented
15#11720929C211yesmaximal, characteristic, complemented
16#10594635—31nomaximal
17#10589736—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×C4×C3⋊D9C2211yescharacteristic
20C2×#6226C2211yescharacteristic, complemented
21C2×C4×D3×C9C2211yescharacteristic
22C2×C3×C4×D9C2211yescharacteristic
23C2×C9×Dic6C2211yescharacteristic, complemented
24C2×C3×Dic18C2211yescharacteristic, complemented
25C2×D3×Dic9C2211yescharacteristic
26C2×(C3⋊D9)⋊C4C2211yescharacteristic
27C2×Dic3×D9C2211yescharacteristic
28C2×#6189C2211yescharacteristic, complemented
29C3×C9×C4⋊C4C2211yescharacteristic, complemented
30#88536C2211yescharacteristic
31#88536C2211yescharacteristic
32#88534C2211yescharacteristic, complemented
33#88534C2211yescharacteristic, complemented
34C9×(C2×D3)⋊C4C2211yescharacteristic
35C9×(C2×D3)⋊C4C2211yescharacteristic
36C3×(C2×D9)⋊C4C2211yescharacteristic
37C3×(C2×D9)⋊C4C2211yescharacteristic
38C9×Dic3⋊C4C2211yescharacteristic, complemented
39C9×Dic3⋊C4C2211yescharacteristic, complemented
40C3×C4⋊Dic9C2211yescharacteristic, complemented
41C3×C4⋊Dic9C2211yescharacteristic, complemented
42(C2×D3)⋊Dic9C2211yescharacteristic
43(C2×D3)⋊Dic9C2211yescharacteristic
44#88445C2211yescharacteristic
45#88445C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47(C2×D9)⋊Dic3C2211yescharacteristic
48Dic3⋊Dic9C2211yescharacteristic, complemented
49#88442C2211yescharacteristic, complemented
50Dic9⋊Dic3C2211yescharacteristic, complemented
51Dic9⋊Dic3C2211yescharacteristic, complemented
52Dic9⋊Dic3C2211yescharacteristic, complemented
53#64105—31no—
54C3×#897—31no—
55C3×#896D311yescharacteristic
56#63921—31no—
57D3×(C2×D3)⋊C4—31no—
58D3×(C2×D3)⋊C4—31no—
59#63899—31no—
60#63896—31no—
61#63895—31no—
62#63888—31no—
63#63887—31no—
64#63887—31no—
65#63871—31no—
66#63857—31no—
67#63851—31no—
68C9×C22⋊Q8—31no—
69#63508—31no—
70#63508—31no—
71C2×(C2×D9)⋊C4—31no—
72#63486—31no—
73#63459—31no—
74#63459D311yescharacteristic, complemented
75#63458—31no—
76#63458—31no—
77#63458—31no—
78#63458—31no—
79#63458—61no—
80C22⋊C4×D9—31no—
81C22⋊C4×D9—31no—
82#63440—31no—
83#63440—31no—
84C22×C3⋊D9C2311yescharacteristic
85C22×D3×C9C2311yescharacteristic
86C22×C3×D9C2311yescharacteristic
87C2×D3×D9—41no—
88C2×D3×D9—41no—
89C2×D3×D9Q814yescomplemented
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C4×C3⋊D9—41no—
97#6226—41no—
98C2×C9×Dic3C2311yescharacteristic
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C4×D3×C9—41no—
105C3×C4×D9—41no—
106C9×Dic6—41no—
107C3×Dic18—41no—
108D3×Dic9—41no—
109(C3⋊D9)⋊C4—41no—
110Dic3×D9—41no—
111#6189—41no—
112#5634—91no—
113#5634—91no—
114C22×D32—31no—
115C2×C4×C3⋊D3—31no—
116C2×#634—31no—
117C2×C3×C4×D3—31no—
118C2×C3×C4×D3C2×D311yescharacteristic
119C2×C3×Dic6—31no—
120C2×C3×Dic6C2×D311yescharacteristic
121C2×#627—31no—
122C2×#624—31no—
123C2×D3×Dic3—31no—
124C2×D3×Dic3—31no—
125C23×D9—31no—
126C32×C4⋊C4C2×D311yescharacteristic
127#3752—31no—
128#3752—31no—
129#3750—31no—
130#3750—31no—
131C3×(C2×D3)⋊C4—31no—
132C3×(C2×D3)⋊C4—31no—
133C3×(C2×D3)⋊C4C2×D311yescharacteristic
134C3×(C2×D3)⋊C4C2×D311yescharacteristic
135C3×C4⋊Dic3—31no—
136C3×C4⋊Dic3—31no—
137C3×Dic3⋊C4C2×D311yescharacteristic
138C3×Dic3⋊C4C2×D311yescharacteristic
139#3724—31no—
140Dic3⋊Dic3—31no—
141Dic3⋊Dic3—31no—
142Dic3⋊Dic3—31no—
143Dic3⋊Dic3—31no—
144#3722—31no—
145#3722—31no—
146(C2×D3)⋊Dic3—31no—
147(C2×D3)⋊Dic3—31no—
148(C2×D3)⋊Dic3—31no—
149(C2×D3)⋊Dic3—31no—
150C2×Q8×C9—31no—
151C22×C4×C9—31no—
152C22×Dic9—31no—
153C2×C4×D9—31no—
154C2×C4×D9—31no—
155C2×C4×D9—31no—
156C2×C4×D9—61no—
157C2×C4×D9C2×D311yescharacteristic
158C2×Dic18—31no—
159C2×Dic18—31no—
160C2×Dic18—61no—
161C2×Dic18C2×D311yescharacteristic, complemented
162C9×C4⋊C4—21no—
163C9×C4⋊C4—31no—
164C9×C4⋊C4—31no—
165C9×C4⋊C4C2×D311yescharacteristic, complemented
166C9×C22⋊C4—31no—
167C9×C22⋊C4—31no—
168#3676—31no—
169#3676—31no—
170(C2×D9)⋊C4—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—61no—
177(C2×D9)⋊C4—61no—
178(C2×D9)⋊C4C2×D311yescharacteristic
179(C2×D9)⋊C4C2×D311yescharacteristic
180C4⋊Dic9—31no—
181C4⋊Dic9C2×D311yescharacteristic, complemented
182C4⋊Dic9C2×D311yescharacteristic, complemented
183Dic9⋊C4—31no—
184Dic9⋊C4—31no—
185Dic9⋊C4—31no—
186Dic9⋊C4—31no—
187Dic9⋊C4—31no—
188Dic9⋊C4—31no—
189Dic9⋊C4—61no—
190Dic9⋊C4—61no—
191C22×C3×C9C2411yescharacteristic
192C2×C3⋊D9—21no—
193C2×C3⋊D9—21no—
194C2×C3⋊D9C2×Q812yes—
195C2×D3×C9—21no—
196C2×D3×C9—21no—
197C2×D3×C9C2×Q812yes—
198C2×C3×D9—21no—
199C2×C3×D9—21no—
200C2×C3×D9C2×Q812yes—
201D3×D9—44no—
202C3×C4×C9—21no—
203C3×C4×C9—21no—
204C3×C4×C9—21no—
205C3⋊Dic9—21no—
206C3⋊Dic9—21no—
207C3⋊Dic9—21no—
208C9×Dic3—21no—
209C9×Dic3—21no—
210C9×Dic3—21no—
211C3×Dic9—21no—
212C3×Dic9—21no—
213C3×Dic9—21no—
214C3×C22⋊Q8—31no—
215C3×C22⋊Q8—91no—
216#946—91no—
217#946—91no—
218#946—91no—
219#946—91no—
220C2×(C2×D3)⋊C4—91no—
221C2×(C2×D3)⋊C4—91no—
222#924—91no—
223#924—91no—
224#897—31no—
225#897—91no—
226#897—91no—
227#897—91no—
228#896—91no—
229#896—91no—
230#896—91no—
231#896—91no—
232#896—91no—
233#896—91no—
234#896—91no—
235#896—181no—
236#896D911yescharacteristic, complemented
237D3×C22⋊C4—91no—
238D3×C22⋊C4—91no—
239D3×C22⋊C4—91no—
240D3×C22⋊C4—91no—
241#878—91no—
242#878—91no—
243#878—91no—
244#878—91no—
245C22×C3⋊D3—31no—
246C22×C3×D3—31no—
247C22×C3×D3C22×D311yescharacteristic
248C2×D32—34no—
249C2×D32—121no—
250C2×D32—121no—
251C2×C32×C4C22×D311yescharacteristic
252C2×C32×C4C22×D311yescharacteristic
253C2×C32×C4C22×D311yescharacteristic
254C2×C3⋊Dic3—31no—
255C2×C3⋊Dic3—31no—
256C2×C3⋊Dic3—31no—
257C4×C3⋊D3—121no—
258#634—121no—
259C2×C3×Dic3—31no—
260C2×C3×Dic3—31no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3C22×D311yescharacteristic
263C2×C3×Dic3C22×D311yescharacteristic
264C2×C3×Dic3C22×D311yescharacteristic
265C3×C4×D3—41no—
266C3×C4×D3—121no—
267C3×Dic6—41no—
268C3×Dic6—121no—
269#627—121no—
270#624—121no—
271D3×Dic3—121no—
272D3×Dic3—121no—
273C23×C9—31no—
274C22×D9—31no—
275C22×D9—34no—
276C22×D9—61no—
277C22×D9—121no—
278C22×D9—121no—
279C22×D9C22×D311yescharacteristic
280Q8×C9—121no—
281C2×C4×C9—21no—
282C2×C4×C9—21no—
283C2×C4×C9—21no—
284C2×C4×C9—31no—
285C2×C4×C9—31no—
286C2×C4×C9—31no—
287C2×C4×C9—121no—
288C2×C4×C9C22×D311yescharacteristic
289C2×C4×C9C22×D311yescharacteristic
290C2×C4×C9C22×D311yescharacteristic
291C2×Dic9—31no—
292C2×Dic9—31no—
293C2×Dic9—31no—
294C2×Dic9—61no—
295C2×Dic9—61no—
296C2×Dic9—61no—
297C2×Dic9—121no—
298C2×Dic9C22×D311yescharacteristic
299C2×Dic9C22×D311yescharacteristic
300C2×Dic9C22×D311yescharacteristic
301C4×D9—41no—
302C4×D9—121no—
303C4×D9—121no—
304C4×D9—122no—
305C4×D9—121no—
306Dic18—41no—
307Dic18—121no—
308Dic18—121no—
309Dic18—122no—
310#543—271noSylow
311C2×C3×C9C22×Q811yescharacteristic
312C2×C3×C9H(5,𝔽2)11yescharacteristic
313C2×C3×C9H(5,𝔽2)11yescharacteristic
314C3⋊D9—22no—
315D3×C9—22no—
316C3×D9—22no—
317C23×D3—91no—
318C23×D3—91no—
319C2×C3×Q8—31no—
320C2×C3×Q8—91no—
321C22×C3×C4—31no—
322C22×C3×C4—91no—
323C22×Dic3—91no—
324C22×Dic3—91no—
325C2×C4×D3—31no—
326C2×C4×D3—91no—
327C2×C4×D3—91no—
328C2×C4×D3—91no—
329C2×C4×D3—91no—
330C2×C4×D3—91no—
331C2×C4×D3—91no—
332C2×C4×D3—181no—
333C2×C4×D3C2×D911yescharacteristic
334C2×Dic6—31no—
335C2×Dic6—91no—
336C2×Dic6—91no—
337C2×Dic6—91no—
338C2×Dic6—91no—
339C2×Dic6—181no—
340C2×Dic6C2×D911yescharacteristic, complemented
341C3×C4⋊C4—21no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—91no—
345C3×C4⋊C4—91no—
346C3×C4⋊C4C2×D911yescharacteristic, complemented
347C3×C4⋊C4D3211yescharacteristic
348C3×C22⋊C4—31no—
349C3×C22⋊C4—31no—
350C3×C22⋊C4—91no—
351C3×C22⋊C4—91no—
352#217—91no—
353#217—91no—
354#217—91no—
355#217—91no—
356(C2×D3)⋊C4—31no—
357(C2×D3)⋊C4—31no—
358(C2×D3)⋊C4—91no—
359(C2×D3)⋊C4—91no—
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—181no—
371(C2×D3)⋊C4—181no—
372(C2×D3)⋊C4C2×D911yescharacteristic
373(C2×D3)⋊C4C2×D911yescharacteristic
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—91no—
377C4⋊Dic3—91no—
378C4⋊Dic3—91no—
379C4⋊Dic3—91no—
380Dic3⋊C4—91no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—91no—
385Dic3⋊C4—91no—
386Dic3⋊C4—91no—
387Dic3⋊C4—91no—
388Dic3⋊C4—91no—
389Dic3⋊C4—91no—
390Dic3⋊C4—181no—
391Dic3⋊C4—181no—
392Dic3⋊C4C2×D911yescharacteristic, complemented
393Dic3⋊C4C2×D911yescharacteristic, complemented
394C22×C32C23×D311yescharacteristic
395C2×C3⋊D3—32no—
396C2×C3⋊D3—61no—
397C2×C3⋊D3—61no—
398C2×C3×D3—21no—
399C2×C3×D3—21no—
400C2×C3×D3—32no—
401C2×C3×D3—61no—
402C2×C3×D3—61no—
403C2×C3×D3D3×Q812yes—
404D32—124no—
405C32×C4—21no—
406C32×C4—21no—
407C32×C4—21no—
408C3⋊Dic3—61no—
409C3⋊Dic3—61no—
410C3⋊Dic3—61no—
411C3×Dic3—21no—
412C3×Dic3—21no—
413C3×Dic3—21no—
414C3×Dic3—61no—
415C3×Dic3—61no—
416C3×Dic3—61no—
417C22×C9—21no—
418C22×C9—32no—
419C22×C9—61no—
420C22×C9—61no—
421C22×C9C23×D311yescharacteristic
422C2×D9—21no—
423C2×D9—21no—
424C2×D9—32no—
425C2×D9—62no—
426C2×D9—61no—
427C2×D9—61no—
428C2×D9—121no—
429C2×D9—121no—
430C2×D9—124no—
431C2×D9D3×Q812yes—
432C4×C9—21no—
433C4×C9—21no—
434C4×C9—21no—
435C4×C9—41no—
436C4×C9—41no—
437C4×C9—41no—
438C4×C9—61no—
439C4×C9—61no—
440C4×C9—61no—
441Dic9—21no—
442Dic9—21no—
443Dic9—21no—
444Dic9—62no—
445Dic9—61no—
446Dic9—61no—
447Dic9—61no—
448Dic9—121no—
449Dic9—121no—
450C22⋊Q8—31no—
451C22⋊Q8—91no—
452C22⋊Q8—271no—
453C22⋊Q8—271no—
454C22⋊Q8—271no—
455C22⋊Q8—271no—
456C22⋊Q8—271no—
457C22⋊Q8—271no—
458C22⋊Q8—271no—
459C22⋊Q8—271no—
460C22⋊Q8—271no—
461C22⋊Q8—271no—
462C2×C22⋊C4—271no—
463C2×C22⋊C4—271no—
464C2×C22⋊C4—271no—
465C3×C9#54311yescharacteristic, complemented, Sylow
466C23×C3—31no—
467C23×C3—91no—
468C22×D3—31no—
469C22×D3—94no—
470C22×D3—91no—
471C22×D3—91no—
472C22×D3—94no—
473C22×D3—181no—
474C22×D3—361no—
475C22×D3—361no—
476C22×D3—361no—
477C22×D3—361no—
478C22×D3C22×D911yescharacteristic
479C3×Q8—121no—
480C3×Q8—361no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—31no—
487C2×C3×C4—91no—
488C2×C3×C4—91no—
489C2×C3×C4—91no—
490C2×C3×C4—121no—
491C2×C3×C4—361no—
492C2×C3×C4C22×D911yescharacteristic
493C2×C3×C4C22×D911yescharacteristic
494C2×C3×C4C22×D911yescharacteristic
495C2×C3×C4C2×D3211yescharacteristic
496C2×C3×C4C2×D3211yescharacteristic
497C2×C3×C4C2×D3211yescharacteristic
498C2×Dic3—31no—
499C2×Dic3—31no—
500C2×Dic3—31no—
501C2×Dic3—91no—
502C2×Dic3—91no—
503C2×Dic3—91no—
504C2×Dic3—91no—
505C2×Dic3—91no—
506C2×Dic3—91no—
507C2×Dic3—181no—
508C2×Dic3—181no—
509C2×Dic3—181no—
510C2×Dic3—361no—
511C2×Dic3—361no—
512C2×Dic3C22×D911yescharacteristic
513C2×Dic3C22×D911yescharacteristic
514C2×Dic3C22×D911yescharacteristic
515C4×D3—41no—
516C4×D3—121no—
517C4×D3—361no—
518C4×D3—361no—
519C4×D3—361no—
520C4×D3—361no—
521C4×D3—362no—
522C4×D3—361no—
523C4×D3—361no—
524Dic6—41no—
525Dic6—121no—
526Dic6—361no—
527Dic6—361no—
528Dic6—361no—
529Dic6—361no—
530Dic6—362no—
531C2×C32#100411yescharacteristic
532C2×C32C2×D3×Q811yescharacteristic
533C2×C32#100911yescharacteristic
534C3⋊D3—62no—
535C3×D3—22no—
536C3×D3—62no—
537C2×C9—21no—
538C2×C9—21no—
539C2×C9—21no—
540C2×C9—62no—
541C2×C9#100411yescharacteristic
542C2×C9C2×D3×Q811yescharacteristic
543C2×C9#100911yescharacteristic
544D9—22no—
545D9—62no—
546D9—122no—
547C24—271no—
548C2×Q8—31no—
549C2×Q8—91no—
550C2×Q8—271no—
551C2×Q8—271no—
552C22×C4—31no—
553C22×C4—91no—
554C22×C4—271no—
555C22×C4—271no—
556C22×C4—271no—
557C22×C4—271no—
558C4⋊C4—31no—
559C4⋊C4—31no—
560C4⋊C4—91no—
561C4⋊C4—91no—
562C4⋊C4—271no—
563C4⋊C4—271no—
564C4⋊C4—271no—
565C4⋊C4—271no—
566C4⋊C4—271no—
567C4⋊C4—271no—
568C4⋊C4—271no—
569C4⋊C4D3×D911yescharacteristic, complemented
570C22⋊C4—31no—
571C22⋊C4—31no—
572C22⋊C4—91no—
573C22⋊C4—91no—
574C22⋊C4—271no—
575C22⋊C4—271no—
576C22⋊C4—271no—
577C22⋊C4—271no—
578C22⋊C4—271no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22×C3—21no—
583C22×C3—32no—
584C22×C3—61no—
585C22×C3—61no—
586C22×C3—92no—
587C22×C3—181no—
588C22×C3—181no—
589C22×C3C23×D911yescharacteristic
590C22×C3C22×D3211yescharacteristic
591C2×D3—21no—
592C2×D3—21no—
593C2×D3—32no—
594C2×D3—61no—
595C2×D3—61no—
596C2×D3—92no—
597C2×D3—92no—
598C2×D3—182no—
599C2×D3—181no—
600C2×D3—181no—
601C2×D3—181no—
602C2×D3—181no—
603C2×D3—361no—
604C2×D3—361no—
605C2×D3—364no—
606C2×D3—364no—
607C2×D3Q8×D912yes—
608C3×C4—21no—
609C3×C4—21no—
610C3×C4—21no—
611C3×C4—21no—
612C3×C4—21no—
613C3×C4—21no—
614C3×C4—41no—
615C3×C4—41no—
616C3×C4—41no—
617C3×C4—61no—
618C3×C4—61no—
619C3×C4—61no—
620C3×C4—181no—
621C3×C4—181no—
622C3×C4—181no—
623Dic3—21no—
624Dic3—21no—
625Dic3—21no—
626Dic3—61no—
627Dic3—61no—
628Dic3—61no—
629Dic3—182no—
630Dic3—181no—
631Dic3—181no—
632Dic3—181no—
633Dic3—181no—
634Dic3—181no—
635Dic3—181no—
636Dic3—361no—
637Dic3—361no—
638C32#563411yescharacteristic
639C9—21no—
640C9#563411yescharacteristic, complemented
641C23—31no—
642C23—91no—
643C23—274no—
644C23—271no—
645C23—1081no—
646C23—1081no—
647Q8—121no—
648Q8—361no—
649Q8—1081no—
650Q8—1081no—
651C2×C4—31no—
652C2×C4—31no—
653C2×C4—31no—
654C2×C4—91no—
655C2×C4—91no—
656C2×C4—91no—
657C2×C4—121no—
658C2×C4—271no—
659C2×C4—271no—
660C2×C4—271no—
661C2×C4—361no—
662C2×C4—1081no—
663C2×C4—1081no—
664C2×C4—1081no—
665C2×C4—1081no—
666C2×C4C2×D3×D911yescharacteristic
667C2×C4C2×D3×D911yescharacteristic
668C2×C4C2×D3×D911yescharacteristic
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—62no—
673C2×C3—182no—
674C2×C3#6371011yescharacteristic
675C2×C3C2×Q8×D911yescharacteristic
676C2×C3#6371511yescharacteristic
677C2×C3#6430711yescharacteristic
678C2×C3#6431411yescharacteristic
679C2×C3D32×Q811yescharacteristic
680D3—22no—
681D3—62no—
682D3—182no—
683D3—182no—
684D3—362no—
685C22—32no—
686C22—61no—
687C22—61no—
688C22—92no—
689C22—181no—
690C22—181no—
691C22—272no—
692C22—541no—
693C22—541no—
694C22—1084no—
695C22C22×D3×D911yescharacteristic
696C4—21no—
697C4—21no—
698C4—21no—
699C4—61no—
700C4—61no—
701C4—61no—
702C4—181no—
703C4—181no—
704C4—181no—
705C4—541no—
706C4—541no—
707C4—541no—
708C3—21no—
709C3#1058973611yescharacteristic, complemented
710C3#1059463511yescharacteristic
711C2—62no—
712C2—182no—
713C2—542no—
714C2#1172247711yescharacteristic
715C2#1172250011yescharacteristic
716C2D3×Q8×D911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
prime radicalC22×D3×D9C22
hypercenterC4⋊C4D3×D9
hypocenterC3×C9#543
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. #11721752C2semidirect
2. C9×#896C2semidirect
3. C3×#63459C2semidirect
7. #11721026C2semidirect
8. #11721018C2semidirect
9. #11720996C2semidirect
10. #11720995C2semidirect
11. #11720985C2semidirect
12. #11720984C2semidirect
13. #11720961C2semidirect
14. #11720939C2semidirect
15. #11720929C2semidirect
20. C2×#6226C22semidirect
23. C2×C9×Dic6C22semidirect
24. C2×C3×Dic18C22semidirect
28. C2×#6189C22semidirect
29. C3×C9×C4⋊C4C22semidirect
32. #88534C22semidirect
33. #88534C22semidirect
38. C9×Dic3⋊C4C22semidirect
39. C9×Dic3⋊C4C22semidirect
40. C3×C4⋊Dic9C22semidirect
41. C3×C4⋊Dic9C22semidirect
48. Dic3⋊Dic9C22semidirect
49. #88442C22semidirect
50. Dic9⋊Dic3C22semidirect
51. Dic9⋊Dic3C22semidirect
52. Dic9⋊Dic3C22semidirect
74. #63459D3semidirect
89. C2×D3×D9Q8semidirect
161. C2×Dic18C2×D3semidirect
165. C9×C4⋊C4C2×D3semidirect
181. C4⋊Dic9C2×D3semidirect
182. C4⋊Dic9C2×D3semidirect
236. #896D9semidirect
340. C2×Dic6C2×D9semidirect
346. C3×C4⋊C4C2×D9semidirect
392. Dic3⋊C4C2×D9semidirect
393. Dic3⋊C4C2×D9semidirect
465. C3×C9#543semidirect
569. C4⋊C4D3×D9semidirect
640. C9#5634semidirect
709. C3#10589736semidirect

Maximal subgroups

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

subgroupindex
#117217522
C9×#8962
C3×#634592
#117210482
D3×(C2×D9)⋊C42
D9×(C2×D3)⋊C42
#117210262
#117210182
#117209962
#117209952
#117209852
#117209842
#117209612
#117209392
#117209292
#105946353
#105897363