Finite Group Databasebeta

← #13148116

Subgroups — #13148116

Order 1728.

858 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
1C22⋊C4×C3⋊D9C211yesmaximal, characteristic
2C9×#878C211yesmaximal, characteristic, complemented
3C3×#63440C211yesmaximal, characteristic, complemented
4#11721274C211yesmaximal, characteristic
5C2×#88445C211yesmaximal, characteristic
6#11721253C211yesmaximal, characteristic, complemented
7#11721249C211yesmaximal, characteristic, complemented
8#11720995C211yesmaximal, characteristic, complemented
9#11720994C211yesmaximal, characteristic, complemented
10#11720986C211yesmaximal, characteristic, complemented
11#11720985C211yesmaximal, characteristic, complemented
12#11720936C211yesmaximal, characteristic, complemented
13#11720929C211yesmaximal, characteristic, complemented
14#11720923C211yesmaximal, characteristic, complemented
15#11720923C211yesmaximal, characteristic, complemented
16#10594180—31nomaximal
17#10589736—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C2×C4×C3⋊D9C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic
21C22×C9×Dic3C2211yescharacteristic
22C22×C3×Dic9C2211yescharacteristic
23C2×C9×Dic6C2211yescharacteristic, complemented
24C2×C3×Dic18C2211yescharacteristic, complemented
25C2×(C3⋊D9)⋊C4C2211yescharacteristic
26C2×(C3⋊D9)⋊C4C2211yescharacteristic
27C2×#6189C2211yescharacteristic, complemented
28C2×#6189C2211yescharacteristic, complemented
29C3×C9×C22⋊C4C2211yescharacteristic
30#88551C2211yescharacteristic
31#88536C2211yescharacteristic
32#88536C2211yescharacteristic
33C9×#217C2211yescharacteristic
34C3×#3676C2211yescharacteristic
35C9×C4⋊Dic3C2211yescharacteristic, complemented
36C9×Dic3⋊C4C2211yescharacteristic, complemented
37C9×Dic3⋊C4C2211yescharacteristic, complemented
38C3×C4⋊Dic9C2211yescharacteristic, complemented
39C3×Dic9⋊C4C2211yescharacteristic, complemented
40C3×Dic9⋊C4C2211yescharacteristic, complemented
41#88445C2211yescharacteristic
42#88445C2211yescharacteristic
43#88445C2211yescharacteristic
44#88445C2211yescharacteristic
45#88445C2211yescharacteristic
46#88445C2211yescharacteristic
47Dic3⋊Dic9C2211yescharacteristic, complemented
48Dic3⋊Dic9C2211yescharacteristic, complemented
49#88442C2211yescharacteristic, complemented
50#88442C2211yescharacteristic, complemented
51Dic9⋊Dic3C2211yescharacteristic, complemented
52Dic9⋊Dic3C2211yescharacteristic, complemented
53C22⋊C4×C3⋊D3—31no—
54C3×#878—31no—
55C3×#878D311yescharacteristic
56#63974—31no—
57#63964—31no—
58#63964—31no—
59C2×#3722—31no—
60#63895—31no—
61#63895—31no—
62#63888—31no—
63#63888—31no—
64#63871—31no—
65#63871—31no—
66#63865—31no—
67#63865—31no—
68C9×C22⋊Q8—31no—
69#63508—31no—
70#63508—31no—
71C2×(C2×D9)⋊C4—31no—
72#63486—31no—
73#63459—31no—
74#63459—31no—
75#63458—31no—
76#63458—31no—
77#63458—31no—
78#63458—31no—
79C22⋊C4×D9—31no—
80C22⋊C4×D9—31no—
81C22⋊C4×D9—61no—
82#63440—31no—
83#63440D311yescharacteristic, complemented
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9—41no—
86C22×C3⋊D9—41no—
87C22×C3⋊D9Q814yescomplemented
88C22×C3⋊D9C2311yescharacteristic
89C22×C3⋊D9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3⋊Dic9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94C4×C3⋊D9—41no—
95C4×C3⋊D9—41no—
96C2×C9×Dic3—41no—
97C2×C9×Dic3C2311yescharacteristic
98C2×C9×Dic3C2311yescharacteristic
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C3×Dic9—41no—
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C9×Dic6—41no—
107C3×Dic18—41no—
108(C3⋊D9)⋊C4—41no—
109(C3⋊D9)⋊C4—41no—
110#6189—41no—
111#6189—41no—
112#5634—91no—
113#5634—91no—
114C23×C3⋊D3—31no—
115C2×C4×C3⋊D3—31no—
116C2×C4×C3⋊D3—31no—
117C22×C3×Dic3—31no—
118C22×C3×Dic3C2×D311yescharacteristic
119C2×C3×Dic6—31no—
120C2×C3×Dic6C2×D311yescharacteristic
121C2×#627—31no—
122C2×#627—31no—
123C2×#624—31no—
124C2×#624—31no—
125C23×D9—31no—
126C23×D9—61no—
127C32×C22⋊C4C2×D311yescharacteristic
128#3757—31no—
129#3752—31no—
130#3752—31no—
131C3×#217—31no—
132C3×#217C2×D311yescharacteristic
133C3×C4⋊Dic3—31no—
134C3×C4⋊Dic3C2×D311yescharacteristic
135C3×Dic3⋊C4—31no—
136C3×Dic3⋊C4—31no—
137C3×Dic3⋊C4C2×D311yescharacteristic
138C3×Dic3⋊C4C2×D311yescharacteristic
139#3724—31no—
140#3724—31no—
141Dic3⋊Dic3—31no—
142Dic3⋊Dic3—31no—
143Dic3⋊Dic3—31no—
144Dic3⋊Dic3—31no—
145#3722—31no—
146#3722—31no—
147#3722—31no—
148#3722—31no—
149#3722—31no—
150#3722—31no—
151C2×Q8×C9—31no—
152C22×C4×C9—31no—
153C22×Dic9C2×D311yescharacteristic
154C2×C4×D9—31no—
155C2×C4×D9—31no—
156C2×C4×D9—31no—
157C2×C4×D9—31no—
158C2×C4×D9—61no—
159C2×C4×D9—61no—
160C2×Dic18—31no—
161C2×Dic18—31no—
162C2×Dic18C2×D311yescharacteristic, complemented
163C9×C4⋊C4—31no—
164C9×C4⋊C4—31no—
165C9×C4⋊C4—31no—
166C9×C22⋊C4—21no—
167C9×C22⋊C4—31no—
168C9×C22⋊C4C2×D311yescharacteristic
169#3676—31no—
170#3676—61no—
171#3676C2×D311yescharacteristic
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—31no—
179(C2×D9)⋊C4—31no—
180(C2×D9)⋊C4—61no—
181(C2×D9)⋊C4—61no—
182C4⋊Dic9—31no—
183C4⋊Dic9—31no—
184C4⋊Dic9C2×D311yescharacteristic, complemented
185Dic9⋊C4—31no—
186Dic9⋊C4—31no—
187Dic9⋊C4—31no—
188Dic9⋊C4—31no—
189Dic9⋊C4C2×D311yescharacteristic, complemented
190Dic9⋊C4C2×D311yescharacteristic, complemented
191C22×C3×C9—21no—
192C22×C3×C9—21no—
193C22×C3×C9C2×Q812yes—
194C22×C3×C9C2411yescharacteristic
195C2×C3⋊D9—21no—
196C2×C3⋊D9—21no—
197C2×C3⋊D9—21no—
198C2×C3⋊D9—21no—
199C2×C3⋊D9—44no—
200C2×C3⋊D9C2×Q812yes—
201C2×C3⋊D9C2×Q812yes—
202C3×C4×C9—21no—
203C3×C4×C9—21no—
204C3⋊Dic9—21no—
205C3⋊Dic9—21no—
206C9×Dic3—21no—
207C9×Dic3—21no—
208C9×Dic3—21no—
209C9×Dic3—21no—
210C3×Dic9—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—91no—
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—91no—
236D3×C22⋊C4—91no—
237D3×C22⋊C4—91no—
238D3×C22⋊C4—91no—
239D3×C22⋊C4—91no—
240D3×C22⋊C4—181no—
241#878—31no—
242#878—91no—
243#878—91no—
244#878D911yescharacteristic, complemented
245C23×C32C22×D311yescharacteristic
246C22×C3⋊D3—31no—
247C22×C3⋊D3—31no—
248C22×C3⋊D3—34no—
249C22×C3⋊D3—121no—
250C22×C3⋊D3—121no—
251C2×C32×C4C22×D311yescharacteristic
252C2×C32×C4C22×D311yescharacteristic
253C2×C3⋊Dic3—31no—
254C2×C3⋊Dic3—31no—
255C4×C3⋊D3—121no—
256C4×C3⋊D3—121no—
257C2×C3×Dic3—31no—
258C2×C3×Dic3—31no—
259C2×C3×Dic3—31no—
260C2×C3×Dic3—31no—
261C2×C3×Dic3—41no—
262C2×C3×Dic3—121no—
263C2×C3×Dic3C22×D311yescharacteristic
264C2×C3×Dic3C22×D311yescharacteristic
265C2×C3×Dic3C22×D311yescharacteristic
266C2×C3×Dic3C22×D311yescharacteristic
267C3×Dic6—41no—
268C3×Dic6—121no—
269#627—121no—
270#627—121no—
271#624—121no—
272#624—121no—
273C23×C9—21no—
274C23×C9C22×D311yescharacteristic
275C22×D9—31no—
276C22×D9—31no—
277C22×D9—34no—
278C22×D9—61no—
279C22×D9—61no—
280C22×D9—64no—
281C22×D9—121no—
282C22×D9—121no—
283C22×D9—122no—
284C22×D9—122no—
285Q8×C9—121no—
286C2×C4×C9—21no—
287C2×C4×C9—21no—
288C2×C4×C9—31no—
289C2×C4×C9—31no—
290C2×C4×C9—31no—
291C2×C4×C9—31no—
292C2×C4×C9—121no—
293C2×C4×C9C22×D311yescharacteristic
294C2×C4×C9C22×D311yescharacteristic
295C2×Dic9—31no—
296C2×Dic9—31no—
297C2×Dic9—41no—
298C2×Dic9—61no—
299C2×Dic9—61no—
300C2×Dic9C22×D311yescharacteristic
301C2×Dic9C22×D311yescharacteristic
302C2×Dic9C22×D311yescharacteristic
303C2×Dic9C22×D311yescharacteristic
304C4×D9—121no—
305C4×D9—121no—
306C4×D9—121no—
307C4×D9—121no—
308C4×D9—122no—
309C4×D9—122no—
310Dic18—41no—
311Dic18—121no—
312Dic18—121no—
313#543—271noSylow
314C2×C3×C9—22no—
315C2×C3×C9C22×Q811yescharacteristic
316C2×C3×C9H(5,𝔽2)11yescharacteristic
317C2×C3×C9H(5,𝔽2)11yescharacteristic
318C3⋊D9—22no—
319C3⋊D9—22no—
320C23×D3—91no—
321C23×D3—91no—
322C23×D3—181no—
323C2×C3×Q8—31no—
324C2×C3×Q8—91no—
325C22×C3×C4—31no—
326C22×C3×C4—91no—
327C22×Dic3—31no—
328C22×Dic3C2×D911yescharacteristic
329C2×C4×D3—91no—
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—31no—
340C2×Dic6—91no—
341C2×Dic6—91no—
342C2×Dic6—91no—
343C2×Dic6—91no—
344C2×Dic6C2×D911yescharacteristic, complemented
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—91no—
349C3×C4⋊C4—91no—
350C3×C4⋊C4—91no—
351C3×C22⋊C4—21no—
352C3×C22⋊C4—31no—
353C3×C22⋊C4—91no—
354C3×C22⋊C4C2×D911yescharacteristic
355C3×C22⋊C4D3211yescharacteristic
356#217—31no—
357#217—91no—
358#217—91no—
359#217—181no—
360#217C2×D911yescharacteristic
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—91no—
376(C2×D3)⋊C4—91no—
377(C2×D3)⋊C4—181no—
378(C2×D3)⋊C4—181no—
379C4⋊Dic3—31no—
380C4⋊Dic3—91no—
381C4⋊Dic3—91no—
382C4⋊Dic3—91no—
383C4⋊Dic3—91no—
384C4⋊Dic3C2×D911yescharacteristic, complemented
385Dic3⋊C4—31no—
386Dic3⋊C4—31no—
387Dic3⋊C4—91no—
388Dic3⋊C4—91no—
389Dic3⋊C4—91no—
390Dic3⋊C4—91no—
391Dic3⋊C4—91no—
392Dic3⋊C4—91no—
393Dic3⋊C4—91no—
394Dic3⋊C4—91no—
395Dic3⋊C4C2×D911yescharacteristic, complemented
396Dic3⋊C4C2×D911yescharacteristic, complemented
397C22×C32—21no—
398C22×C32—21no—
399C22×C32D3×Q812yes—
400C22×C32C23×D311yescharacteristic
401C2×C3⋊D3—32no—
402C2×C3⋊D3—32no—
403C2×C3⋊D3—61no—
404C2×C3⋊D3—61no—
405C2×C3⋊D3—61no—
406C2×C3⋊D3—61no—
407C2×C3⋊D3—124no—
408C32×C4—21no—
409C32×C4—21no—
410C3⋊Dic3—61no—
411C3⋊Dic3—61no—
412C3×Dic3—21no—
413C3×Dic3—21no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—61no—
417C3×Dic3—61no—
418C3×Dic3—61no—
419C3×Dic3—61no—
420C22×C9—21no—
421C22×C9—21no—
422C22×C9—21no—
423C22×C9—22no—
424C22×C9—41no—
425C22×C9—41no—
426C22×C9D3×Q812yes—
427C22×C9C23×D311yescharacteristic
428C2×D9—32no—
429C2×D9—32no—
430C2×D9—62no—
431C2×D9—62no—
432C2×D9—62no—
433C2×D9—62no—
434C2×D9—61no—
435C2×D9—61no—
436C2×D9—61no—
437C2×D9—61no—
438C2×D9—121no—
439C2×D9—121no—
440C2×D9—124no—
441C2×D9—128no—
442C4×C9—21no—
443C4×C9—21no—
444C4×C9—41no—
445C4×C9—41no—
446C4×C9—61no—
447C4×C9—61no—
448C4×C9—61no—
449C4×C9—61no—
450Dic9—21no—
451Dic9—21no—
452Dic9—21no—
453Dic9—21no—
454Dic9—61no—
455Dic9—61no—
456Dic9—121no—
457Dic9—121no—
458C22⋊Q8—31no—
459C22⋊Q8—91no—
460C22⋊Q8—271no—
461C22⋊Q8—271no—
462C22⋊Q8—271no—
463C22⋊Q8—271no—
464C22⋊Q8—271no—
465C22⋊Q8—271no—
466C22⋊Q8—271no—
467C22⋊Q8—271no—
468C22⋊Q8—271no—
469C22⋊Q8—271no—
470C2×C22⋊C4—271no—
471C2×C22⋊C4—271no—
472C2×C22⋊C4—271no—
473C3×C9#54311yescharacteristic, complemented, Sylow
474C23×C3—21no—
475C23×C3C22×D911yescharacteristic
476C23×C3C2×D3211yescharacteristic
477C22×D3—91no—
478C22×D3—91no—
479C22×D3—91no—
480C22×D3—91no—
481C22×D3—94no—
482C22×D3—94no—
483C22×D3—181no—
484C22×D3—181no—
485C22×D3—184no—
486C22×D3—361no—
487C22×D3—361no—
488C22×D3—361no—
489C22×D3—361no—
490C22×D3—362no—
491C22×D3—362no—
492C3×Q8—121no—
493C3×Q8—361no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—91no—
501C2×C3×C4—91no—
502C2×C3×C4—91no—
503C2×C3×C4—91no—
504C2×C3×C4—121no—
505C2×C3×C4—361no—
506C2×C3×C4C22×D911yescharacteristic
507C2×C3×C4C22×D911yescharacteristic
508C2×C3×C4C2×D3211yescharacteristic
509C2×C3×C4C2×D3211yescharacteristic
510C2×Dic3—31no—
511C2×Dic3—31no—
512C2×Dic3—31no—
513C2×Dic3—31no—
514C2×Dic3—41no—
515C2×Dic3—91no—
516C2×Dic3—91no—
517C2×Dic3—91no—
518C2×Dic3—91no—
519C2×Dic3—121no—
520C2×Dic3—181no—
521C2×Dic3—181no—
522C2×Dic3C22×D911yescharacteristic
523C2×Dic3C22×D911yescharacteristic
524C2×Dic3C22×D911yescharacteristic
525C2×Dic3C22×D911yescharacteristic
526C4×D3—361no—
527C4×D3—361no—
528C4×D3—361no—
529C4×D3—361no—
530C4×D3—361no—
531C4×D3—361no—
532C4×D3—361no—
533C4×D3—361no—
534C4×D3—362no—
535C4×D3—362no—
536Dic6—41no—
537Dic6—121no—
538Dic6—361no—
539Dic6—361no—
540Dic6—361no—
541Dic6—361no—
542C2×C32—22no—
543C2×C32#100411yescharacteristic
544C2×C32C2×D3×Q811yescharacteristic
545C2×C32#100911yescharacteristic
546C3⋊D3—62no—
547C3⋊D3—62no—
548C2×C9—22no—
549C2×C9—21no—
550C2×C9—21no—
551C2×C9—21no—
552C2×C9—42no—
553C2×C9#100411yescharacteristic
554C2×C9C2×D3×Q811yescharacteristic
555C2×C9#100911yescharacteristic
556D9—64no—
557D9—62no—
558D9—62no—
559D9—122no—
560C24—271no—
561C2×Q8—31no—
562C2×Q8—91no—
563C2×Q8—271no—
564C2×Q8—271no—
565C22×C4—31no—
566C22×C4—91no—
567C22×C4—271no—
568C22×C4—271no—
569C22×C4—271no—
570C22×C4—271no—
571C4⋊C4—31no—
572C4⋊C4—31no—
573C4⋊C4—31no—
574C4⋊C4—91no—
575C4⋊C4—91no—
576C4⋊C4—91no—
577C4⋊C4—271no—
578C4⋊C4—271no—
579C4⋊C4—271no—
580C4⋊C4—271no—
581C4⋊C4—271no—
582C4⋊C4—271no—
583C22⋊C4—31no—
584C22⋊C4—91no—
585C22⋊C4—271no—
586C22⋊C4—271no—
587C22⋊C4—271no—
588C22⋊C4—271no—
589C22⋊C4—271no—
590C22⋊C4—271no—
591C22⋊C4—271no—
592C22⋊C4—271no—
593C22⋊C4—271no—
594C22⋊C4D3×D911yescharacteristic
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—22no—
600C22×C3—21no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3Q8×D912yes—
604C22×C3C23×D911yescharacteristic
605C22×C3#379712yes—
606C22×C3C22×D3211yescharacteristic
607C2×D3—92no—
608C2×D3—92no—
609C2×D3—92no—
610C2×D3—92no—
611C2×D3—182no—
612C2×D3—182no—
613C2×D3—182no—
614C2×D3—182no—
615C2×D3—181no—
616C2×D3—181no—
617C2×D3—181no—
618C2×D3—181no—
619C2×D3—181no—
620C2×D3—181no—
621C2×D3—181no—
622C2×D3—181no—
623C2×D3—361no—
624C2×D3—361no—
625C2×D3—364no—
626C2×D3—364no—
627C2×D3—368no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—41no—
633C3×C4—41no—
634C3×C4—61no—
635C3×C4—61no—
636C3×C4—61no—
637C3×C4—61no—
638C3×C4—181no—
639C3×C4—181no—
640C3×C4—181no—
641C3×C4—181no—
642Dic3—21no—
643Dic3—21no—
644Dic3—21no—
645Dic3—21no—
646Dic3—61no—
647Dic3—61no—
648Dic3—61no—
649Dic3—61no—
650Dic3—181no—
651Dic3—181no—
652Dic3—181no—
653Dic3—181no—
654Dic3—361no—
655Dic3—361no—
656C32#563411yescharacteristic
657C9—21no—
658C9#563411yescharacteristic, complemented
659C23—271no—
660C23—271no—
661C23—274no—
662C23—1081no—
663C23—1081no—
664C23C2×D3×D911yescharacteristic
665Q8—121no—
666Q8—361no—
667Q8—1081no—
668Q8—1081no—
669C2×C4—31no—
670C2×C4—31no—
671C2×C4—31no—
672C2×C4—31no—
673C2×C4—91no—
674C2×C4—91no—
675C2×C4—91no—
676C2×C4—91no—
677C2×C4—121no—
678C2×C4—271no—
679C2×C4—271no—
680C2×C4—361no—
681C2×C4—1081no—
682C2×C4—1081no—
683C2×C4—1081no—
684C2×C4—1081no—
685C2×C4C2×D3×D911yescharacteristic
686C2×C4C2×D3×D911yescharacteristic
687C2×C3—22no—
688C2×C3—22no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—42no—
693C2×C3#6371011yescharacteristic
694C2×C3C2×Q8×D911yescharacteristic
695C2×C3#6371511yescharacteristic
696C2×C3C2×#379711yescharacteristic
697C2×C3#6431411yescharacteristic
698C2×C3#6431411yescharacteristic
699D3—184no—
700D3—182no—
701D3—182no—
702D3—182no—
703D3—182no—
704D3—362no—
705C22—21no—
706C22—21no—
707C22—272no—
708C22—272no—
709C22—541no—
710C22—541no—
711C22—541no—
712C22—541no—
713C22—1084no—
714C22(C3⋊D9)⋊Q812yes—
715C22C22×D3×D911yescharacteristic
716C4—21no—
717C4—21no—
718C4—61no—
719C4—61no—
720C4—61no—
721C4—61no—
722C4—181no—
723C4—181no—
724C4—181no—
725C4—181no—
726C4—541no—
727C4—541no—
728C3—21no—
729C3#1058973611yescharacteristic, complemented
730C3#1059418011yescharacteristic
731C2—22no—
732C2—542no—
733C2—542no—
734C2C2×(C3⋊D9)⋊Q811yescharacteristic
735C2#1172250011yescharacteristic
736C2#1172250111yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radicalC23×C3⋊D9C22
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#543
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C9×#878C2semidirect
3. C3×#63440C2semidirect
6. #11721253C2semidirect
7. #11721249C2semidirect
8. #11720995C2semidirect
9. #11720994C2semidirect
10. #11720986C2semidirect
11. #11720985C2semidirect
12. #11720936C2semidirect
13. #11720929C2semidirect
14. #11720923C2semidirect
15. #11720923C2semidirect
23. C2×C9×Dic6C22semidirect
24. C2×C3×Dic18C22semidirect
27. C2×#6189C22semidirect
28. C2×#6189C22semidirect
35. C9×C4⋊Dic3C22semidirect
36. C9×Dic3⋊C4C22semidirect
37. C9×Dic3⋊C4C22semidirect
38. C3×C4⋊Dic9C22semidirect
39. C3×Dic9⋊C4C22semidirect
40. C3×Dic9⋊C4C22semidirect
47. Dic3⋊Dic9C22semidirect
48. Dic3⋊Dic9C22semidirect
49. #88442C22semidirect
50. #88442C22semidirect
51. Dic9⋊Dic3C22semidirect
52. Dic9⋊Dic3C22semidirect
83. #63440D3semidirect
87. C22×C3⋊D9Q8semidirect
162. C2×Dic18C2×D3semidirect
184. C4⋊Dic9C2×D3semidirect
189. Dic9⋊C4C2×D3semidirect
190. Dic9⋊C4C2×D3semidirect
244. #878D9semidirect
344. C2×Dic6C2×D9semidirect
384. C4⋊Dic3C2×D9semidirect
395. Dic3⋊C4C2×D9semidirect
396. Dic3⋊C4C2×D9semidirect
473. C3×C9#543semidirect
658. C9#5634semidirect
729. C3#10589736semidirect

Maximal subgroups

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

subgroupindex
C22⋊C4×C3⋊D92
C9×#8782
C3×#634402
#117212742
C2×#884452
#117212532
#117212492
#117209952
#117209942
#117209862
#117209852
#117209362
#117209292
#117209232
#105941803
#105897363