Finite Group Databasebeta

← #13148352

Subgroups — #13148352

Order 1728.

796 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721723C211yesmaximal, characteristic, complemented
2C9×#884C211yesmaximal, characteristic, complemented
3C3×#63446C211yesmaximal, characteristic, complemented
4#11721290C211yesmaximal, characteristic, complemented
5#11721290C211yesmaximal, characteristic, complemented
6#11721281C211yesmaximal, characteristic, complemented
7#11721270C211yesmaximal, characteristic, complemented
8#11721043C211yesmaximal, characteristic, complemented
9#11721032C211yesmaximal, characteristic, complemented
10#11721031C211yesmaximal, characteristic, complemented
11#11721028C211yesmaximal, characteristic, complemented
12C4×#6194C211yesmaximal, characteristic, complemented
13#11721015C211yesmaximal, characteristic, complemented
14#11720981C211yesmaximal, characteristic, complemented
15#11720928C211yesmaximal, characteristic, complemented
16#10594223—31nomaximal
17#10589717—31nomaximal
18C22×C3⋊Dic9C2211yescharacteristic
19C2×C9×#67C2211yescharacteristic
20C2×C9×#67C2211yescharacteristic
21C2×C3×#611C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C2×C9×D12C2211yescharacteristic
24C2×C4×D3×C9C2211yescharacteristic
25C2×C3×D36C2211yescharacteristic
26C2×C3×C4×D9C2211yescharacteristic
27C2×#6194C2211yescharacteristic
28C2×#6194C2211yescharacteristic
29C2×#6194C2211yescharacteristic
30C2×#6194C2211yescharacteristic
31C2×D3×Dic9C2211yescharacteristic
32C2×Dic3×D9C2211yescharacteristic
33C3×C9×C22⋊C4C2211yescharacteristic
34#88551C2211yescharacteristic
35#88534C2211yescharacteristic
36#88534C2211yescharacteristic
37C4×C3⋊Dic9C2211yescharacteristic
38C4×C3⋊Dic9C2211yescharacteristic
39C9×(C2×D3)⋊C4C2211yescharacteristic
40C3×(C2×D9)⋊C4C2211yescharacteristic
41C9×Dic3⋊C4C2211yescharacteristic
42C3×Dic9⋊C4C2211yescharacteristic
43(C2×D3)⋊Dic9C2211yescharacteristic
44(C2×D3)⋊Dic9C2211yescharacteristic
45(C2×D3)⋊Dic9C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47(C2×D9)⋊Dic3C2211yescharacteristic
48(C2×D9)⋊Dic3C2211yescharacteristic
49Dic3⋊Dic9C2211yescharacteristic
50#88442C2211yescharacteristic
51#88442C2211yescharacteristic
52Dic9⋊Dic3C2211yescharacteristic
53#64086—31no—
54C3×#884—31no—
55C3×#884D311yescharacteristic
56#63980—31no—
57#63980—31no—
58#63970—31no—
59#63970—31no—
60#63914—31no—
61#63905—31no—
62#63905—31no—
63#63902—31no—
64C4×#625—31no—
65#63884—31no—
66#63884—31no—
67#63870—31no—
68C9×#121—31no—
69#63502—31no—
70#63501—31no—
71#63501—31no—
72#63501—31no—
73#63500—31no—
74#63497—31no—
75#63491—31no—
76C4×#611—31no—
77#63456—31no—
78#63451—31no—
79#63446D311yescharacteristic, complemented
80#63445—31no—
81#611⋊C4—31no—
82#63439—31no—
83#63439—61no—
84C23×C3×C9C2311yescharacteristic
85C22×D3×C9C2311yescharacteristic
86C22×D3×C9C2311yescharacteristic
87C22×C3×D9C2311yescharacteristic
88C22×C3×D9C2311yescharacteristic
89C2×C3×C4×C9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3⋊Dic9—22no—
92C2×C3⋊Dic9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C9×#67—41no—
97C9×#67—41no—
98C3×#611—41no—
99C3×#611—41no—
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C9×D12—41no—
105C4×D3×C9—41no—
106C3×D36—41no—
107C3×C4×D9—41no—
108#6194—22no—
109#6194—22no—
110#6194—41no—
111#6194—41no—
112D3×Dic9—41no—
113Dic3×D9—41no—
114#5615—91no—
115#5615—91no—
116C22×C3⋊Dic3—31no—
117C2×C3×#67—31no—
118C2×C3×#67—31no—
119C2×C3×#67C2×D311yescharacteristic
120C2×C3×#67C2×D311yescharacteristic
121C2×C3×D12—31no—
122C2×C3×D12C2×D311yescharacteristic
123C2×C3×C4×D3—31no—
124C2×C3×C4×D3C2×D311yescharacteristic
125C2×#625—31no—
126C2×#625—31no—
127C2×#625—31no—
128C2×#625—31no—
129C2×D3×Dic3—31no—
130C2×D3×Dic3—31no—
131C32×C22⋊C4C2×D311yescharacteristic
132#3757—31no—
133#3750—31no—
134#3750—31no—
135C4×C3⋊Dic3—31no—
136C4×C3⋊Dic3—31no—
137C3×(C2×D3)⋊C4—31no—
138C3×(C2×D3)⋊C4C2×D311yescharacteristic
139C3×Dic3⋊C4—31no—
140C3×Dic3⋊C4C2×D311yescharacteristic
141#3724—31no—
142#3724—31no—
143Dic3⋊Dic3—31no—
144Dic3⋊Dic3—31no—
145(C2×D3)⋊Dic3—31no—
146(C2×D3)⋊Dic3—31no—
147(C2×D3)⋊Dic3—31no—
148(C2×D3)⋊Dic3—31no—
149(C2×D3)⋊Dic3—31no—
150(C2×D3)⋊Dic3—31no—
151C2×D4×C9—31no—
152C2×D4×C9—31no—
153C2×D4×C9—31no—
154C22×C4×C9—31no—
155C2×#611—31no—
156C2×#611—31no—
157C2×#611—31no—
158C2×#611—31no—
159C2×#611C2×D311yescharacteristic
160C2×#611C2×D311yescharacteristic
161C22×Dic9—31no—
162C22×Dic9—31no—
163C22×Dic9—61no—
164C2×D36C2×D311yescharacteristic
165C2×C4×D9—31no—
166C2×C4×D9C2×D311yescharacteristic
167C9×C4⋊C4—31no—
168C9×C22⋊C4—21no—
169C9×C22⋊C4—31no—
170C9×C22⋊C4C2×D311yescharacteristic
171#3676—31no—
172#3676—31no—
173#3676—31no—
174#3676—31no—
175#3676—61no—
176(C2×D9)⋊C4—31no—
177(C2×D9)⋊C4—31no—
178(C2×D9)⋊C4—31no—
179(C2×D9)⋊C4C2×D311yescharacteristic
180C4⋊Dic9—31no—
181Dic9⋊C4—31no—
182Dic9⋊C4—31no—
183Dic9⋊C4—31no—
184Dic9⋊C4—31no—
185Dic9⋊C4—31no—
186Dic9⋊C4—61no—
187Dic9⋊C4—61no—
188Dic9⋊C4C2×D311yescharacteristic
189C4×Dic9—31no—
190C4×Dic9—31no—
191C4×Dic9—61no—
192C4×Dic9—61no—
193C22×C3×C9—21no—
194C22×C3×C9—21no—
195C22×C3×C9—21no—
196C22×C3×C9C2411yescharacteristic
197C2×D3×C9—21no—
198C2×D3×C9—21no—
199C2×D3×C9—21no—
200C2×D3×C9—21no—
201C2×D3×C9—21no—
202C2×D3×C9—21no—
203C2×C3×D9—21no—
204C2×C3×D9—21no—
205C2×C3×D9—21no—
206C2×C3×D9—21no—
207C2×C3×D9—21no—
208C2×C3×D9—21no—
209C3×C4×C9—21no—
210C3×C4×C9—21no—
211C3⋊Dic9—21no—
212C3⋊Dic9—21no—
213C3⋊Dic9—21no—
214C3⋊Dic9#4112yes—
215C9×Dic3—21no—
216C9×Dic3—21no—
217C3×Dic9—21no—
218C3×Dic9—21no—
219C3×#121—31no—
220C3×#121—91no—
221#940—91no—
222#940—91no—
223#939—91no—
224#939—91no—
225#939—91no—
226#939—91no—
227#939—91no—
228#939—91no—
229#938—91no—
230#938—91no—
231#935—91no—
232#935—91no—
233#929—91no—
234#929—91no—
235C4×#67—91no—
236C4×#67—91no—
237#894—91no—
238#894—91no—
239#889—91no—
240#889—91no—
241#884—31no—
242#884D911yescharacteristic, complemented
243#883—91no—
244#883—91no—
245#67⋊C4—91no—
246#67⋊C4—91no—
247#877—91no—
248#877—91no—
249#877—181no—
250C23×C32C22×D311yescharacteristic
251C22×C3×D3—31no—
252C22×C3×D3—31no—
253C22×C3×D3C22×D311yescharacteristic
254C22×C3×D3C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C22×D311yescharacteristic
257C2×C3⋊Dic3—31no—
258C2×C3⋊Dic3—31no—
259C2×C3⋊Dic3—31no—
260C2×C3⋊Dic3—31no—
261C2×C3⋊Dic3—62no—
262C3×#67—41no—
263C3×#67—41no—
264C3×#67—121no—
265C3×#67—121no—
266C2×C3×Dic3—31no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3C22×D311yescharacteristic
269C2×C3×Dic3C22×D311yescharacteristic
270C3×D12—41no—
271C3×D12—121no—
272C3×C4×D3—41no—
273C3×C4×D3—121no—
274#625—62no—
275#625—62no—
276#625—121no—
277#625—121no—
278D3×Dic3—121no—
279D3×Dic3—121no—
280C23×C9—21no—
281C23×C9—31no—
282C23×C9—31no—
283C23×C9C22×D311yescharacteristic
284C22×D9C22×D311yescharacteristic
285C22×D9C22×D311yescharacteristic
286D4×C9—121no—
287D4×C9—121no—
288D4×C9—121no—
289C2×C4×C9—21no—
290C2×C4×C9—21no—
291C2×C4×C9—31no—
292C2×C4×C9—31no—
293C2×C4×C9—121no—
294C2×C4×C9C22×D311yescharacteristic
295C2×C4×C9C22×D311yescharacteristic
296#611—41no—
297#611—41no—
298#611—62no—
299#611—62no—
300#611—121no—
301#611—121no—
302C2×Dic9—31no—
303C2×Dic9—31no—
304C2×Dic9—31no—
305C2×Dic9—31no—
306C2×Dic9—61no—
307C2×Dic9—61no—
308C2×Dic9—61no—
309C2×Dic9—61no—
310C2×Dic9—62no—
311C2×Dic9—64no—
312C2×Dic9—121no—
313C2×Dic9C22×D311yescharacteristic
314C2×Dic9C22×D311yescharacteristic
315D36—41no—
316C4×D9—41no—
317C4×D9—121no—
318#540—271noSylow
319C2×C3×C9—41no—
320C2×C3×C9C2×#4111yescharacteristic
321C2×C3×C9H(5,𝔽2)11yescharacteristic
322C2×C3×C9H(5,𝔽2)11yescharacteristic
323D3×C9—41no—
324D3×C9—41no—
325C3×D9—41no—
326C3×D9—41no—
327C2×C3×D4—31no—
328C2×C3×D4—31no—
329C2×C3×D4—31no—
330C2×C3×D4—91no—
331C2×C3×D4—91no—
332C2×C3×D4—91no—
333C22×C3×C4—31no—
334C22×C3×C4—91no—
335C2×#67—31no—
336C2×#67—31no—
337C2×#67—91no—
338C2×#67—91no—
339C2×#67—91no—
340C2×#67—91no—
341C2×#67—91no—
342C2×#67—91no—
343C2×#67—91no—
344C2×#67—91no—
345C2×#67C2×D911yescharacteristic
346C2×#67C2×D911yescharacteristic
347C22×Dic3—91no—
348C22×Dic3—91no—
349C22×Dic3—91no—
350C22×Dic3—91no—
351C22×Dic3—181no—
352C2×D12—31no—
353C2×D12C2×D911yescharacteristic
354C2×C4×D3—31no—
355C2×C4×D3—91no—
356C2×C4×D3—91no—
357C2×C4×D3C2×D911yescharacteristic
358C3×C4⋊C4—31no—
359C3×C4⋊C4—91no—
360C3×C22⋊C4—21no—
361C3×C22⋊C4—31no—
362C3×C22⋊C4—91no—
363C3×C22⋊C4C2×D911yescharacteristic
364C3×C22⋊C4D3211yescharacteristic
365#217—91no—
366#217—91no—
367#217—91no—
368#217—91no—
369#217—91no—
370#217—91no—
371#217—91no—
372#217—91no—
373#217—181no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—91no—
376(C2×D3)⋊C4—91no—
377(C2×D3)⋊C4—91no—
378(C2×D3)⋊C4—91no—
379(C2×D3)⋊C4—91no—
380(C2×D3)⋊C4—91no—
381(C2×D3)⋊C4C2×D911yescharacteristic
382C4⋊Dic3—91no—
383C4⋊Dic3—91no—
384Dic3⋊C4—31no—
385Dic3⋊C4—91no—
386Dic3⋊C4—91no—
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⋊C4—181no—
396Dic3⋊C4—181no—
397Dic3⋊C4C2×D911yescharacteristic
398C4×Dic3—91no—
399C4×Dic3—91no—
400C4×Dic3—91no—
401C4×Dic3—91no—
402C4×Dic3—181no—
403C4×Dic3—181no—
404C22×C32—21no—
405C22×C32—21no—
406C22×C32—21no—
407C22×C32C23×D311yescharacteristic
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—61no—
415C2×C3×D3—61no—
416C2×C3×D3—61no—
417C2×C3×D3—61no—
418C2×C3×D3—61no—
419C2×C3×D3—61no—
420C32×C4—21no—
421C32×C4—21no—
422C3⋊Dic3—32no—
423C3⋊Dic3—61no—
424C3⋊Dic3—61no—
425C3⋊Dic3—61no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—61no—
429C3×Dic3—61no—
430C22×C9—22no—
431C22×C9—21no—
432C22×C9—21no—
433C22×C9—21no—
434C22×C9—21no—
435C22×C9—41no—
436C22×C9—41no—
437C22×C9—61no—
438C22×C9—61no—
439C22×C9—61no—
440C22×C9—61no—
441C22×C9—61no—
442C22×C9—61no—
443C22×C9C23×D311yescharacteristic
444C2×D9—21no—
445C2×D9—21no—
446C2×D9—21no—
447C2×D9—21no—
448C2×D9—21no—
449C2×D9—21no—
450C4×C9—21no—
451C4×C9—21no—
452C4×C9—41no—
453C4×C9—41no—
454C4×C9—61no—
455C4×C9—61no—
456Dic9—21no—
457Dic9—21no—
458Dic9—32no—
459Dic9—62no—
460Dic9—62no—
461Dic9—61no—
462Dic9—61no—
463Dic9—61no—
464Dic9—121no—
465Dic9—121no—
466#127—271no—
467#125—271no—
468#123—271no—
469#123—271no—
470#123—271no—
471#123—271no—
472#121—31no—
473#121—91no—
474#121—271no—
475#121—271no—
476#121—271no—
477#121—271no—
478C4×D4—271no—
479C4×D4—271no—
480#117—271no—
481C3×C9#54011yescharacteristic, complemented, Sylow
482C23×C3—21no—
483C23×C3—31no—
484C23×C3—31no—
485C23×C3—91no—
486C23×C3—91no—
487C23×C3C22×D911yescharacteristic
488C23×C3C2×D3211yescharacteristic
489C22×D3—31no—
490C22×D3—31no—
491C22×D3C22×D911yescharacteristic
492C22×D3C22×D911yescharacteristic
493C3×D4—121no—
494C3×D4—121no—
495C3×D4—121no—
496C3×D4—361no—
497C3×D4—361no—
498C3×D4—361no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—91no—
504C2×C3×C4—91no—
505C2×C3×C4—121no—
506C2×C3×C4—361no—
507C2×C3×C4C22×D911yescharacteristic
508C2×C3×C4C22×D911yescharacteristic
509C2×C3×C4C2×D3211yescharacteristic
510C2×C3×C4C2×D3211yescharacteristic
511#67—41no—
512#67—41no—
513#67—121no—
514#67—121no—
515#67—182no—
516#67—182no—
517#67—182no—
518#67—182no—
519#67—361no—
520#67—361no—
521#67—361no—
522#67—361no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—91no—
526C2×Dic3—91no—
527C2×Dic3—91no—
528C2×Dic3—91no—
529C2×Dic3—91no—
530C2×Dic3—91no—
531C2×Dic3—91no—
532C2×Dic3—91no—
533C2×Dic3—181no—
534C2×Dic3—181no—
535C2×Dic3—181no—
536C2×Dic3—181no—
537C2×Dic3—182no—
538C2×Dic3—182no—
539C2×Dic3—184no—
540C2×Dic3—361no—
541C2×Dic3—361no—
542C2×Dic3C22×D911yescharacteristic
543C2×Dic3C22×D911yescharacteristic
544D12—41no—
545D12—121no—
546C4×D3—41no—
547C4×D3—121no—
548C4×D3—361no—
549C4×D3—361no—
550C2×C32—41no—
551C2×C32#100411yescharacteristic
552C2×C32#100411yescharacteristic
553C2×C32D3×#4111yescharacteristic
554C3×D3—41no—
555C3×D3—41no—
556C3×D3—121no—
557C3×D3—121no—
558C2×C9—21no—
559C2×C9—21no—
560C2×C9—21no—
561C2×C9—42no—
562C2×C9—41no—
563C2×C9—121no—
564C2×C9—121no—
565C2×C9#100411yescharacteristic
566C2×C9#100411yescharacteristic
567C2×C9D3×#4111yescharacteristic
568D9—41no—
569D9—41no—
570C2×D4—31no—
571C2×D4—31no—
572C2×D4—31no—
573C2×D4—91no—
574C2×D4—91no—
575C2×D4—91no—
576C2×D4—271no—
577C2×D4—271no—
578C2×D4—271no—
579C2×D4—271no—
580C22×C4—31no—
581C22×C4—91no—
582C22×C4—271no—
583C22×C4—271no—
584C22×C4—271no—
585C4⋊C4—31no—
586C4⋊C4—91no—
587C4⋊C4—271no—
588C4⋊C4—271no—
589C4⋊C4—271no—
590C4⋊C4—271no—
591C4⋊C4—271no—
592C4⋊C4—271no—
593C22⋊C4—31no—
594C22⋊C4—91no—
595C22⋊C4—271no—
596C22⋊C4—271no—
597C22⋊C4—271no—
598C22⋊C4—271no—
599C22⋊C4—271no—
600C22⋊C4—271no—
601C22⋊C4—271no—
602C22⋊C4D3×D911yescharacteristic
603C42—271no—
604C42—271no—
605C22×C3—22no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—61no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3—61no—
619C22×C3—61no—
620C22×C3—61no—
621C22×C3—181no—
622C22×C3—181no—
623C22×C3—181no—
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—21no—
633C2×D3—21no—
634C2×D3—21no—
635C2×D3—61no—
636C2×D3—61no—
637C2×D3—61no—
638C2×D3—61no—
639C2×D3—61no—
640C2×D3—61no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—61no—
648C3×C4—61no—
649C3×C4—181no—
650C3×C4—181no—
651Dic3—21no—
652Dic3—21no—
653Dic3—61no—
654Dic3—61no—
655Dic3—92no—
656Dic3—92no—
657Dic3—182no—
658Dic3—182no—
659Dic3—181no—
660Dic3—181no—
661Dic3—181no—
662Dic3—181no—
663Dic3—181no—
664Dic3—181no—
665Dic3—361no—
666Dic3—361no—
667C32#561511yescharacteristic
668C9—21no—
669C9#561511yescharacteristic, complemented
670C23—31no—
671C23—31no—
672C23—91no—
673C23—91no—
674C23C2×D3×D911yescharacteristic
675D4—121no—
676D4—121no—
677D4—121no—
678D4—361no—
679D4—361no—
680D4—361no—
681D4—542no—
682D4—542no—
683D4—1081no—
684D4—1081no—
685C2×C4—31no—
686C2×C4—31no—
687C2×C4—91no—
688C2×C4—91no—
689C2×C4—121no—
690C2×C4—271no—
691C2×C4—271no—
692C2×C4—271no—
693C2×C4—271no—
694C2×C4—361no—
695C2×C4—542no—
696C2×C4—1081no—
697C2×C4—1081no—
698C2×C4C2×D3×D911yescharacteristic
699C2×C4C2×D3×D911yescharacteristic
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—42no—
704C2×C3—41no—
705C2×C3—41no—
706C2×C3—121no—
707C2×C3—121no—
708C2×C3—361no—
709C2×C3—361no—
710C2×C3#6371011yescharacteristic
711C2×C3#6371011yescharacteristic
712C2×C3#41×D911yescharacteristic
713C2×C3#6430611yescharacteristic
714C2×C3#6431311yescharacteristic
715C2×C3#6431311yescharacteristic
716D3—41no—
717D3—41no—
718D3—121no—
719D3—121no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—61no—
724C22—61no—
725C22—61no—
726C22—61no—
727C22—61no—
728C22—61no—
729C22—181no—
730C22—181no—
731C22—181no—
732C22—181no—
733C22—181no—
734C22—181no—
735C22C22×D3×D911yescharacteristic
736C4—21no—
737C4—21no—
738C4—61no—
739C4—61no—
740C4—181no—
741C4—181no—
742C4—272no—
743C4—541no—
744C4—541no—
745C4—541no—
746C3—21no—
747C3#1058971711yescharacteristic, complemented
748C3#1059422311yescharacteristic
749C2—41no—
750C2—121no—
751C2—121no—
752C2—361no—
753C2—361no—
754C2#1172247511yescharacteristic
755C2#1172249911yescharacteristic
756C2#1172249911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#540
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. #11721723C2semidirect
2. C9×#884C2semidirect
3. C3×#63446C2semidirect
4. #11721290C2semidirect
5. #11721290C2semidirect
6. #11721281C2semidirect
7. #11721270C2semidirect
8. #11721043C2semidirect
9. #11721032C2semidirect
10. #11721031C2semidirect
11. #11721028C2semidirect
12. C4×#6194C2semidirect
13. #11721015C2semidirect
14. #11720981C2semidirect
15. #11720928C2semidirect
79. #63446D3semidirect
242. #884D9semidirect
481. C3×C9#540semidirect
669. C9#5615semidirect
747. C3#10589717semidirect

Maximal subgroups

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

subgroupindex
#117217232
C9×#8842
C3×#634462
#117212902
#117212812
#117212702
#117210432
#117210322
#117210312
#117210282
C4×#61942
#117210152
#117209812
#117209282
#105942233
#105897173