Finite Group Databasebeta

← #13148037

Subgroups — #13148037

Order 1728.

798 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721729C211yesmaximal, characteristic, complemented
2C9×#67⋊C4C211yesmaximal, characteristic, complemented
3C3×#63446C211yesmaximal, characteristic, complemented
4#11721289C211yesmaximal, characteristic, complemented
5#11721277C211yesmaximal, characteristic, complemented
6#11721270C211yesmaximal, characteristic, complemented
7#11721259C211yesmaximal, characteristic, complemented
8#11721041C211yesmaximal, characteristic, complemented
9#11721037C211yesmaximal, characteristic, complemented
10#11721031C211yesmaximal, characteristic, complemented
11C4×#6192C211yesmaximal, characteristic, complemented
12#11720983C211yesmaximal, characteristic, complemented
13#11720974C211yesmaximal, characteristic, complemented
14#11720954C211yesmaximal, characteristic, complemented
15#11720914C211yesmaximal, characteristic, complemented
16#10594100—31nomaximal
17#10589664—31nomaximal
18C2×#6233C2211yescharacteristic
19C2×C4×C3⋊D9C2211yescharacteristic
20C2×C9×#67C2211yescharacteristic
21C2×C3×#611C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C22×C9×Dic3C2211yescharacteristic
24C2×C4×D3×C9C2211yescharacteristic
25C2×C3×D36C2211yescharacteristic
26C2×C3×C4×D9C2211yescharacteristic
27C2×#6195C2211yescharacteristic
28C2×#6194C2211yescharacteristic
29C2×#6194C2211yescharacteristic
30C2×#6192C2211yescharacteristic
31C2×#6192C2211yescharacteristic
32C2×Dic3×D9C2211yescharacteristic
33C3×C9×C22⋊C4C2211yescharacteristic
34#88551C2211yescharacteristic
35#88536C2211yescharacteristic
36C4⋊(C3⋊Dic9)C2211yescharacteristic
37#88534C2211yescharacteristic
38C9×(C2×D3)⋊C4C2211yescharacteristic
39C3×(C2×D9)⋊C4C2211yescharacteristic
40C9×Dic3⋊C4C2211yescharacteristic
41C4×C9×Dic3C2211yescharacteristic
42C3×Dic9⋊C4C2211yescharacteristic
43(C2×D3)⋊Dic9C2211yescharacteristic
44#88445C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47(C2×D9)⋊Dic3C2211yescharacteristic
48Dic3⋊Dic9C2211yescharacteristic
49Dic3⋊Dic9C2211yescharacteristic
50#88442C2211yescharacteristic
51#88442C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53#64092—31no—
54C3×#884—31no—
55C3×#67⋊C4D311yescharacteristic
56#63979—31no—
57#63978—31no—
58#63970—31no—
59#63961—31no—
60#63912—31no—
61#63908—31no—
62#63905—31no—
63C4×#626—31no—
64#63886—31no—
65#63877—31no—
66#63850—31no—
67#63845—31no—
68C4×D4×C9—31no—
69#63502—31no—
70#63500—31no—
71#63492—31no—
72#63492—31no—
73#63491—31no—
74#63491—31no—
75#63457—31no—
76#63452—31no—
77#63446—31no—
78#63446D311yescharacteristic, complemented
79#63445—31no—
80#63445—31no—
81#63445—61no—
82C4×D36—31no—
83#63434—31no—
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C22×D3×C9C2311yescharacteristic
87C22×C3×D9C2311yescharacteristic
88C22×C3×D9C2311yescharacteristic
89C2×C3×C4×C9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91#6233—41no—
92C2×C3⋊Dic9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C4×C3⋊D9—41no—
96C9×#67—22no—
97C3×#611—41no—
98C3×#611—41no—
99C2×C9×Dic3—41no—
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C4×D3×C9—41no—
106C3×D36—41no—
107C3×C4×D9—41no—
108#6195—41no—
109#6194—41no—
110#6194—41no—
111#6192—22no—
112#6192—41no—
113Dic3×D9—22no—
114#5615—91no—
115#5562—91no—
116C2×#638—31no—
117C2×C4×C3⋊D3—31no—
118C2×C3×#67—31no—
119C2×C3×#67—31no—
120C2×C3×#67C2×D311yescharacteristic
121C22×C3×Dic3C2×D311yescharacteristic
122C2×C3×D12—31no—
123C2×C3×C4×D3—31no—
124C2×C3×C4×D3C2×D311yescharacteristic
125C2×#626—31no—
126C2×#626—31no—
127C2×#626—31no—
128C2×#625—31no—
129C2×#625—31no—
130C2×D3×Dic3—31no—
131C32×C22⋊C4C2×D311yescharacteristic
132#3757—31no—
133#3752—31no—
134C4⋊(C3⋊Dic3)—31no—
135#3750—31no—
136C3×(C2×D3)⋊C4—31no—
137C3×(C2×D3)⋊C4C2×D311yescharacteristic
138C3×Dic3⋊C4—31no—
139C3×Dic3⋊C4C2×D311yescharacteristic
140C3×C4×Dic3C2×D311yescharacteristic
141#3724—31no—
142#3724—31no—
143Dic3⋊Dic3—31no—
144Dic3⋊Dic3—31no—
145#3722—31no—
146(C2×D3)⋊Dic3—31no—
147(C2×D3)⋊Dic3—31no—
148(C2×D3)⋊Dic3—31no—
149(C2×D3)⋊Dic3—31no—
150Dic32—31no—
151C2×D4×C9—31no—
152C22×C4×C9—31no—
153C22×C4×C9—31no—
154C2×#611—31no—
155C2×#611—31no—
156C2×#611—31no—
157C2×#611—31no—
158C2×#611—61no—
159C2×#611C2×D311yescharacteristic
160C2×#611C2×D311yescharacteristic
161C2×D36—31no—
162C2×D36—31no—
163C2×D36C2×D311yescharacteristic
164C2×C4×D9—31no—
165C2×C4×D9—31no—
166C2×C4×D9—61no—
167C2×C4×D9C2×D311yescharacteristic
168C9×C4⋊C4—31no—
169C9×C22⋊C4—21no—
170C9×C22⋊C4—31no—
171C9×C22⋊C4C2×D311yescharacteristic
172C42×C9—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)⋊C4—31no—
180(C2×D9)⋊C4—31no—
181(C2×D9)⋊C4—61no—
182(C2×D9)⋊C4C2×D311yescharacteristic
183C4⋊Dic9—31no—
184C4⋊Dic9—31no—
185C4⋊Dic9—31no—
186C4⋊Dic9—61no—
187Dic9⋊C4—31no—
188Dic9⋊C4—31no—
189Dic9⋊C4—31no—
190Dic9⋊C4—61no—
191Dic9⋊C4C2×D311yescharacteristic
192C4×Dic9—31no—
193C22×C3×C9—21no—
194C22×C3×C9—21no—
195C22×C3×C9—21no—
196C22×C3×C9C2411yescharacteristic
197C2×C3⋊D9—21no—
198C2×C3⋊D9—21no—
199C2×C3⋊D9—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—
214C9×Dic3—21no—
215C9×Dic3—21no—
216C9×Dic3#4112yes—
217C3×Dic9—21no—
218C3×Dic9—21no—
219C3×#121—91no—
220C3×C4×D4—31no—
221#940—91no—
222#940—91no—
223#939—91no—
224#939—91no—
225#939—91no—
226#938—91no—
227#938—91no—
228#935—91no—
229#930—91no—
230#930—91no—
231#929—91no—
232#929—91no—
233#929—91no—
234C4×#67—91no—
235#895—91no—
236#894—91no—
237#890—91no—
238#889—91no—
239#884—31no—
240#884—91no—
241#884—91no—
242#883—91no—
243#883—91no—
244#883—91no—
245#883—181no—
246#67⋊C4D911yescharacteristic, complemented
247#877—91no—
248C4×D12—91no—
249#872—91no—
250C23×C32C22×D311yescharacteristic
251C22×C3⋊D3—31no—
252C22×C3×D3—31no—
253C22×C3×D3—31no—
254C22×C3×D3C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C22×D311yescharacteristic
257#638—121no—
258C2×C3⋊Dic3—31no—
259C2×C3⋊Dic3—31no—
260C2×C3⋊Dic3—31no—
261C4×C3⋊D3—121no—
262C3×#67—22no—
263C3×#67—121no—
264C3×#67—121no—
265C2×C3×Dic3—31no—
266C2×C3×Dic3—31no—
267C2×C3×Dic3—41no—
268C2×C3×Dic3C22×D311yescharacteristic
269C2×C3×Dic3C22×D311yescharacteristic
270C2×C3×Dic3C22×D311yescharacteristic
271C3×D12—121no—
272C3×C4×D3—41no—
273C3×C4×D3—121no—
274#626—62no—
275#626—121no—
276#626—121no—
277#625—121no—
278#625—121no—
279D3×Dic3—62no—
280C23×C9—21no—
281C23×C9—31no—
282C23×C9C22×D311yescharacteristic
283C22×D9—31no—
284C22×D9—61no—
285C22×D9C22×D311yescharacteristic
286C22×D9C22×D311yescharacteristic
287D4×C9—62no—
288C2×C4×C9—21no—
289C2×C4×C9—21no—
290C2×C4×C9—31no—
291C2×C4×C9—31no—
292C2×C4×C9—31no—
293C2×C4×C9—121no—
294C2×C4×C9—121no—
295C2×C4×C9C22×D311yescharacteristic
296C2×C4×C9C22×D311yescharacteristic
297#611—41no—
298#611—41no—
299#611—121no—
300#611—121no—
301#611—121no—
302#611—121no—
303#611—122no—
304C2×Dic9—31no—
305C2×Dic9—31no—
306C2×Dic9—31no—
307C2×Dic9—61no—
308C2×Dic9—61no—
309C2×Dic9—61no—
310C2×Dic9C22×D311yescharacteristic
311C2×Dic9C22×D311yescharacteristic
312D36—41no—
313D36—62no—
314D36—121no—
315C4×D9—41no—
316C4×D9—62no—
317C4×D9—121no—
318C4×D9—122no—
319#540—271noSylow
320C2×C3×C9—41no—
321C2×C3×C9C2×#4111yescharacteristic
322C2×C3×C9H(5,𝔽2)11yescharacteristic
323C2×C3×C9H(5,𝔽2)11yescharacteristic
324C3⋊D9—41no—
325D3×C9—41no—
326C3×D9—41no—
327C3×D9—41no—
328C2×C3×D4—31no—
329C2×C3×D4—91no—
330C2×C3×D4—91no—
331C2×C3×D4—91no—
332C22×C3×C4—31no—
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×#67—91no—
346C2×#67—181no—
347C2×#67C2×D911yescharacteristic
348C22×Dic3—91no—
349C22×Dic3C2×D911yescharacteristic
350C2×D12—31no—
351C2×D12—91no—
352C2×D12—91no—
353C2×D12—91no—
354C2×C4×D3—31no—
355C2×C4×D3—91no—
356C2×C4×D3—91no—
357C2×C4×D3—91no—
358C2×C4×D3—181no—
359C2×C4×D3C2×D911yescharacteristic
360C3×C4⋊C4—31no—
361C3×C4⋊C4—91no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—31no—
364C3×C22⋊C4—91no—
365C3×C22⋊C4C2×D911yescharacteristic
366C3×C22⋊C4D3211yescharacteristic
367C3×C42—31no—
368#217—91no—
369#217—91no—
370#217—91no—
371#217—91no—
372#217—91no—
373#217—91no—
374#217—181no—
375(C2×D3)⋊C4—31no—
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)⋊C4—91no—
382(C2×D3)⋊C4—91no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—181no—
385(C2×D3)⋊C4C2×D911yescharacteristic
386C4⋊Dic3—91no—
387C4⋊Dic3—91no—
388C4⋊Dic3—91no—
389C4⋊Dic3—91no—
390C4⋊Dic3—181no—
391Dic3⋊C4—31no—
392Dic3⋊C4—91no—
393Dic3⋊C4—91no—
394Dic3⋊C4—91no—
395Dic3⋊C4—91no—
396Dic3⋊C4—91no—
397Dic3⋊C4—91no—
398Dic3⋊C4—91no—
399Dic3⋊C4—91no—
400Dic3⋊C4—181no—
401Dic3⋊C4C2×D911yescharacteristic
402C4×Dic3—91no—
403C4×Dic3—91no—
404C4×Dic3C2×D911yescharacteristic
405C22×C32—21no—
406C22×C32—21no—
407C22×C32—21no—
408C22×C32C23×D311yescharacteristic
409C2×C3⋊D3—61no—
410C2×C3⋊D3—61no—
411C2×C3⋊D3—61no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—61no—
416C2×C3×D3—61no—
417C2×C3×D3—61no—
418C2×C3×D3—61no—
419C2×C3×D3—61no—
420C2×C3×D3—61no—
421C32×C4—21no—
422C32×C4—21no—
423C3⋊Dic3—61no—
424C3⋊Dic3—61no—
425C3⋊Dic3—61no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—61no—
429C3×Dic3—61no—
430C3×Dic3#23512yes—
431C22×C9—21no—
432C22×C9—21no—
433C22×C9—21no—
434C22×C9—21no—
435C22×C9—41no—
436C22×C9—41no—
437C22×C9—41no—
438C22×C9—61no—
439C22×C9—61no—
440C22×C9—61no—
441C22×C9C23×D311yescharacteristic
442C2×D9—21no—
443C2×D9—21no—
444C2×D9—21no—
445C2×D9—21no—
446C2×D9—21no—
447C2×D9—21no—
448C2×D9—62no—
449C2×D9—61no—
450C2×D9—61no—
451C2×D9—61no—
452C2×D9—121no—
453C2×D9—121no—
454C4×C9—21no—
455C4×C9—21no—
456C4×C9—32no—
457C4×C9—41no—
458C4×C9—41no—
459C4×C9—61no—
460C4×C9—61no—
461Dic9—21no—
462Dic9—21no—
463Dic9—61no—
464Dic9—61no—
465Dic9—61no—
466Dic9—121no—
467Dic9—121no—
468Dic9—121no—
469#127—271no—
470#125—271no—
471#123—271no—
472#123—271no—
473#123—271no—
474#123—271no—
475#121—91no—
476#121—271no—
477#121—271no—
478#121—271no—
479#121—271no—
480#121—271no—
481C4×D4—31no—
482C4×D4—271no—
483#117—271no—
484C3×C9#54011yescharacteristic, complemented, Sylow
485C23×C3—21no—
486C23×C3—31no—
487C23×C3—91no—
488C23×C3—91no—
489C23×C3C22×D911yescharacteristic
490C23×C3C2×D3211yescharacteristic
491C22×D3—31no—
492C22×D3—31no—
493C22×D3—91no—
494C22×D3—91no—
495C22×D3—181no—
496C22×D3C22×D911yescharacteristic
497C3×D4—62no—
498C3×D4—361no—
499C3×D4—361no—
500C3×D4—361no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—91no—
507C2×C3×C4—91no—
508C2×C3×C4—121no—
509C2×C3×C4—121no—
510C2×C3×C4—361no—
511C2×C3×C4C22×D911yescharacteristic
512C2×C3×C4C22×D911yescharacteristic
513C2×C3×C4C2×D3211yescharacteristic
514C2×C3×C4C2×D3211yescharacteristic
515#67—22no—
516#67—121no—
517#67—121no—
518#67—182no—
519#67—361no—
520#67—361no—
521#67—361no—
522#67—361no—
523#67—361no—
524#67—361no—
525#67—361no—
526#67—361no—
527#67—362no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—41no—
531C2×Dic3—91no—
532C2×Dic3—91no—
533C2×Dic3—91no—
534C2×Dic3—91no—
535C2×Dic3—91no—
536C2×Dic3—91no—
537C2×Dic3—181no—
538C2×Dic3—181no—
539C2×Dic3—181no—
540C2×Dic3—182no—
541C2×Dic3C22×D911yescharacteristic
542C2×Dic3C22×D911yescharacteristic
543C2×Dic3C22×D911yescharacteristic
544D12—121no—
545D12—182no—
546D12—361no—
547D12—361no—
548C4×D3—41no—
549C4×D3—121no—
550C4×D3—182no—
551C4×D3—361no—
552C4×D3—361no—
553C4×D3—362no—
554C2×C32—41no—
555C2×C32C2×#23511yescharacteristic
556C2×C32#100411yescharacteristic
557C2×C32#100911yescharacteristic
558C3⋊D3—121no—
559C3×D3—41no—
560C3×D3—121no—
561C3×D3—121no—
562C2×C9—21no—
563C2×C9—21no—
564C2×C9—21no—
565C2×C9—41no—
566C2×C9—81no—
567C2×C9—121no—
568C2×C9#100411yescharacteristic
569C2×C9#100411yescharacteristic
570C2×C9D3×#4111yescharacteristic
571D9—41no—
572D9—41no—
573D9—122no—
574D9—121no—
575C2×D4—31no—
576C2×D4—91no—
577C2×D4—91no—
578C2×D4—91no—
579C2×D4—271no—
580C2×D4—271no—
581C2×D4—271no—
582C2×D4—271no—
583C2×D4—271no—
584C2×D4—271no—
585C22×C4—31no—
586C22×C4—31no—
587C22×C4—91no—
588C22×C4—271no—
589C22×C4—271no—
590C4⋊C4—31no—
591C4⋊C4—91no—
592C4⋊C4—271no—
593C4⋊C4—271no—
594C4⋊C4—271no—
595C4⋊C4—271no—
596C4⋊C4—271no—
597C4⋊C4—271no—
598C22⋊C4—31no—
599C22⋊C4—91no—
600C22⋊C4—271no—
601C22⋊C4—271no—
602C22⋊C4—271no—
603C22⋊C4—271no—
604C22⋊C4—271no—
605C22⋊C4—271no—
606C22⋊C4—271no—
607C22⋊C4D3×D911yescharacteristic
608C42—31no—
609C42—271no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—61no—
621C22×C3—61no—
622C22×C3—61no—
623C22×C3—181no—
624C22×C3—181no—
625C22×C3—181no—
626C22×C3—181no—
627C22×C3—181no—
628C22×C3—181no—
629C22×C3C23×D911yescharacteristic
630C22×C3C22×D3211yescharacteristic
631C2×D3—21no—
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—61no—
635C2×D3—61no—
636C2×D3—61no—
637C2×D3—61no—
638C2×D3—61no—
639C2×D3—61no—
640C2×D3—182no—
641C2×D3—181no—
642C2×D3—181no—
643C2×D3—181no—
644C2×D3—181no—
645C2×D3—181no—
646C2×D3—181no—
647C2×D3—361no—
648C2×D3—361no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—32no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—61no—
657C3×C4—61no—
658C3×C4—181no—
659C3×C4—181no—
660Dic3—21no—
661Dic3—21no—
662Dic3—61no—
663Dic3—61no—
664Dic3—181no—
665Dic3—181no—
666Dic3—181no—
667Dic3—181no—
668Dic3—181no—
669Dic3—181no—
670Dic3—361no—
671Dic3—361no—
672Dic3—361no—
673Dic3#369712yes—
674C32#556211yescharacteristic
675C9—21no—
676C9#561511yescharacteristic, complemented
677C23—31no—
678C23—91no—
679C23—91no—
680C23—271no—
681C23C2×D3×D911yescharacteristic
682D4—62no—
683D4—361no—
684D4—361no—
685D4—361no—
686D4—542no—
687D4—1081no—
688D4—1081no—
689D4—1081no—
690D4—1081no—
691D4—1081no—
692C2×C4—31no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—91no—
696C2×C4—91no—
697C2×C4—121no—
698C2×C4—121no—
699C2×C4—271no—
700C2×C4—271no—
701C2×C4—271no—
702C2×C4—361no—
703C2×C4—542no—
704C2×C4—1081no—
705C2×C4C2×D3×D911yescharacteristic
706C2×C4C2×D3×D911yescharacteristic
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—41no—
711C2×C3—41no—
712C2×C3—81no—
713C2×C3—121no—
714C2×C3—361no—
715C2×C3—361no—
716C2×C3C2×#369711yescharacteristic
717C2×C3#6371011yescharacteristic
718C2×C3#6371511yescharacteristic
719C2×C3D3×#23511yescharacteristic
720C2×C3#6431311yescharacteristic
721C2×C3#6431411yescharacteristic
722D3—41no—
723D3—121no—
724D3—121no—
725D3—362no—
726D3—361no—
727D3—361no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—61no—
732C22—61no—
733C22—61no—
734C22—181no—
735C22—181no—
736C22—181no—
737C22—181no—
738C22—181no—
739C22—181no—
740C22—541no—
741C22—541no—
742C22—541no—
743C22C22×D3×D911yescharacteristic
744C4—21no—
745C4—21no—
746C4—32no—
747C4—61no—
748C4—61no—
749C4—181no—
750C4—181no—
751C4—541no—
752C4—541no—
753C4—541no—
754C3—21no—
755C3#1058966411yescharacteristic, complemented
756C3#1059410011yescharacteristic
757C2—41no—
758C2—121no—
759C2—361no—
760C2—361no—
761C2—1081no—
762C2D3×#369711yescharacteristic
763C2#1172249911yescharacteristic
764C2#1172250111yescharacteristic
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. #11721729C2semidirect
2. C9×#67⋊C4C2semidirect
3. C3×#63446C2semidirect
4. #11721289C2semidirect
5. #11721277C2semidirect
6. #11721270C2semidirect
7. #11721259C2semidirect
8. #11721041C2semidirect
9. #11721037C2semidirect
10. #11721031C2semidirect
11. C4×#6192C2semidirect
12. #11720983C2semidirect
13. #11720974C2semidirect
14. #11720954C2semidirect
15. #11720914C2semidirect
78. #63446D3semidirect
246. #67⋊C4D9semidirect
484. C3×C9#540semidirect
676. C9#5615semidirect
755. C3#10589664semidirect

Maximal subgroups

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

subgroupindex
#117217292
C9×#67⋊C42
C3×#634462
#117212892
#117212772
#117212702
#117212592
#117210412
#117210372
#117210312
C4×#61922
#117209832
#117209742
#117209542
#117209142
#105941003
#105896643