Finite Group Databasebeta

← #13150218

Subgroups — #13150218

Order 1728.

1040 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88736C211yesmaximal, characteristic, complemented
2C2×#88658C211yesmaximal, characteristic, complemented
3C3×#63491C211yesmaximal, characteristic, complemented
4C2×C9×Dic3⋊C4C211yesmaximal, characteristic, complemented
5#11721277C211yesmaximal, characteristic, complemented
6#11721251C211yesmaximal, characteristic, complemented
7#11721240C211yesmaximal, characteristic, complemented
8#11721005C211yesmaximal, characteristic, complemented
9#11720997C211yesmaximal, characteristic, complemented
10#11720996C211yesmaximal, characteristic, complemented
11#11720980C211yesmaximal, characteristic, complemented
12#11720978C211yesmaximal, characteristic, complemented
13#11720941C211yesmaximal, characteristic, complemented
14#11720923C211yesmaximal, characteristic, complemented
15#11720905C211yesmaximal, characteristic, complemented
16#10594917—31nomaximal
17#10589609—31nomaximal
18C22×C3×C4×C9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21#88736—24no—
22C2×C4⋊(C3⋊D9)C2211yescharacteristic
23C2×C4×C3⋊D9C2211yescharacteristic
24C2×C4×C3⋊D9C2211yescharacteristic
25C2×#6226C2211yescharacteristic
26C2×C3×#611C2211yescharacteristic
27C22×C9×Dic3C2211yescharacteristic
28C22×C9×Dic3C2211yescharacteristic
29C2×#6192C2211yescharacteristic
30C2×#6192C2211yescharacteristic
31C2×(C3⋊D9)⋊C4C2211yescharacteristic
32C2×(C3⋊D9)⋊C4C2211yescharacteristic
33#88658—24no—
34C2×Dic3×D9C2211yescharacteristic
35C2×#6189C2211yescharacteristic
36C3×#3676C2211yescharacteristic
37C3×(C2×D9)⋊C4C2211yescharacteristic
38C3×(C2×D9)⋊C4C2211yescharacteristic
39C9×Dic3⋊C4C2211yescharacteristic
40C9×Dic3⋊C4C2211yescharacteristic
41C9×Dic3⋊C4C2211yescharacteristic
42C9×Dic3⋊C4C2211yescharacteristic
43C3×Dic9⋊C4C2211yescharacteristic
44C3×Dic9⋊C4C2211yescharacteristic
45#88445C2211yescharacteristic
46#88445C2211yescharacteristic
47#88445C2211yescharacteristic
48#88445C2211yescharacteristic
49(C2×D9)⋊Dic3C2211yescharacteristic
50Dic3⋊Dic9C2211yescharacteristic
51#88442C2211yescharacteristic
52Dic9⋊Dic3C2211yescharacteristic
53Dic9⋊Dic3C2211yescharacteristic
54Dic3×Dic9C2211yescharacteristic
55C2×#3828—31no—
56C2×#3804—31no—
57C3×#929—31no—
58C2×C3×Dic3⋊C4D311yescharacteristic
59#63978—31no—
60#63966—31no—
61#63952—31no—
62#63910—31no—
63#63897—31no—
64#63896—31no—
65#63883—31no—
66#63881—31no—
67#63865—31no—
68#63853—31no—
69#63840—31no—
70C2×#3697—31no—
71C2×#3697—31no—
72C2×#3697—61no—
73C2×C9×C4⋊C4—31no—
74#63492—31no—
75#63491—31no—
76#63491D311yescharacteristic, complemented
77C4×#611—31no—
78#63458—31no—
79#63458—31no—
80#63457—31no—
81#63456—31no—
82#63456—31no—
83#63455—31no—
84C4⋊C4×D9—31no—
85#63450—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×C3×D9C2311yescharacteristic
90C2×C3×C4×C9—22no—
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93#6233—22no—
94#6233D414yescomplemented
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C4⋊(C3⋊D9)—22no—
98C4×C3⋊D9—22no—
99C4×C3⋊D9—22no—
100#6226—22no—
101C3×#611—22no—
102C2×C9×Dic3—22no—
103C2×C9×Dic3—22no—
104C2×C9×Dic3C2311yescharacteristic
105C2×C9×Dic3C2311yescharacteristic
106C2×C9×Dic3C2311yescharacteristic
107C2×C9×Dic3C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111#6192—22no—
112#6192—22no—
113(C3⋊D9)⋊C4—22no—
114(C3⋊D9)⋊C4—22no—
115Dic3×D9—22no—
116#6189—22no—
117#5655—91no—
118#5507—91no—
119C22×C32×C4C2×D311yescharacteristic
120C2×#638—31no—
121C2×#638—31no—
122#3828—64no—
123C2×C4⋊(C3⋊D3)—31no—
124C2×C4×C3⋊D3—31no—
125C2×C4×C3⋊D3—31no—
126C2×#634—31no—
127C2×C3×#67—31no—
128C22×C3×Dic3C2×D311yescharacteristic
129C22×C3×Dic3C2×D311yescharacteristic
130C2×#627—31no—
131C2×#626—31no—
132C2×#626—31no—
133C2×#624—31no—
134C2×#624—31no—
135#3804—64no—
136C2×D3×Dic3—31no—
137C3×#217—31no—
138C3×(C2×D3)⋊C4—31no—
139C3×(C2×D3)⋊C4—31no—
140C3×Dic3⋊C4—31no—
141C3×Dic3⋊C4—31no—
142C3×Dic3⋊C4C2×D311yescharacteristic
143C3×Dic3⋊C4C2×D311yescharacteristic
144C3×Dic3⋊C4C2×D311yescharacteristic
145C3×Dic3⋊C4C2×D311yescharacteristic
146#3724—31no—
147Dic3⋊Dic3—31no—
148Dic3⋊Dic3—31no—
149Dic3⋊Dic3—31no—
150#3722—31no—
151#3722—31no—
152#3722—31no—
153#3722—31no—
154(C2×D3)⋊Dic3—31no—
155Dic32—31no—
156C22×C4×C9—21no—
157C22×C4×C9—31no—
158C22×C4×C9—31no—
159C22×C4×C9C2×D311yescharacteristic
160C2×#611—31no—
161C2×#611—31no—
162C2×#611—61no—
163C2×#611—61no—
164C2×#611C2×D311yescharacteristic
165#3697—64no—
166#3697—64no—
167#3697—68no—
168C2×D36—31no—
169C2×D36—31no—
170C2×D36—31no—
171C2×D36—61no—
172C2×C4×D9—31no—
173C2×C4×D9—31no—
174C2×C4×D9—31no—
175C2×C4×D9—31no—
176C2×C4×D9—31no—
177C2×C4×D9—61no—
178C2×C4×D9—61no—
179C2×Dic18—31no—
180C2×Dic18—31no—
181C2×Dic18—61no—
182C9×C4⋊C4—31no—
183C9×C4⋊C4—31no—
184C9×C4⋊C4—31no—
185C9×C4⋊C4—31no—
186#3676C2×D311yescharacteristic
187(C2×D9)⋊C4—31no—
188(C2×D9)⋊C4—31no—
189(C2×D9)⋊C4—31no—
190(C2×D9)⋊C4—31no—
191(C2×D9)⋊C4—31no—
192(C2×D9)⋊C4C2×D311yescharacteristic
193(C2×D9)⋊C4C2×D311yescharacteristic
194C4⋊Dic9—31no—
195Dic9⋊C4—31no—
196Dic9⋊C4—31no—
197Dic9⋊C4—31no—
198Dic9⋊C4C2×D311yescharacteristic
199Dic9⋊C4C2×D311yescharacteristic
200C4×Dic9—31no—
201C22×C3×C9—21no—
202C22×C3×C9—21no—
203C22×C3×C9C2×D412yes—
204C22×C3×C9C2411yescharacteristic
205C2×C3⋊D9—21no—
206C2×C3⋊D9—21no—
207C2×C3⋊D9—21no—
208C2×C3⋊D9—21no—
209C2×C3⋊D9—21no—
210C2×C3⋊D9C2×D412yes—
211C2×C3×D9—21no—
212C2×C3×D9—21no—
213C2×C3×D9—21no—
214C3×C4×C9—21no—
215C3×C4×C9—21no—
216C3⋊Dic9—21no—
217C3⋊Dic9C2×D412yes—
218C9×Dic3—21no—
219C9×Dic3—21no—
220C9×Dic3—21no—
221C9×Dic3#4112yescomplemented
222C3×Dic9—21no—
223C3×Dic9—21no—
224C3×Dic9—21no—
225C2×#237—91no—
226C2×#235—91no—
227C2×#235—91no—
228C2×#235—91no—
229C2×#235—181no—
230C3×#123—91no—
231C2×C3×C4⋊C4—31no—
232#939—91no—
233#930—91no—
234#929—31no—
235#929—91no—
236C4×#67—91no—
237C2×Dic3⋊C4D911yescharacteristic, complemented
238#896—91no—
239#896—91no—
240#896—91no—
241#895—91no—
242#894—91no—
243#894—91no—
244#894—91no—
245#893—91no—
246D3×C4⋊C4—91no—
247D3×C4⋊C4—91no—
248#888—91no—
249#888—91no—
250#886—91no—
251#884—91no—
252#883—91no—
253#67⋊C4—91no—
254#67⋊C4—91no—
255#878—91no—
256C23×C32C22×D311yescharacteristic
257C22×C3⋊D3—31no—
258C22×C3⋊D3—31no—
259C22×C3×D3—31no—
260C2×C32×C4—22no—
261C2×C32×C4C22×D311yescharacteristic
262C2×C32×C4C22×D311yescharacteristic
263#638—34no—
264#638—62no—
265C2×C3⋊Dic3—31no—
266C2×C3⋊Dic3—31no—
267C4⋊(C3⋊D3)—62no—
268C4×C3⋊D3—62no—
269C4×C3⋊D3—62no—
270#634—62no—
271C3×#67—62no—
272C2×C3×Dic3—22no—
273C2×C3×Dic3—22no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3C22×D311yescharacteristic
278C2×C3×Dic3C22×D311yescharacteristic
279C2×C3×Dic3C22×D311yescharacteristic
280C2×C3×Dic3C22×D311yescharacteristic
281#627—62no—
282#626—62no—
283#626—62no—
284#624—62no—
285#624—62no—
286D3×Dic3—62no—
287C23×C9—21no—
288C23×C9C22×D311yescharacteristic
289C22×D9—31no—
290C22×D9—31no—
291C22×D9—61no—
292C22×D9—61no—
293C22×D9C22×D311yescharacteristic
294C2×C4×C9—24no—
295C2×C4×C9—22no—
296C2×C4×C9—21no—
297C2×C4×C9—21no—
298C2×C4×C9—31no—
299C2×C4×C9—31no—
300C2×C4×C9—31no—
301C2×C4×C9—31no—
302C2×C4×C9—62no—
303C2×C4×C9—62no—
304C2×C4×C9C22×D311yescharacteristic
305C2×C4×C9C22×D311yescharacteristic
306#611—22no—
307#611—34no—
308#611—64no—
309#611—64no—
310#611—62no—
311C2×Dic9—31no—
312C2×Dic9—31no—
313C2×Dic9—61no—
314C2×Dic9—61no—
315C2×Dic9C22×D311yescharacteristic
316C2×Dic9C22×D311yescharacteristic
317C2×Dic9C22×D311yescharacteristic
318D36—62no—
319D36—64no—
320D36—62no—
321D36—62no—
322C4×D9—62no—
323C4×D9—62no—
324C4×D9—62no—
325C4×D9—62no—
326C4×D9—62no—
327C4×D9—64no—
328C4×D9—64no—
329Dic18—62no—
330Dic18—62no—
331Dic18—64no—
332#547—271noSylow
333C2×C3×C9—22no—
334C2×C3×C9C22×D411yescharacteristic
335C2×C3×C9C2×#4111yescharacteristic
336C2×C3×C92−1+411yescharacteristic
337C3⋊D9—22no—
338C3⋊D9—41no—
339C3×D9—41no—
340C2×C3×D4—91no—
341C22×C3×C4—21no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4C2×D911yescharacteristic
345C22×C3×C4D3211yescharacteristic
346C2×#67—31no—
347C2×#67—91no—
348C2×#67—91no—
349C2×#67—91no—
350C2×#67—91no—
351C2×#67—91no—
352C2×#67—91no—
353C2×#67—181no—
354C2×#67—181no—
355C22×Dic3—91no—
356C22×Dic3C2×D911yescharacteristic
357C22×Dic3C2×D911yescharacteristic
358#237—184no—
359#235—184no—
360#235—184no—
361#235—184no—
362#235—188no—
363C2×D12—91no—
364C2×D12—91no—
365C2×D12—91no—
366C2×D12—91no—
367C2×D12—181no—
368C2×C4×D3—91no—
369C2×C4×D3—91no—
370C2×C4×D3—91no—
371C2×C4×D3—91no—
372C2×C4×D3—91no—
373C2×C4×D3—91no—
374C2×C4×D3—91no—
375C2×C4×D3—91no—
376C2×C4×D3—91no—
377C2×C4×D3—181no—
378C2×C4×D3—181no—
379C2×Dic6—91no—
380C2×Dic6—91no—
381C2×Dic6—91no—
382C2×Dic6—91no—
383C2×Dic6—181no—
384C3×C4⋊C4—31no—
385C3×C4⋊C4—31no—
386C3×C4⋊C4—31no—
387C3×C4⋊C4—31no—
388C3×C4⋊C4—91no—
389C3×C4⋊C4—91no—
390C3×C22⋊C4—91no—
391C3×C22⋊C4—91no—
392C3×C22⋊C4—91no—
393#217—31no—
394#217—91no—
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—91no—
398(C2×D3)⋊C4—91no—
399(C2×D3)⋊C4—91no—
400(C2×D3)⋊C4—91no—
401(C2×D3)⋊C4—91no—
402(C2×D3)⋊C4—91no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—91no—
405(C2×D3)⋊C4—91no—
406C4⋊Dic3—91no—
407C4⋊Dic3—91no—
408C4⋊Dic3—91no—
409Dic3⋊C4—31no—
410Dic3⋊C4—31no—
411Dic3⋊C4—91no—
412Dic3⋊C4—91no—
413Dic3⋊C4—91no—
414Dic3⋊C4—91no—
415Dic3⋊C4—91no—
416Dic3⋊C4C2×D911yescharacteristic
417Dic3⋊C4C2×D911yescharacteristic
418Dic3⋊C4C2×D911yescharacteristic
419Dic3⋊C4C2×D911yescharacteristic
420C4×Dic3—91no—
421C4×Dic3—91no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32D3×D412yes—
425C22×C32C23×D311yescharacteristic
426C2×C3⋊D3—32no—
427C2×C3⋊D3—61no—
428C2×C3⋊D3—61no—
429C2×C3⋊D3—61no—
430C2×C3⋊D3—61no—
431C2×C3⋊D3—61no—
432C2×C3×D3—61no—
433C2×C3×D3—61no—
434C2×C3×D3—61no—
435C32×C4—21no—
436C32×C4—21no—
437C3⋊Dic3—32no—
438C3⋊Dic3—61no—
439C3×Dic3—21no—
440C3×Dic3—21no—
441C3×Dic3—21no—
442C3×Dic3—61no—
443C3×Dic3—61no—
444C3×Dic3—61no—
445C3×Dic3#23512yes—
446C22×C9—21no—
447C22×C9—21no—
448C22×C9—21no—
449C22×C9—22no—
450C22×C9—41no—
451C22×C9—41no—
452C22×C9D3×D412yes—
453C22×C9C23×D311yescharacteristic
454C2×D9—21no—
455C2×D9—21no—
456C2×D9—21no—
457C2×D9—32no—
458C2×D9—62no—
459C2×D9—61no—
460C2×D9—61no—
461C2×D9—62no—
462C2×D9—61no—
463C2×D9—61no—
464C2×D9—61no—
465C2×D9—121no—
466C2×D9—121no—
467C2×D9—121no—
468C2×D9—121no—
469C4×C9—22no—
470C4×C9—22no—
471C4×C9—21no—
472C4×C9—21no—
473C4×C9—32no—
474C4×C9—61no—
475C4×C9—61no—
476C4×C9—61no—
477Dic9—21no—
478Dic9—21no—
479Dic9—21no—
480Dic9—32no—
481Dic9—62no—
482Dic9—62no—
483Dic9—61no—
484C2×#41—271no—
485C2×#41—271no—
486C4⋊Q8—271no—
487#123—91no—
488#123—271no—
489#123—271no—
490#123—271no—
491C22⋊Q8—271no—
492C22⋊Q8—271no—
493#121—271no—
494#121—271no—
495C4×D4—271no—
496C4×D4—271no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—271no—
499C3×C9#54711yescharacteristic, complemented, Sylow
500C23×C3—21no—
501C23×C3—91no—
502C23×C3C22×D911yescharacteristic
503C23×C3C2×D3211yescharacteristic
504C22×D3—31no—
505C22×D3—91no—
506C22×D3—91no—
507C22×D3—91no—
508C22×D3—91no—
509C22×D3—181no—
510C22×D3—181no—
511C3×D4—182no—
512C2×C3×C4—24no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—62no—
522C2×C3×C4—62no—
523C2×C3×C4—91no—
524C2×C3×C4—91no—
525C2×C3×C4—91no—
526C2×C3×C4C22×D911yescharacteristic
527C2×C3×C4C22×D911yescharacteristic
528C2×C3×C4C2×D3211yescharacteristic
529C2×C3×C4C2×D3211yescharacteristic
530#67—62no—
531#67—94no—
532#67—94no—
533#67—184no—
534#67—182no—
535#67—184no—
536#67—182no—
537#67—182no—
538#67—182no—
539C2×Dic3—22no—
540C2×Dic3—22no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—91no—
545C2×Dic3—91no—
546C2×Dic3—91no—
547C2×Dic3—91no—
548C2×Dic3—181no—
549C2×Dic3—181no—
550C2×Dic3—182no—
551C2×Dic3C22×D911yescharacteristic
552C2×Dic3C22×D911yescharacteristic
553C2×Dic3C22×D911yescharacteristic
554C2×Dic3C22×D911yescharacteristic
555D12—182no—
556D12—182no—
557D12—184no—
558D12—182no—
559D12—182no—
560C4×D3—182no—
561C4×D3—182no—
562C4×D3—182no—
563C4×D3—182no—
564C4×D3—182no—
565C4×D3—182no—
566C4×D3—182no—
567C4×D3—182no—
568C4×D3—184no—
569C4×D3—184no—
570C4×D3—182no—
571Dic6—182no—
572Dic6—182no—
573Dic6—182no—
574Dic6—182no—
575Dic6—184no—
576C2×C32—22no—
577C2×C32C2×#23511yescharacteristic
578C2×C32C2×D3×D411yescharacteristic
579C2×C32#100711yescharacteristic
580C3⋊D3—62no—
581C3⋊D3—121no—
582C3×D3—121no—
583C2×C9—22no—
584C2×C9—21no—
585C2×C9—21no—
586C2×C9—21no—
587C2×C9—42no—
588C2×C9C2×D3×D411yescharacteristic
589C2×C9D3×#4111yescharacteristic
590C2×C9#101011yescharacteristic
591D9—41no—
592D9—62no—
593D9—122no—
594D9—122no—
595D9—121no—
596#41—544no—
597#41—544no—
598C2×Q8—271no—
599C2×Q8—271no—
600C2×D4—91no—
601C2×D4—271no—
602C2×D4—271no—
603C2×D4—271no—
604C2×D4—271no—
605C2×D4—271no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—271no—
609C22×C4—271no—
610C22×C4—271no—
611C22×C4—271no—
612C22×C4—271no—
613C22×C4D3×D911yescharacteristic
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—31no—
617C4⋊C4—31no—
618C4⋊C4—91no—
619C4⋊C4—91no—
620C4⋊C4—271no—
621C4⋊C4—271no—
622C4⋊C4—271no—
623C4⋊C4—271no—
624C22⋊C4—91no—
625C22⋊C4—91no—
626C22⋊C4—91no—
627C22⋊C4—271no—
628C22⋊C4—271no—
629C22⋊C4—271no—
630C22⋊C4—271no—
631C22⋊C4—271no—
632C42—271no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—22no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—181no—
642C22×C3—181no—
643C22×C3—181no—
644C22×C3D4×D912yes—
645C22×C3C23×D911yescharacteristic
646C22×C3#381112yes—
647C22×C3C22×D3211yescharacteristic
648C2×D3—61no—
649C2×D3—61no—
650C2×D3—61no—
651C2×D3—92no—
652C2×D3—92no—
653C2×D3—182no—
654C2×D3—181no—
655C2×D3—181no—
656C2×D3—181no—
657C2×D3—181no—
658C2×D3—182no—
659C2×D3—181no—
660C2×D3—181no—
661C2×D3—181no—
662C2×D3—181no—
663C2×D3—181no—
664C2×D3—181no—
665C2×D3—361no—
666C2×D3—361no—
667C2×D3—361no—
668C2×D3—361no—
669C3×C4—22no—
670C3×C4—22no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—32no—
676C3×C4—61no—
677C3×C4—61no—
678C3×C4—61no—
679C3×C4—181no—
680C3×C4—181no—
681C3×C4—181no—
682Dic3—21no—
683Dic3—21no—
684Dic3—21no—
685Dic3—61no—
686Dic3—61no—
687Dic3—61no—
688Dic3—92no—
689Dic3—92no—
690Dic3—182no—
691Dic3—182no—
692Dic3—181no—
693Dic3—181no—
694Dic3#369712yescomplemented
695C32#550711yescharacteristic
696C9—21no—
697C9#565511yescharacteristic, complemented
698C23—91no—
699C23—271no—
700C23—271no—
701C23C2×D3×D911yescharacteristic
702Q8—542no—
703Q8—542no—
704D4—182no—
705D4—274no—
706D4—542no—
707D4—542no—
708D4—542no—
709D4—542no—
710C2×C4—22no—
711C2×C4—31no—
712C2×C4—31no—
713C2×C4—31no—
714C2×C4—31no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—91no—
718C2×C4—91no—
719C2×C4—91no—
720C2×C4—271no—
721C2×C4—271no—
722C2×C4—542no—
723C2×C4—542no—
724C2×C4—542no—
725C2×C4—542no—
726C2×C4—542no—
727C2×C4C2×D3×D911yescharacteristic
728C2×C4C2×D3×D911yescharacteristic
729C2×C3—22no—
730C2×C3—22no—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—42no—
735C2×C3—361no—
736C2×C3C2×#369711yescharacteristic
737C2×C3C2×D4×D911yescharacteristic
738C2×C3#6371311yescharacteristic
739C2×C3#6429711yescharacteristic
740C2×C3D3×#23511yescharacteristic
741C2×C3C2×#381111yescharacteristic
742D3—121no—
743D3—182no—
744D3—182no—
745D3—362no—
746D3—362no—
747D3—361no—
748D3—361no—
749C22—21no—
750C22—21no—
751C22—181no—
752C22—181no—
753C22—181no—
754C22—272no—
755C22—541no—
756C22—541no—
757C22—541no—
758C22—541no—
759C22—541no—
760C22#8866812yes—
761C22C22×D3×D911yescharacteristic
762C4—21no—
763C4—21no—
764C4—32no—
765C4—61no—
766C4—61no—
767C4—61no—
768C4—181no—
769C4—181no—
770C4—181no—
771C4—272no—
772C4—541no—
773C3—21no—
774C3#1058960911yescharacteristic, complemented
775C3#1059491711yescharacteristic
776C2—22no—
777C2—361no—
778C2—542no—
779C2—1081no—
780C2#1172245811yescharacteristic
781C2D3×#369711yescharacteristic
782C2C2×#8866811yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
socleC22×C32C23×D3
hypercenterC22×C4D3×D9
hypocenterC3×C9#547
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. C2×#88736C2semidirect
2. C2×#88658C2semidirect
3. C3×#63491C2semidirect
4. C2×C9×Dic3⋊C4C2semidirect
5. #11721277C2semidirect
6. #11721251C2semidirect
7. #11721240C2semidirect
8. #11721005C2semidirect
9. #11720997C2semidirect
10. #11720996C2semidirect
11. #11720980C2semidirect
12. #11720978C2semidirect
13. #11720941C2semidirect
14. #11720923C2semidirect
15. #11720905C2semidirect
76. #63491D3semidirect
94. #6233D4semidirect
221. C9×Dic3#41semidirect
237. C2×Dic3⋊C4D9semidirect
499. C3×C9#547semidirect
694. Dic3#3697semidirect
697. C9#5655semidirect
774. C3#10589609semidirect

Maximal subgroups

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

subgroupindex
C2×#887362
C2×#886582
C3×#634912
C2×C9×Dic3⋊C42
#117212772
#117212512
#117212402
#117210052
#117209972
#117209962
#117209802
#117209782
#117209412
#117209232
#117209052
#105949173
#105896093