Finite Group Databasebeta

← #11819163

Subgroups — #11819163

Order 1152.

1009 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592365C211yesmaximal, characteristic
2C3×C3⋊#401C211yesmaximal, characteristic, complemented
3C3×#4658C211yesmaximal, characteristic, complemented
4#10591375C211yesmaximal, characteristic
5#10591371C211yesmaximal, characteristic
6#10591371C211yesmaximal, characteristic
7#10591370C211yesmaximal, characteristic
8#10591367C211yesmaximal, characteristic
9#10591341C211yesmaximal, characteristic, complemented
10#10591335C211yesmaximal, characteristic, complemented
11#10591335C211yesmaximal, characteristic, complemented
12#10591334C211yesmaximal, characteristic, complemented
13#10591290C211yesmaximal, characteristic
14#10591229C211yesmaximal, characteristic, complemented
15#10591207C211yesmaximal, characteristic, complemented
16#78430—31nomaximal
17#78348—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×#624C2211yescharacteristic
20C22×#624C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×Dic3⋊Dic3C2211yescharacteristic
28C2×Dic3⋊Dic3C2211yescharacteristic
29C2×Dic3⋊Dic3C2211yescharacteristic
30C2×Dic3⋊Dic3C2211yescharacteristic
31C2×#3722C2211yescharacteristic
32C2×#3722C2211yescharacteristic
33C32×#95C2211yescharacteristic
34#63658C2211yescharacteristic
35C3×C3⋊#95C2211yescharacteristic
36C3×C3⋊#95C2211yescharacteristic
37C3×C3⋊#95C2211yescharacteristic
38C3×C3⋊#95C2211yescharacteristic
39C3×C3⋊#95C2211yescharacteristic
40C3×C3⋊#95C2211yescharacteristic
41C3×C3⋊#95C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45#63579C2211yescharacteristic
46#63579C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53C3×#401—31no—
54C3×#400—31no—
55#4989—31no—
56#4987—31no—
57#4986—31no—
58#4978—31no—
59#4668—31no—
60#4668—31no—
61#4668—31no—
62#4667—31no—
63#4666—31no—
64#4666—31no—
65#4666—61no—
66#4664—31no—
67#4664—31no—
68#4664—31no—
69#4664—31no—
70D3×#95—31no—
71D3×#95—31no—
72C3⋊#401D311yescharacteristic, complemented
73#4660—31no—
74#4659—31no—
75#4658—31no—
76#4658D311yescharacteristic, complemented
77#4655—31no—
78#4655—31no—
79#4654—31no—
80#4654—31no—
81#4653—31no—
82#4651—31no—
83#4651—31no—
84C23×C3⋊D3C2311yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C3⋊Dic3C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C2×C4×C3⋊D3—22no—
92C2×C4×C3⋊D3—22no—
93C2×C4×C3⋊D3—41no—
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C2×#624—22no—
103C2×#624—22no—
104C2×#624—22no—
105C2×#624—22no—
106C2×#624—22no—
107C2×#624—41no—
108#3752—22no—
109#3752—22no—
110C4×C3⋊Dic3—22no—
111C4×C3⋊Dic3—41no—
112C3×Dic3⋊C4—41no—
113C3×Dic3⋊C4—41no—
114Dic3⋊Dic3—22no—
115Dic3⋊Dic3—22no—
116Dic3⋊Dic3—22no—
117Dic3⋊Dic3—41no—
118#3722—22no—
119#3722—22no—
120#2493—91noSylow
121C22×C4×D3—31no—
122C22×C4×D3—31no—
123C22×C4×D3—31no—
124C22×C4×D3—31no—
125C22×C4×D3—31no—
126C22×C4×D3—31no—
127C22×C4×D3—61no—
128C2×C3×C4⋊C4—31no—
129C2×C3×C4⋊C4—31no—
130C2×(C2×D3)⋊C4—31no—
131C2×(C2×D3)⋊C4—31no—
132C2×(C2×D3)⋊C4—31no—
133C2×(C2×D3)⋊C4—31no—
134C2×(C2×D3)⋊C4—31no—
135C2×(C2×D3)⋊C4—31no—
136C2×(C2×D3)⋊C4—31no—
137C2×(C2×D3)⋊C4—31no—
138C2×(C2×D3)⋊C4—61no—
139C2×(C2×D3)⋊C4—61no—
140C2×C4⋊Dic3—31no—
141C2×C4⋊Dic3—31no—
142C2×C4⋊Dic3—31no—
143C2×C4⋊Dic3—31no—
144C2×Dic3⋊C4—31no—
145C2×Dic3⋊C4—31no—
146C2×Dic3⋊C4—31no—
147C2×Dic3⋊C4—31no—
148C2×Dic3⋊C4C2×D311yescharacteristic
149C2×Dic3⋊C4C2×D311yescharacteristic
150C2×C4×Dic3—31no—
151C2×C4×Dic3—31no—
152C2×C4×Dic3—31no—
153C2×C4×Dic3—31no—
154C2×C4×Dic3—61no—
155C2×C4×Dic3—61no—
156C3×#95—21no—
157C3×#95—31no—
158C3×#95—31no—
159C3×#95—31no—
160C3×#95—31no—
161C3×#95—31no—
162C3×#95—31no—
163C3×#95—31no—
164C3×#95—31no—
165C3×#95—31no—
166C3×#95—31no—
167C3×#95C2×D311yescharacteristic
168C3×#95C2×D311yescharacteristic
169C3⋊#95—31no—
170C3⋊#95—31no—
171C3⋊#95—31no—
172C3⋊#95—31no—
173C3⋊#95—31no—
174C3⋊#95—31no—
175C3⋊#95—31no—
176C3⋊#95—31no—
177C3⋊#95—31no—
178C3⋊#95—31no—
179C3⋊#95—31no—
180C3⋊#95—31no—
181C3⋊#95—31no—
182C3⋊#95—31no—
183C3⋊#95—31no—
184C3⋊#95—31no—
185C3⋊#95—31no—
186C3⋊#95—31no—
187C3⋊#95—61no—
188C3⋊#95C2×D311yescharacteristic
189C3⋊#95C2×D311yescharacteristic
190C3⋊#95C2×D311yescharacteristic
191C3⋊#95C2×D311yescharacteristic
192C3⋊#95C2×D311yescharacteristic
193C3⋊#95C2×D311yescharacteristic
194C3⋊#95C2×D311yescharacteristic
195C3⋊#95C2×D311yescharacteristic
196C3⋊#95C2×D311yescharacteristic
197C3⋊#95C2×D311yescharacteristic
198C23×C32C2411yescharacteristic
199C22×C3⋊D3—21no—
200C22×C3⋊D3—21no—
201C22×C3⋊D3—21no—
202C22×C3⋊D3—21no—
203C22×C3⋊D3#4112yes—
204C22×C3⋊D3#4112yes—
205C22×C3⋊D3#4112yes—
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—21no—
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C3⋊Dic3—21no—
216C2×C3⋊Dic3—21no—
217C2×C3⋊Dic3—21no—
218C2×C3⋊Dic3—21no—
219C2×C3⋊Dic3—21no—
220C2×C3⋊Dic3—21no—
221C2×C3⋊Dic3—21no—
222C2×C3⋊Dic3—21no—
223C2×C3⋊Dic3#4112yes—
224C4×C3⋊D3—44no—
225C2×C3×Dic3—21no—
226C2×C3×Dic3—21no—
227C2×C3×Dic3—21no—
228C2×C3×Dic3—21no—
229C2×C3×Dic3—21no—
230C2×C3×Dic3—21no—
231C2×C3×Dic3—21no—
232C2×C3×Dic3—21no—
233C2×C3×Dic3—21no—
234C2×C3×Dic3—21no—
235C2×C3×Dic3—21no—
236C2×C3×Dic3—21no—
237C2×C3×Dic3—21no—
238C2×C3×Dic3—21no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3#4112yes—
249#624—44no—
250#624—44no—
251#401—31no—
252#400—31no—
253#400—91no—
254#400—91no—
255#387—91no—
256#387—91no—
257#387—91no—
258#385—91no—
259#385—91no—
260#383—91no—
261#381—91no—
262#381—91no—
263#380—91no—
264C4×C22⋊C4—91no—
265C2×#95—91no—
266C23×D3—31no—
267C23×D3—31no—
268C23×D3—61no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—31no—
273C22×C3×C4—31no—
274C22×C3×C4—31no—
275C22×C3×C4—31no—
276C22×C3×C4—31no—
277C22×C3×C4—31no—
278C22×C3×C4—31no—
279C22×C3×C4—31no—
280C22×C3×C4C22×D311yescharacteristic
281C22×C3×C4C22×D311yescharacteristic
282C22×C3×C4C22×D311yescharacteristic
283C22×C3×C4C22×D311yescharacteristic
284C22×C3×C4C22×D311yescharacteristic
285C22×C3×C4C22×D311yescharacteristic
286C22×Dic3—31no—
287C22×Dic3—31no—
288C22×Dic3—31no—
289C22×Dic3—31no—
290C22×Dic3—31no—
291C22×Dic3—31no—
292C22×Dic3—61no—
293C22×Dic3—61no—
294C22×Dic3—61no—
295C22×Dic3C22×D311yescharacteristic
296C22×Dic3C22×D311yescharacteristic
297C22×Dic3C22×D311yescharacteristic
298C22×Dic3C22×D311yescharacteristic
299C22×Dic3C22×D311yescharacteristic
300C22×Dic3C22×D311yescharacteristic
301C22×Dic3C22×D311yescharacteristic
302C22×Dic3C22×D311yescharacteristic
303C2×C4×D3—62no—
304C2×C4×D3—62no—
305C2×C4×D3—62no—
306C2×C4×D3—62no—
307C2×C4×D3—62no—
308C2×C4×D3—62no—
309C2×C4×D3—62no—
310C2×C4×D3—62no—
311C2×C4×D3—62no—
312C2×C4×D3—62no—
313C2×C4×D3—62no—
314C2×C4×D3—62no—
315C2×C4×D3—62no—
316C2×C4×D3—64no—
317C2×C4×D3—62no—
318C2×C4×D3—122no—
319C2×C4×D3—121no—
320C2×C4×D3—121no—
321C2×C4×D3—121no—
322C2×C4×D3—121no—
323C2×C4×D3—122no—
324C3×C4⋊C4—121no—
325C3×C4⋊C4—121no—
326(C2×D3)⋊C4—62no—
327(C2×D3)⋊C4—62no—
328(C2×D3)⋊C4—62no—
329(C2×D3)⋊C4—62no—
330(C2×D3)⋊C4—62no—
331(C2×D3)⋊C4—62no—
332(C2×D3)⋊C4—62no—
333(C2×D3)⋊C4—62no—
334(C2×D3)⋊C4—64no—
335(C2×D3)⋊C4—64no—
336C4⋊Dic3—62no—
337C4⋊Dic3—62no—
338C4⋊Dic3—62no—
339C4⋊Dic3—121no—
340Dic3⋊C4—41no—
341Dic3⋊C4—41no—
342Dic3⋊C4—62no—
343Dic3⋊C4—62no—
344Dic3⋊C4—62no—
345Dic3⋊C4—121no—
346C4×Dic3—62no—
347C4×Dic3—62no—
348C4×Dic3—122no—
349C4×Dic3—121no—
350C4×Dic3—121no—
351C4×Dic3—122no—
352C22×C32C2×#4111yescharacteristic
353C22×C32C2×#4111yescharacteristic
354C22×C32C2×#4111yescharacteristic
355C22×C32C2×#4111yescharacteristic
356C22×C32C2×#4111yescharacteristic
357C22×C32H(5,𝔽2)11yescharacteristic
358C22×C322−1+411yescharacteristic
359C2×C3⋊D3—22no—
360C2×C3⋊D3—22no—
361C2×C3⋊D3—22no—
362C2×C3⋊D3—22no—
363C2×C3⋊D3—22no—
364C2×C3⋊D3—22no—
365C2×C3⋊D3#12614yes—
366C32×C4—41no—
367C32×C4—41no—
368C32×C4—41no—
369C3⋊Dic3—22no—
370C3⋊Dic3—41no—
371C3⋊Dic3—41no—
372C3×Dic3—22no—
373C3×Dic3—41no—
374C3×Dic3—41no—
375C3×Dic3—41no—
376C3×Dic3—41no—
377C3×Dic3—41no—
378C3×Dic3—41no—
379C3×Dic3—41no—
380C23×C4—91no—
381C23×C4—91no—
382C23×C4—91no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—31no—
385C2×C4⋊C4—91no—
386C2×C4⋊C4—91no—
387C2×C4⋊C4—91no—
388C2×C4⋊C4—91no—
389C2×C22⋊C4—91no—
390C2×C22⋊C4—91no—
391C2×C22⋊C4—91no—
392C2×C22⋊C4—91no—
393C2×C42—91no—
394C2×C42—91no—
395#95—31no—
396#95—31no—
397#95—31no—
398#95—31no—
399#95—31no—
400#95—31no—
401#95—31no—
402#95—31no—
403#95—31no—
404#95—31no—
405#95—91no—
406#95—91no—
407#95—91no—
408#95—91no—
409#95—91no—
410#95—91no—
411#95—91no—
412#95—91no—
413#95—91no—
414#95D3211yescharacteristic
415C23×C3—21no—
416C23×C3C23×D311yescharacteristic
417C23×C3C23×D311yescharacteristic
418C22×D3—32no—
419C22×D3—32no—
420C22×D3—32no—
421C22×D3—32no—
422C22×D3—32no—
423C22×D3—32no—
424C22×D3—62no—
425C22×D3—62no—
426C22×D3—62no—
427C22×D3—61no—
428C22×D3—61no—
429C22×D3—61no—
430C22×D3—61no—
431C22×D3—61no—
432C22×D3—61no—
433C22×D3—61no—
434C22×D3—61no—
435C22×D3—121no—
436C22×D3—121no—
437C22×D3—121no—
438C22×D3—121no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—32no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—61no—
468C2×C3×C4—61no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—32no—
514C2×Dic3—32no—
515C2×Dic3—62no—
516C2×Dic3—62no—
517C2×Dic3—62no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—62no—
523C2×Dic3—62no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—121no—
537C2×Dic3—121no—
538C2×Dic3—121no—
539C2×Dic3—121no—
540C2×Dic3#23912yes—
541C4×D3—124no—
542C4×D3—124no—
543C4×D3—124no—
544C4×D3—124no—
545C4×D3—124no—
546C4×D3—124no—
547C4×D3—128no—
548C2×C32C2×#12611yescharacteristic
549C2×C32#52911yescharacteristic
550C2×C32#53911yescharacteristic
551C2×C32#55111yescharacteristic
552C2×C32#55111yescharacteristic
553C2×C32#55211yescharacteristic
554C2×C32#55211yescharacteristic
555C3⋊D3—24no—
556C24—91no—
557C22×C4—31no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—31no—
564C22×C4—31no—
565C22×C4—91no—
566C22×C4—91no—
567C22×C4—91no—
568C22×C4—182no—
569C22×C4—182no—
570C22×C4—182no—
571C22×C4—182no—
572C22×C4—182no—
573C22×C4—182no—
574C22×C4—182no—
575C22×C4—361no—
576C22×C4—361no—
577C22×C4C2×D3211yescharacteristic
578C22×C4C2×D3211yescharacteristic
579C22×C4C2×D3211yescharacteristic
580C4⋊C4—121no—
581C4⋊C4—121no—
582C4⋊C4—182no—
583C4⋊C4—182no—
584C4⋊C4—182no—
585C4⋊C4—361no—
586C22⋊C4—182no—
587C22⋊C4—182no—
588C22⋊C4—182no—
589C22⋊C4—182no—
590C42—182no—
591C42—361no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3#100411yescharacteristic
600C22×C3C2×#23911yescharacteristic
601C22×C3D3×#4111yescharacteristic
602C22×C3D3×#4111yescharacteristic
603C22×C3D3×#4111yescharacteristic
604C22×C3D3×#4111yescharacteristic
605C22×C3D3×#4111yescharacteristic
606C22×C3D3×#4111yescharacteristic
607C22×C3D3×#4111yescharacteristic
608C22×C3D3×#4111yescharacteristic
609C22×C3D3×#4111yescharacteristic
610C22×C3#100911yescharacteristic
611C22×C3#101011yescharacteristic
612C22×C3#101011yescharacteristic
613C2×D3—34no—
614C2×D3—34no—
615C2×D3—64no—
616C2×D3—62no—
617C2×D3—62no—
618C2×D3—62no—
619C2×D3—62no—
620C2×D3—62no—
621C2×D3—62no—
622C2×D3—62no—
623C2×D3—62no—
624C2×D3—62no—
625C2×D3—62no—
626C2×D3—62no—
627C2×D3—62no—
628C2×D3—122no—
629C2×D3—122no—
630C2×D3—122no—
631C2×D3—122no—
632C2×D3—122no—
633C2×D3—122no—
634C3×C4—42no—
635C3×C4—42no—
636C3×C4—42no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—62no—
644C3×C4—121no—
645C3×C4—121no—
646C3×C4—121no—
647C3×C4—121no—
648C3×C4—121no—
649C3×C4—121no—
650C3×C4—121no—
651Dic3—22no—
652Dic3—41no—
653Dic3—41no—
654Dic3—41no—
655Dic3—41no—
656Dic3—41no—
657Dic3—41no—
658Dic3—41no—
659Dic3—64no—
660Dic3—62no—
661Dic3—62no—
662Dic3—122no—
663Dic3—122no—
664Dic3—121no—
665Dic3—121no—
666Dic3—121no—
667Dic3—121no—
668C32#249311yescharacteristic, complemented, Sylow
669C23—92no—
670C23—92no—
671C23—92no—
672C23—181no—
673C23—181no—
674C23—181no—
675C23—181no—
676C23C22×D3211yescharacteristic
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—32no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—92no—
711C2×C4—181no—
712C2×C4—181no—
713C2×C4—181no—
714C2×C4—181no—
715C2×C4—181no—
716C2×C4—181no—
717C2×C4—181no—
718C2×C4—181no—
719C2×C4—364no—
720C2×C4—364no—
721C2×C4—364no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3#563711yescharacteristic
730C2×C3#566011yescharacteristic
731C2×C3#567911yescharacteristic
732C2×C3#569111yescharacteristic
733C2×C3#569411yescharacteristic
734C2×C3D3×#12611yescharacteristic
735C2×C3D3×#12611yescharacteristic
736C2×C3#570511yescharacteristic
737C2×C3#570511yescharacteristic
738C2×C3#570611yescharacteristic
739C2×C3#570711yescharacteristic
740C2×C3#570811yescharacteristic
741C2×C3#570811yescharacteristic
742C2×C3#570811yescharacteristic
743D3—64no—
744D3—64no—
745D3—124no—
746C22—94no—
747C22—182no—
748C22—182no—
749C22—182no—
750C22—182no—
751C22—182no—
752C22—182no—
753C22#6430611yescharacteristic
754C22#6430611yescharacteristic
755C22#6430611yescharacteristic
756C22#6430911yescharacteristic
757C22#6431211yescharacteristic
758C22#6431411yescharacteristic
759C22D3×#23911yescharacteristic
760C4—41no—
761C4—41no—
762C4—41no—
763C4—62no—
764C4—121no—
765C4—121no—
766C4—121no—
767C4—121no—
768C4—121no—
769C4—121no—
770C4—121no—
771C4—182no—
772C4—361no—
773C4—361no—
774C3—21no—
775C3#7834811yescharacteristic, complemented
776C3#7843011yescharacteristic, complemented
777C2—184no—
778C2#1059402011yescharacteristic
779C2#1059415311yescharacteristic
780C2#1059415511yescharacteristic
781C2#1059422711yescharacteristic
782C2#1059446211yescharacteristic
783C2#1059446511yescharacteristic
784C2#1059465511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32#2493
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C3×C3⋊#401C2semidirect
3. C3×#4658C2semidirect
9. #10591341C2semidirect
10. #10591335C2semidirect
11. #10591335C2semidirect
12. #10591334C2semidirect
14. #10591229C2semidirect
15. #10591207C2semidirect
72. C3⋊#401D3semidirect
76. #4658D3semidirect
668. C32#2493semidirect
775. C3#78348semidirect
776. C3#78430semidirect

Maximal subgroups

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

subgroupindex
#105923652
C3×C3⋊#4012
C3×#46582
#105913752
#105913712
#105913702
#105913672
#105913412
#105913352
#105913342
#105912902
#105912292
#105912072
#784303
#783483