Finite Group Databasebeta

← #11817836

Subgroups — #11817836

Order 1152.

1113 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63861C211yesmaximal, characteristic, complemented
2C2×#63841C211yesmaximal, characteristic, complemented
3#10592353C211yesmaximal, characteristic, complemented
4C3×#4677C211yesmaximal, characteristic, complemented
5C3×#4668C211yesmaximal, characteristic, complemented
6#10591388C211yesmaximal, characteristic
7#10591385C211yesmaximal, characteristic
8#10591381C211yesmaximal, characteristic
9#10591324C211yesmaximal, characteristic, complemented
10#10591307C211yesmaximal, characteristic, complemented
11#10591307C211yesmaximal, characteristic, complemented
12#10591282C211yesmaximal, characteristic, complemented
13#10591274C211yesmaximal, characteristic, complemented
14#10591264C211yesmaximal, characteristic, complemented
15#10591214C211yesmaximal, characteristic, complemented
16#78027—31nomaximal
17#74451—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×#625C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C3×(C2×D3)⋊C4C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44C2×Dic32C2211yescharacteristic
45#63861—24no—
46#63841—24no—
47C32×#95C2211yescharacteristic
48#63658C2211yescharacteristic
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×#926—31no—
56C2×#898—31no—
57C2×#892—31no—
58C2×#879—31no—
59C3×#399—31no—
60C3×#385—31no—
61#5213—31no—
62#4993—31no—
63#4990—31no—
64#4990—31no—
65#4983—31no—
66#4981—31no—
67#4976—31no—
68Dic3×C4⋊C4—31no—
69Dic3×C4⋊C4—31no—
70#4959—31no—
71#4959—31no—
72#4957—31no—
73#4957—31no—
74#4956—31no—
75#4951—31no—
76#4951—31no—
77#4949—31no—
78#4945—31no—
79#4677D311yescharacteristic, complemented
80#4669—31no—
81#4668D311yescharacteristic, complemented
82#4654—31no—
83#4654—31no—
84#4654—61no—
85#4647—31no—
86C23×C3×D3C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C2×C3×C4×D3—22no—
102C2×C3×C4×D3—22no—
103C2×C3×C4×D3—22no—
104C2×#625—22no—
105C2×#625—22no—
106C2×#625—41no—
107C4⋊(C3⋊Dic3)D414yescomplemented
108#3750—22no—
109C4×C3⋊Dic3—22no—
110C3×(C2×D3)⋊C4—22no—
111C3×(C2×D3)⋊C4—22no—
112C3×(C2×D3)⋊C4—22no—
113C3×(C2×D3)⋊C4—22no—
114C3×(C2×D3)⋊C4—41no—
115C3×C4⋊Dic3—22no—
116C3×C4⋊Dic3—22no—
117C3×C4⋊Dic3—22no—
118C3×C4⋊Dic3—41no—
119C3×Dic3⋊C4—22no—
120#3724—22no—
121#3724—41no—
122#3724—41no—
123(C2×D3)⋊Dic3—22no—
124(C2×D3)⋊Dic3—22no—
125(C2×D3)⋊Dic3—22no—
126(C2×D3)⋊Dic3—22no—
127(C2×D3)⋊Dic3—22no—
128(C2×D3)⋊Dic3—41no—
129Dic32—22no—
130Dic32—22no—
131Dic32—22no—
132#2479—91noSylow
133C23×C3×C4—31no—
134C22×#67—31no—
135C22×#67—31no—
136C22×C4×D3C2×D311yescharacteristic
137C2×C3×C4⋊C4—31no—
138C2×C3×C4⋊C4—31no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C4⋊C4—31no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C22⋊C4—31no—
143C2×C3×C22⋊C4—31no—
144C2×C3×C22⋊C4—31no—
145C2×C3×C22⋊C4—31no—
146C2×C3×C22⋊C4—31no—
147C2×#217—31no—
148C2×#217—31no—
149C2×#217—31no—
150C2×#217—31no—
151C2×#217—31no—
152C2×#217—31no—
153C2×(C2×D3)⋊C4—31no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4—31no—
157C2×(C2×D3)⋊C4—31no—
158C2×(C2×D3)⋊C4—31no—
159C2×(C2×D3)⋊C4C2×D311yescharacteristic
160C2×(C2×D3)⋊C4C2×D311yescharacteristic
161C2×(C2×D3)⋊C4C2×D311yescharacteristic
162C2×(C2×D3)⋊C4C2×D311yescharacteristic
163C2×(C2×D3)⋊C4C2×D311yescharacteristic
164#926—64no—
165C2×C4⋊Dic3—31no—
166C2×C4⋊Dic3—31no—
167C2×C4⋊Dic3—61no—
168C2×C4⋊Dic3C2×D311yescharacteristic
169C2×C4⋊Dic3C2×D311yescharacteristic
170C2×C4⋊Dic3C2×D311yescharacteristic
171C2×C4⋊Dic3C2×D311yescharacteristic
172C2×Dic3⋊C4—31no—
173C2×Dic3⋊C4—31no—
174C2×Dic3⋊C4—31no—
175C2×Dic3⋊C4—31no—
176C2×Dic3⋊C4—31no—
177C2×Dic3⋊C4—31no—
178C2×Dic3⋊C4—31no—
179C2×Dic3⋊C4—31no—
180C2×Dic3⋊C4—61no—
181C2×Dic3⋊C4C2×D311yescharacteristic
182C2×C4×Dic3—31no—
183C2×C4×Dic3—31no—
184C2×C4×Dic3—31no—
185C2×C4×Dic3—31no—
186C2×C4×Dic3—31no—
187C2×C4×Dic3—31no—
188C2×C4×Dic3—31no—
189C2×C4×Dic3—31no—
190C2×C4×Dic3—61no—
191#898—64no—
192#892—64no—
193#879—64no—
194C3×#95—21no—
195C3×#95—31no—
196C3×#95C2×D311yescharacteristic
197C3×#95C2×D311yescharacteristic
198C3⋊#95—31no—
199C3⋊#95—31no—
200C3⋊#95—31no—
201C3⋊#95—31no—
202C3⋊#95—31no—
203C3⋊#95—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—61no—
211C3⋊#95—61no—
212C3⋊#95—61no—
213C3⋊#95C2×D311yescharacteristic
214C23×C32C2411yescharacteristic
215C22×C3×D3—21no—
216C22×C3×D3—21no—
217C22×C3×D3—21no—
218C22×C3×D3—21no—
219C22×C3×D3—21no—
220C22×C3×D3—21no—
221C22×C3×D3—21no—
222C22×C3×D3—21no—
223C22×C3×D3—21no—
224C22×C3×D3—21no—
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—21no—
228C22×C3×D3#4112yes—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4C2×D412yes—
237C2×C32×C4#4112yes—
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⋊Dic3C2×D412yes—
248C2×C3⋊Dic3C2×D412yes—
249C2×C3⋊Dic3#4112yes—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3#4112yes—
268C3×C4×D3—28no—
269#625—44no—
270C2×#126—91no—
271C2×#117—91no—
272#399—31no—
273#399—91no—
274#398—91no—
275#394—91no—
276#390—91no—
277#389—91no—
278#388—91no—
279#388—91no—
280#388—91no—
281#387—91no—
282#386—91no—
283#385—31no—
284C4×C4⋊C4—91no—
285C24×C3—31no—
286C24×C3—31no—
287C23×D3C22×D311yescharacteristic
288C23×D3C22×D311yescharacteristic
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—62no—
299C22×C3×C4—62no—
300C22×C3×C4—62no—
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C2×#67—62no—
308C2×#67—62no—
309C2×#67—62no—
310C2×#67—62no—
311C2×#67—121no—
312C2×#67—121no—
313C22×Dic3—31no—
314C22×Dic3—31no—
315C22×Dic3—31no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—31no—
319C22×Dic3—31no—
320C22×Dic3—31no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—61no—
325C22×Dic3C22×D311yescharacteristic
326C22×Dic3C22×D311yescharacteristic
327C22×Dic3C22×D311yescharacteristic
328C22×Dic3C22×D311yescharacteristic
329C22×Dic3C22×D311yescharacteristic
330C22×Dic3C22×D311yescharacteristic
331C2×C4×D3—22no—
332C2×C4×D3—22no—
333C2×C4×D3—22no—
334C3×C4⋊C4—62no—
335C3×C4⋊C4—62no—
336C3×C4⋊C4—62no—
337C3×C4⋊C4—62no—
338C3×C4⋊C4—121no—
339C3×C22⋊C4—62no—
340C3×C22⋊C4—62no—
341C3×C22⋊C4—62no—
342C3×C22⋊C4—62no—
343C3×C22⋊C4—121no—
344#217—62no—
345#217—62no—
346#217—62no—
347#217—62no—
348#217—62no—
349#217—121no—
350(C2×D3)⋊C4—22no—
351(C2×D3)⋊C4—22no—
352(C2×D3)⋊C4—22no—
353(C2×D3)⋊C4—22no—
354(C2×D3)⋊C4—41no—
355(C2×D3)⋊C4—62no—
356(C2×D3)⋊C4—62no—
357(C2×D3)⋊C4—62no—
358(C2×D3)⋊C4—62no—
359(C2×D3)⋊C4—62no—
360(C2×D3)⋊C4—121no—
361C4⋊Dic3—22no—
362C4⋊Dic3—22no—
363C4⋊Dic3—22no—
364C4⋊Dic3—34no—
365C4⋊Dic3—34no—
366C4⋊Dic3—41no—
367C4⋊Dic3—64no—
368Dic3⋊C4—22no—
369Dic3⋊C4—62no—
370Dic3⋊C4—62no—
371Dic3⋊C4—62no—
372Dic3⋊C4—62no—
373Dic3⋊C4—122no—
374Dic3⋊C4—121no—
375Dic3⋊C4—121no—
376Dic3⋊C4—121no—
377Dic3⋊C4—121no—
378C4×Dic3—62no—
379C4×Dic3—62no—
380C4×Dic3—62no—
381C4×Dic3—62no—
382C4×Dic3—62no—
383C4×Dic3—62no—
384C4×Dic3—62no—
385C4×Dic3—62no—
386C4×Dic3—122no—
387C22×C32C22×D411yescharacteristic
388C22×C32C2×#4111yescharacteristic
389C22×C32C2×#4111yescharacteristic
390C22×C32C2×#4111yescharacteristic
391C22×C32C2×#4111yescharacteristic
392C22×C32H(5,𝔽2)11yescharacteristic
393C22×C322−1+411yescharacteristic
394C2×C3×D3—22no—
395C2×C3×D3—22no—
396C2×C3×D3—22no—
397C2×C3×D3—41no—
398C2×C3×D3—41no—
399C2×C3×D3—41no—
400C2×C3×D3—41no—
401C2×C3×D3—41no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C32×C4—22no—
409C32×C4—22no—
410C32×C4—41no—
411C3⋊Dic3—22no—
412C3⋊Dic3—22no—
413C3⋊Dic3—22no—
414C3⋊Dic3—41no—
415C3×Dic3—22no—
416C3×Dic3—41no—
417C3×Dic3—41no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C22×D4—91no—
422C23×C4—31no—
423#126—184no—
424#117—184no—
425C2×C4⋊C4—31no—
426C2×C4⋊C4—31no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—91no—
431C2×C4⋊C4—91no—
432C2×C4⋊C4—91no—
433C2×C4⋊C4—91no—
434C2×C4⋊C4—91no—
435C2×C22⋊C4—31no—
436C2×C22⋊C4—31no—
437C2×C22⋊C4—31no—
438C2×C22⋊C4—31no—
439C2×C22⋊C4—31no—
440C2×C22⋊C4—91no—
441C2×C22⋊C4—91no—
442C2×C22⋊C4—91no—
443C2×C22⋊C4—91no—
444C2×C22⋊C4—91no—
445C2×C22⋊C4—91no—
446C2×C42—91no—
447C2×C42—91no—
448C2×C42—91no—
449C2×C42—91no—
450#95—31no—
451#95—91no—
452#95—91no—
453#95—91no—
454#95—91no—
455#95—91no—
456#95—91no—
457#95D3211yescharacteristic
458C23×C3—21no—
459C23×C3—32no—
460C23×C3—61no—
461C23×C3—61no—
462C23×C3—61no—
463C23×C3—61no—
464C23×C3—61no—
465C23×C3—61no—
466C23×C3—61no—
467C23×C3—61no—
468C23×C3—61no—
469C23×C3—61no—
470C23×C3—61no—
471C23×C3—61no—
472C23×C3—61no—
473C23×C3C23×D311yescharacteristic
474C23×C3C23×D311yescharacteristic
475C22×D3—21no—
476C22×D3—21no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—21no—
483C22×D3—21no—
484C22×D3—21no—
485C22×D3—21no—
486C22×D3—21no—
487C22×D3—21no—
488C22×D3#23712yes—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—32no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—68no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4#23512yes—
532C2×C3×C4D3×D412yes—
533C2×C3×C4D3×D412yes—
534C2×C3×C4#23712yes—
535#67—124no—
536#67—124no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—32no—
555C2×Dic3—32no—
556C2×Dic3—32no—
557C2×Dic3—32no—
558C2×Dic3—32no—
559C2×Dic3—32no—
560C2×Dic3—62no—
561C2×Dic3—62no—
562C2×Dic3—62no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—121no—
582C2×Dic3—121no—
583C2×Dic3—121no—
584C2×Dic3—121no—
585C2×Dic3—121no—
586C2×Dic3—121no—
587C2×Dic3—121no—
588C2×Dic3—121no—
589C2×Dic3—121no—
590C2×Dic3#23712yes—
591C4×D3—28no—
592C2×C32#52511yescharacteristic
593C2×C32#52911yescharacteristic
594C2×C32#54211yescharacteristic
595C2×C32#54711yescharacteristic
596C2×C32#55011yescharacteristic
597C2×C32#55111yescharacteristic
598C2×C32#55211yescharacteristic
599C3×D3—42no—
600C3×D3—81no—
601C24—31no—
602C24—31no—
603C2×D4—182no—
604C2×D4—182no—
605C2×D4—361no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—31no—
610C22×C4—31no—
611C22×C4—31no—
612C22×C4—62no—
613C22×C4—62no—
614C22×C4—62no—
615C22×C4—91no—
616C22×C4—91no—
617C22×C4—91no—
618C22×C4—91no—
619C22×C4C2×D3211yescharacteristic
620C22×C4C2×D3211yescharacteristic
621C22×C4C2×D3211yescharacteristic
622C4⋊C4—62no—
623C4⋊C4—62no—
624C4⋊C4—62no—
625C4⋊C4—62no—
626C4⋊C4—94no—
627C4⋊C4—121no—
628C4⋊C4—182no—
629C4⋊C4—182no—
630C4⋊C4—361no—
631C4⋊C4—361no—
632C22⋊C4—62no—
633C22⋊C4—62no—
634C22⋊C4—62no—
635C22⋊C4—62no—
636C22⋊C4—121no—
637C22⋊C4—182no—
638C22⋊C4—182no—
639C22⋊C4—182no—
640C22⋊C4—182no—
641C22⋊C4—182no—
642C22⋊C4—361no—
643C42—182no—
644C42—182no—
645C42—182no—
646C42—182no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—62no—
655C22×C3—62no—
656C22×C3—62no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3C2×#23511yescharacteristic
669C22×C3C2×D3×D411yescharacteristic
670C22×C3C2×D3×D411yescharacteristic
671C22×C3C2×#23711yescharacteristic
672C22×C3C2×#23711yescharacteristic
673C22×C3C2×#23711yescharacteristic
674C22×C3#100411yescharacteristic
675C22×C3#100711yescharacteristic
676C22×C3#100711yescharacteristic
677C22×C3D3×#4111yescharacteristic
678C22×C3D3×#4111yescharacteristic
679C22×C3D3×#4111yescharacteristic
680C22×C3D3×#4111yescharacteristic
681C22×C3#100911yescharacteristic
682C2×D3—22no—
683C2×D3—22no—
684C2×D3—22no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—41no—
694C2×D3—41no—
695C2×D3—41no—
696C3×C4—22no—
697C3×C4—22no—
698C3×C4—22no—
699C3×C4—22no—
700C3×C4—42no—
701C3×C4—42no—
702C3×C4—41no—
703C3×C4—41no—
704C3×C4—62no—
705C3×C4—81no—
706C3×C4—121no—
707C3×C4—121no—
708C3×C4—121no—
709C3×C4—121no—
710C3×C4—121no—
711Dic3—22no—
712Dic3—41no—
713Dic3—41no—
714Dic3—41no—
715Dic3—41no—
716Dic3—41no—
717Dic3—62no—
718Dic3—62no—
719Dic3—62no—
720Dic3—62no—
721Dic3—62no—
722Dic3—62no—
723Dic3—122no—
724Dic3—122no—
725Dic3—122no—
726Dic3—121no—
727Dic3—121no—
728Dic3—241no—
729C32#247911yescharacteristic, complemented, Sylow
730C23—32no—
731C23—61no—
732C23—61no—
733C23—61no—
734C23—61no—
735C23—61no—
736C23—61no—
737C23—61no—
738C23—61no—
739C23—61no—
740C23—61no—
741C23—61no—
742C23—61no—
743C23—61no—
744C23C22×D3211yescharacteristic
745D4—364no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—32no—
754C2×C4—68no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—92no—
773C2×C4—92no—
774C2×C4—92no—
775C2×C4—181no—
776C2×C4—181no—
777C2×C4—181no—
778C2×C4—181no—
779C2×C4—181no—
780C2×C4—181no—
781C2×C4—181no—
782C2×C4—181no—
783C2×C4—181no—
784C2×C4#379512yes—
785C2×C4#380212yes—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—21no—
793C2×C3—122no—
794C2×C3—241no—
795C2×C3#551311yescharacteristic
796C2×C3#553811yescharacteristic
797C2×C3#555311yescharacteristic
798C2×C3#558611yescharacteristic
799C2×C3#563111yescharacteristic
800C2×C3#563111yescharacteristic
801C2×C3#563911yescharacteristic
802C2×C3#564011yescharacteristic
803C2×C3#564311yescharacteristic
804C2×C3#564911yescharacteristic
805C2×C3#565611yescharacteristic
806C2×C3#565811yescharacteristic
807C2×C3#565911yescharacteristic
808C2×C3#571811yescharacteristic
809D3—42no—
810D3—81no—
811C22—62no—
812C22—62no—
813C22—62no—
814C22—121no—
815C22—121no—
816C22—121no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22—121no—
821C22—121no—
822C22—121no—
823C22—121no—
824C22—121no—
825C22C2×#379511yescharacteristic
826C22C2×#380211yescharacteristic
827C22#6430711yescharacteristic
828C22D3×#23711yescharacteristic
829C22D3×#23711yescharacteristic
830C22#6431211yescharacteristic
831C22#6431611yescharacteristic
832C4—22no—
833C4—22no—
834C4—41no—
835C4—62no—
836C4—121no—
837C4—121no—
838C4—121no—
839C4—121no—
840C4—121no—
841C4—182no—
842C4—182no—
843C4—182no—
844C4—361no—
845C3—21no—
846C3#7445111yescharacteristic, complemented
847C3#7802711yescharacteristic, complemented
848C2—122no—
849C2—241no—
850C2#1059390611yescharacteristic
851C2#1059408211yescharacteristic
852C2#1059413111yescharacteristic
853C2#1059430411yescharacteristic
854C2#1059453011yescharacteristic
855C2#1059455111yescharacteristic
856C2#1059455811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC22×#625C22
hypercenter#95D32
hypocenterC32#2479
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. C2×#63861C2semidirect
2. C2×#63841C2semidirect
3. #10592353C2semidirect
4. C3×#4677C2semidirect
5. C3×#4668C2semidirect
9. #10591324C2semidirect
10. #10591307C2semidirect
11. #10591307C2semidirect
12. #10591282C2semidirect
13. #10591274C2semidirect
14. #10591264C2semidirect
15. #10591214C2semidirect
79. #4677D3semidirect
81. #4668D3semidirect
107. C4⋊(C3⋊Dic3)D4semidirect
729. C32#2479semidirect
846. C3#74451semidirect
847. C3#78027semidirect

Maximal subgroups

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

subgroupindex
C2×#638612
C2×#638412
#105923532
C3×#46772
C3×#46682
#105913882
#105913852
#105913812
#105913242
#105913072
#105912822
#105912742
#105912642
#105912142
#780273
#744513