Finite Group Databasebeta

← #11810332

Subgroups — #11810332

Order 1152.

1931 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64146C211yesmaximal, characteristic
2C2×C3×#935C211yesmaximal, characteristic, complemented
3C2×#63974C211yesmaximal, characteristic, complemented
4C2×#63952C211yesmaximal, characteristic, complemented
5C3×#5222C211yesmaximal, characteristic, complemented
6#10591722C211yesmaximal, characteristic, complemented
7#10591714C211yesmaximal, characteristic, complemented
8#10591712C211yesmaximal, characteristic, complemented
9#10591711C211yesmaximal, characteristic, complemented
10#10591702C211yesmaximal, characteristic, complemented
11#10591694C211yesmaximal, characteristic, complemented
12#10591374C211yesmaximal, characteristic, complemented
13#10591367C211yesmaximal, characteristic, complemented
14#10591258C211yesmaximal, characteristic, complemented
15#10591203C211yesmaximal, characteristic, complemented
16#82896—31nomaximal
17#77111—31nomaximal
18C24×C3⋊D3C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic, complemented
23C22×#624C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26#64146—24no—
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic, complemented
34C2×C3×#217C2211yescharacteristic, complemented
35C2×C3×#217C2211yescharacteristic, complemented
36C3×#935—24no—
37C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
38C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
39C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
40#63974—24no—
41C2×#3724C2211yescharacteristic, complemented
42C2×Dic3⋊Dic3C2211yescharacteristic, complemented
43C2×#3722C2211yescharacteristic
44C2×#3722C2211yescharacteristic
45C2×#3722C2211yescharacteristic
46C2×#3722C2211yescharacteristic
47C2×#3722C2211yescharacteristic
48C2×#3722C2211yescharacteristic
49C2×Dic32C2211yescharacteristic, complemented
50#63952—24no—
51C3×C3⋊#95C2211yescharacteristic, complemented
52#63579C2211yescharacteristic, complemented
53#63579C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×C3×#123—31no—
58C2×#937—31no—
59C2×#937—31no—
60C2×#937—61no—
61C2×#935D311yescharacteristic, complemented
62C2×C4×#67—31no—
63C2×#67⋊C4—31no—
64C2×D3×C22⋊C4—31no—
65C2×D3×C22⋊C4—31no—
66C3×#394—31no—
67#5222D311yescharacteristic, complemented
68#5213—31no—
69#4993—31no—
70#4993—31no—
71#4990—31no—
72#4989—31no—
73#4989—31no—
74#4987—31no—
75#4961—31no—
76#4959—31no—
77#4958—31no—
78#4956—31no—
79#4956—31no—
80#4955—31no—
81#4955—31no—
82#4952—31no—
83#4952—31no—
84#4951—31no—
85#4945—31no—
86#4669—31no—
87#4667—31no—
88C24×C32C2311yescharacteristic
89C24×C32C2311yescharacteristic
90C23×C3⋊D3—22no—
91C23×C3⋊D3—22no—
92C23×C3⋊D3—22no—
93C23×C3⋊D3—22no—
94C23×C3⋊D3—22no—
95C23×C3⋊D3—41no—
96C23×C3⋊D3—41no—
97C23×C3⋊D3C2311yescharacteristic
98C23×C3⋊D3C2311yescharacteristic
99C2×C32×D4—22no—
100C2×C32×D4—22no—
101C2×C32×D4—41no—
102C22×C32×C4C2311yescharacteristic
103C2×#638—22no—
104C2×#638—22no—
105C2×#638—22no—
106C2×#638—22no—
107C2×#638—41no—
108C2×#638D414yes—
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3×Dic3—22no—
112C22×C3×Dic3—22no—
113C22×C3×Dic3—41no—
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C2×#624—22no—
123C2×#624—22no—
124C2×#624—22no—
125C2×#624—22no—
126C2×#624—41no—
127C2×#624—41no—
128#3757—22no—
129#3752—22no—
130#3752—22no—
131C3×#217—22no—
132C3×#217—22no—
133C3×#217—22no—
134C3×#217—22no—
135C3×#217—41no—
136C3×#217—41no—
137C3×#217D414yescomplemented
138C3×Dic3⋊C4—22no—
139C3×Dic3⋊C4—22no—
140C3×Dic3⋊C4—41no—
141#3724—22no—
142Dic3⋊Dic3—41no—
143#3722—22no—
144#3722—22no—
145#3722—22no—
146#3722—22no—
147#3722—22no—
148#3722—41no—
149Dic32—22no—
150#2418—91noSylow
151C24×D3—31no—
152C24×D3—31no—
153C24×D3—61no—
154C22×C3×D4—21no—
155C22×C3×D4C2×D311yescharacteristic
156C22×C3×D4C2×D311yescharacteristic
157C23×C3×C4—31no—
158C22×#67—31no—
159C22×#67—31no—
160C22×#67—31no—
161C22×#67—31no—
162C22×#67—61no—
163C22×#67—61no—
164C23×Dic3C2×D311yescharacteristic, complemented
165C22×C4×D3—31no—
166C22×C4×D3—31no—
167C22×C4×D3—31no—
168C22×C4×D3—31no—
169C3×#123—64no—
170C2×C3×C4⋊C4—31no—
171C2×C3×C4⋊C4—31no—
172C2×C3×C4⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C22⋊C4—31no—
175C2×C3×C22⋊C4—31no—
176C2×C3×C22⋊C4—31no—
177C2×C3×C22⋊C4—31no—
178C2×C3×C22⋊C4—31no—
179C2×C3×C22⋊C4—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—61no—
183C2×#217C2×D311yescharacteristic
184C2×#217C2×D311yescharacteristic
185C2×#217C2×D311yescharacteristic
186C2×#217C2×D311yescharacteristic
187C2×#217C2×D311yescharacteristic, complemented
188C2×#217C2×D311yescharacteristic, complemented
189C2×#217C2×D311yescharacteristic, complemented
190#937—64no—
191#937—64no—
192#937—68no—
193#935—24no—
194C4×#67—64no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4—31no—
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4—31no—
205C2×(C2×D3)⋊C4—31no—
206C2×(C2×D3)⋊C4—31no—
207C2×(C2×D3)⋊C4—31no—
208C2×(C2×D3)⋊C4—31no—
209C2×(C2×D3)⋊C4—31no—
210C2×(C2×D3)⋊C4—31no—
211C2×(C2×D3)⋊C4—61no—
212C2×(C2×D3)⋊C4—61no—
213C2×C4⋊Dic3—31no—
214C2×Dic3⋊C4—31no—
215C2×Dic3⋊C4—31no—
216C2×Dic3⋊C4—31no—
217C2×Dic3⋊C4C2×D311yescharacteristic, complemented
218C2×Dic3⋊C4C2×D311yescharacteristic, complemented
219C2×Dic3⋊C4C2×D311yescharacteristic, complemented
220C2×C4×Dic3—31no—
221C2×C4×Dic3—31no—
222#67⋊C4—64no—
223D3×C22⋊C4—64no—
224D3×C22⋊C4—64no—
225C3×#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95—31no—
232C3⋊#95—31no—
233C3⋊#95—31no—
234C3⋊#95—31no—
235C3⋊#95—31no—
236C3⋊#95C2×D311yescharacteristic, complemented
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—21no—
243C23×C32—21no—
244C23×C32—21no—
245C23×C32—21no—
246C23×C32—21no—
247C23×C32—21no—
248C23×C32—21no—
249C23×C32C2×D412yes—
250C23×C32C2×D412yes—
251C23×C32C2411yescharacteristic
252C22×C3⋊D3—21no—
253C22×C3⋊D3—21no—
254C22×C3⋊D3—21no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3—21no—
258C22×C3⋊D3—28no—
259C22×C3⋊D3—21no—
260C22×C3⋊D3—21no—
261C22×C3⋊D3—21no—
262C22×C3⋊D3—21no—
263C22×C3⋊D3—44no—
264C22×C3⋊D3—44no—
265C22×C3⋊D3—44no—
266C22×C3⋊D3—44no—
267C22×C3⋊D3—44no—
268C22×C3⋊D3—44no—
269C22×C3⋊D3C2×D412yes—
270C22×C3⋊D3#4112yes—
271C22×C3⋊D3#4112yes—
272C22×C3⋊D3#4112yes—
273C32×D4—44no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277#638—28no—
278#638—44no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3—21no—
281C2×C3⋊Dic3—21no—
282C2×C3⋊Dic3—21no—
283C2×C3⋊Dic3—21no—
284C2×C3⋊Dic3C2×D412yes—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—44no—
308C2×C3×Dic3C2×D412yes—
309C2×C3×Dic3C2×D412yes—
310#624—44no—
311#624—44no—
312C2×#123—31no—
313C2×#120—91no—
314C2×C4×D4—91no—
315C22×C22⋊C4—91no—
316#399—91no—
317#397—91no—
318#394—31no—
319#394—91no—
320#388—91no—
321#388—91no—
322#386—91no—
323#386—91no—
324#385—91no—
325#380—91no—
326#379—91no—
327C24×C3—21no—
328C24×C3—21no—
329C24×C3C22×D311yescharacteristic
330C24×C3C22×D311yescharacteristic
331C24×C3C22×D311yescharacteristic
332C24×C3C22×D311yescharacteristic
333C23×D3—31no—
334C23×D3—31no—
335C23×D3—31no—
336C23×D3—31no—
337C23×D3—61no—
338C23×D3—61no—
339C23×D3—62no—
340C23×D3—62no—
341C23×D3—62no—
342C23×D3—62no—
343C23×D3—62no—
344C23×D3—62no—
345C23×D3—62no—
346C23×D3—62no—
347C23×D3—62no—
348C23×D3—62no—
349C23×D3—64no—
350C23×D3—122no—
351C23×D3—122no—
352C23×D3—122no—
353C23×D3—122no—
354C23×D3—121no—
355C23×D3—121no—
356C23×D3—121no—
357C23×D3—121no—
358C23×D3—122no—
359C23×D3—122no—
360C2×C3×D4—24no—
361C2×C3×D4—22no—
362C2×C3×D4—22no—
363C2×C3×D4—22no—
364C2×C3×D4—22no—
365C2×C3×D4—42no—
366C2×C3×D4—41no—
367C2×C3×D4—41no—
368C2×C3×D4—42no—
369C22×C3×C4—21no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—62no—
379C22×C3×C4—62no—
380C22×C3×C4—121no—
381C22×C3×C4C22×D311yescharacteristic
382C22×C3×C4C22×D311yescharacteristic
383C2×#67—34no—
384C2×#67—34no—
385C2×#67—64no—
386C2×#67—62no—
387C2×#67—62no—
388C2×#67—62no—
389C2×#67—62no—
390C2×#67—62no—
391C2×#67—62no—
392C2×#67—64no—
393C2×#67—62no—
394C2×#67—62no—
395C2×#67—122no—
396C2×#67—122no—
397C2×#67—122no—
398C2×#67—121no—
399C2×#67—121no—
400C2×#67—122no—
401C22×Dic3—22no—
402C22×Dic3—22no—
403C22×Dic3—31no—
404C22×Dic3—31no—
405C22×Dic3—31no—
406C22×Dic3—31no—
407C22×Dic3—41no—
408C22×Dic3—61no—
409C22×Dic3—61no—
410C22×Dic3C22×D311yescharacteristic
411C22×Dic3C22×D311yescharacteristic
412C22×Dic3C22×D311yescharacteristic
413C22×Dic3C22×D311yescharacteristic
414C22×Dic3C22×D311yescharacteristic
415C22×Dic3C22×D311yescharacteristic
416C22×Dic3C22×D311yescharacteristic
417C22×Dic3C22×D311yescharacteristic
418C2×C4×D3—62no—
419C2×C4×D3—62no—
420C2×C4×D3—62no—
421C2×C4×D3—62no—
422C2×C4×D3—62no—
423C2×C4×D3—62no—
424C2×C4×D3—62no—
425C2×C4×D3—62no—
426C2×C4×D3—121no—
427C2×C4×D3—121no—
428C2×C4×D3—121no—
429C2×C4×D3—121no—
430C3×C4⋊C4—62no—
431C3×C4⋊C4—62no—
432C3×C4⋊C4—121no—
433C3×C22⋊C4—34no—
434C3×C22⋊C4—62no—
435C3×C22⋊C4—62no—
436C3×C22⋊C4—62no—
437C3×C22⋊C4—62no—
438C3×C22⋊C4—121no—
439C3×C22⋊C4—121no—
440#217—22no—
441#217—22no—
442#217—22no—
443#217—22no—
444#217—41no—
445#217—41no—
446#217—62no—
447#217—62no—
448#217—64no—
449#217#6714yescomplemented
450(C2×D3)⋊C4—62no—
451(C2×D3)⋊C4—62no—
452(C2×D3)⋊C4—62no—
453(C2×D3)⋊C4—62no—
454(C2×D3)⋊C4—62no—
455(C2×D3)⋊C4—62no—
456(C2×D3)⋊C4—62no—
457(C2×D3)⋊C4—62no—
458(C2×D3)⋊C4—62no—
459(C2×D3)⋊C4—62no—
460(C2×D3)⋊C4—62no—
461(C2×D3)⋊C4—62no—
462(C2×D3)⋊C4—64no—
463(C2×D3)⋊C4—64no—
464(C2×D3)⋊C4—62no—
465(C2×D3)⋊C4—62no—
466(C2×D3)⋊C4—121no—
467(C2×D3)⋊C4—121no—
468C4⋊Dic3—121no—
469Dic3⋊C4—22no—
470Dic3⋊C4—22no—
471Dic3⋊C4—41no—
472Dic3⋊C4—62no—
473Dic3⋊C4—62no—
474Dic3⋊C4—121no—
475C4×Dic3—62no—
476C4×Dic3—62no—
477C22×C32—22no—
478C22×C32—22no—
479C22×C32—22no—
480C22×C32—22no—
481C22×C32—22no—
482C22×C32—22no—
483C22×C32—41no—
484C22×C32—41no—
485C22×C32—41no—
486C22×C32—41no—
487C22×C32—41no—
488C22×C32—41no—
489C22×C32—41no—
490C22×C32—41no—
491C22×C32C22×D411yescharacteristic
492C22×C32C22×D411yescharacteristic
493C22×C32C2×#4111yescharacteristic
494C22×C32C2×#4111yescharacteristic
495C22×C32C2×#4111yescharacteristic
496C22×C32H(5,𝔽2)11yescharacteristic
497C22×C32H(5,𝔽2)11yescharacteristic
498C2×C3⋊D3—22no—
499C2×C3⋊D3—22no—
500C2×C3⋊D3—22no—
501C2×C3⋊D3—22no—
502C2×C3⋊D3—22no—
503C2×C3⋊D3—22no—
504C2×C3⋊D3—22no—
505C2×C3⋊D3—22no—
506C2×C3⋊D3—22no—
507C2×C3⋊D3—416no—
508C2×C3⋊D3—41no—
509C2×C3⋊D3—41no—
510C2×C3⋊D3—41no—
511C2×C3⋊D3—41no—
512C2×C3⋊D3#12314yescomplemented
513C32×C4—41no—
514C3⋊Dic3—22no—
515C3⋊Dic3—41no—
516C3×Dic3—22no—
517C3×Dic3—22no—
518C3×Dic3—41no—
519C3×Dic3—41no—
520C3×Dic3—41no—
521C3×Dic3—41no—
522C3×Dic3—41no—
523C3×Dic3—41no—
524C25—91no—
525C22×D4—91no—
526C22×D4—91no—
527C22×D4D3211yescharacteristic
528C23×C4—31no—
529C23×C4—91no—
530C23×C4—91no—
531#123—64no—
532#120—184no—
533C4×D4—184no—
534C2×C4⋊C4—31no—
535C2×C4⋊C4—31no—
536C2×C4⋊C4—31no—
537C2×C4⋊C4—91no—
538C2×C4⋊C4—91no—
539C2×C22⋊C4—31no—
540C2×C22⋊C4—31no—
541C2×C22⋊C4—31no—
542C2×C22⋊C4—31no—
543C2×C22⋊C4—31no—
544C2×C22⋊C4—31no—
545C2×C22⋊C4—31no—
546C2×C22⋊C4—91no—
547C2×C22⋊C4—91no—
548C2×C22⋊C4—91no—
549C2×C22⋊C4—91no—
550C2×C22⋊C4—91no—
551C2×C22⋊C4—91no—
552C2×C22⋊C4—91no—
553C2×C22⋊C4—91no—
554C2×C22⋊C4—91no—
555C2×C22⋊C4—184no—
556C2×C42—91no—
557#95—31no—
558#95—91no—
559#95—91no—
560#95—91no—
561#95—91no—
562#95—91no—
563C23×C3—22no—
564C23×C3—22no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3—21no—
578C23×C3—21no—
579C23×C3—21no—
580C23×C3—21no—
581C23×C3—21no—
582C23×C3—21no—
583C23×C3—21no—
584C23×C3—21no—
585C23×C3—21no—
586C23×C3—21no—
587C23×C3—21no—
588C23×C3—21no—
589C23×C3—21no—
590C23×C3—22no—
591C23×C3—22no—
592C23×C3—41no—
593C23×C3—41no—
594C23×C3—41no—
595C23×C3—41no—
596C23×C3—41no—
597C23×C3—41no—
598C23×C3—41no—
599C23×C3—41no—
600C23×C3—41no—
601C23×C3—41no—
602C23×C3D3×D412yes—
603C23×C3D3×D412yes—
604C23×C3D3×D412yes—
605C23×C3C2×#6712yes—
606C23×C3C23×D311yescharacteristic
607C23×C3C23×D311yescharacteristic
608C22×D3—32no—
609C22×D3—32no—
610C22×D3—32no—
611C22×D3—32no—
612C22×D3—32no—
613C22×D3—32no—
614C22×D3—32no—
615C22×D3—32no—
616C22×D3—62no—
617C22×D3—62no—
618C22×D3—62no—
619C22×D3—62no—
620C22×D3—61no—
621C22×D3—61no—
622C22×D3—61no—
623C22×D3—61no—
624C22×D3—61no—
625C22×D3—61no—
626C22×D3—61no—
627C22×D3—61no—
628C22×D3—62no—
629C22×D3—62no—
630C22×D3—68no—
631C22×D3—68no—
632C22×D3—61no—
633C22×D3—61no—
634C22×D3—61no—
635C22×D3—61no—
636C22×D3—61no—
637C22×D3—61no—
638C22×D3—61no—
639C22×D3—61no—
640C22×D3—61no—
641C22×D3—61no—
642C22×D3—61no—
643C22×D3—61no—
644C22×D3—121no—
645C22×D3—121no—
646C22×D3—121no—
647C22×D3—121no—
648C22×D3—121no—
649C22×D3—121no—
650C22×D3—121no—
651C22×D3—121no—
652C22×D3—128no—
653C22×D3—124no—
654C22×D3—124no—
655C22×D3—124no—
656C22×D3—124no—
657C22×D3—124no—
658C22×D3—124no—
659C22×D3—124no—
660C22×D3—124no—
661C22×D3—124no—
662C22×D3—124no—
663C22×D3—128no—
664C22×D3—128no—
665C22×D3—124no—
666C22×D3—124no—
667C22×D3—128no—
668C22×D3—128no—
669C22×D3—128no—
670C22×D3—128no—
671C3×D4—44no—
672C3×D4—44no—
673C3×D4—48no—
674C2×C3×C4—22no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—21no—
678C2×C3×C4—21no—
679C2×C3×C4—21no—
680C2×C3×C4—21no—
681C2×C3×C4—32no—
682C2×C3×C4—32no—
683C2×C3×C4—41no—
684C2×C3×C4—41no—
685C2×C3×C4—61no—
686C2×C3×C4—61no—
687C2×C3×C4—61no—
688C2×C3×C4—61no—
689C2×C3×C4—61no—
690C2×C3×C4—61no—
691C2×C3×C4—61no—
692C2×C3×C4—61no—
693C2×C3×C4—61no—
694C2×C3×C4—61no—
695C2×C3×C4—61no—
696C2×C3×C4—61no—
697C2×C3×C4—61no—
698C2×C3×C4—61no—
699C2×C3×C4—61no—
700C2×C3×C4—61no—
701C2×C3×C4—61no—
702C2×C3×C4—61no—
703C2×C3×C4—61no—
704C2×C3×C4—61no—
705C2×C3×C4—61no—
706C2×C3×C4—61no—
707C2×C3×C4—124no—
708#67—68no—
709#67—68no—
710#67—128no—
711#67—124no—
712#67—124no—
713#67—128no—
714C2×Dic3—21no—
715C2×Dic3—21no—
716C2×Dic3—21no—
717C2×Dic3—21no—
718C2×Dic3—21no—
719C2×Dic3—21no—
720C2×Dic3—21no—
721C2×Dic3—21no—
722C2×Dic3—21no—
723C2×Dic3—21no—
724C2×Dic3—21no—
725C2×Dic3—21no—
726C2×Dic3—21no—
727C2×Dic3—21no—
728C2×Dic3—21no—
729C2×Dic3—21no—
730C2×Dic3—21no—
731C2×Dic3—21no—
732C2×Dic3—21no—
733C2×Dic3—21no—
734C2×Dic3—21no—
735C2×Dic3—21no—
736C2×Dic3—32no—
737C2×Dic3—32no—
738C2×Dic3—44no—
739C2×Dic3—62no—
740C2×Dic3—61no—
741C2×Dic3—61no—
742C2×Dic3—61no—
743C2×Dic3—61no—
744C2×Dic3—62no—
745C2×Dic3—61no—
746C2×Dic3—61no—
747C2×Dic3—61no—
748C2×Dic3—61no—
749C2×Dic3—61no—
750C2×Dic3—61no—
751C2×Dic3—121no—
752C2×Dic3—121no—
753C2×Dic3—121no—
754C2×Dic3—121no—
755C2×Dic3C2×#6712yes—
756C2×Dic3C2×#6712yes—
757C4×D3—124no—
758C4×D3—124no—
759C4×D3—124no—
760C4×D3—124no—
761C2×C32—42no—
762C2×C32—42no—
763C2×C32C2×#12311yescharacteristic
764C2×C32#52511yescharacteristic
765C2×C32#53811yescharacteristic
766C2×C32D4211yescharacteristic
767C2×C32#54611yescharacteristic
768C2×C32#54611yescharacteristic
769C2×C32#55111yescharacteristic
770C3⋊D3—24no—
771C3⋊D3—42no—
772C24—91no—
773C24—91no—
774C24—182no—
775C24—182no—
776C24—182no—
777C24—182no—
778C24—182no—
779C24—361no—
780C24—361no—
781C24C2×D3211yescharacteristic
782C24C2×D3211yescharacteristic
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—41no—
786C2×D4—94no—
787C2×D4—182no—
788C2×D4—182no—
789C2×D4—182no—
790C2×D4—182no—
791C2×D4—361no—
792C22×C4—31no—
793C22×C4—31no—
794C22×C4—31no—
795C22×C4—31no—
796C22×C4—31no—
797C22×C4—31no—
798C22×C4—31no—
799C22×C4—31no—
800C22×C4—62no—
801C22×C4—62no—
802C22×C4—91no—
803C22×C4—91no—
804C22×C4—121no—
805C22×C4—182no—
806C22×C4—182no—
807C22×C4—182no—
808C22×C4—182no—
809C22×C4—361no—
810C22×C4—361no—
811C22×C4C2×D3211yescharacteristic
812C4⋊C4—62no—
813C4⋊C4—62no—
814C4⋊C4—121no—
815C4⋊C4—182no—
816C4⋊C4—361no—
817C22⋊C4—34no—
818C22⋊C4—62no—
819C22⋊C4—62no—
820C22⋊C4—62no—
821C22⋊C4—62no—
822C22⋊C4—121no—
823C22⋊C4—121no—
824C22⋊C4—182no—
825C22⋊C4—182no—
826C22⋊C4—182no—
827C22⋊C4—182no—
828C22⋊C4—182no—
829C22⋊C4—182no—
830C22⋊C4—182no—
831C22⋊C4—182no—
832C22⋊C4—361no—
833C42—182no—
834C22×C3—24no—
835C22×C3—22no—
836C22×C3—22no—
837C22×C3—22no—
838C22×C3—22no—
839C22×C3—22no—
840C22×C3—22no—
841C22×C3—22no—
842C22×C3—22no—
843C22×C3—22no—
844C22×C3—22no—
845C22×C3—22no—
846C22×C3—22no—
847C22×C3—21no—
848C22×C3—21no—
849C22×C3—21no—
850C22×C3—21no—
851C22×C3—21no—
852C22×C3—21no—
853C22×C3—21no—
854C22×C3—42no—
855C22×C3—42no—
856C22×C3—42no—
857C22×C3—42no—
858C22×C3—42no—
859C22×C3—42no—
860C22×C3—42no—
861C22×C3—42no—
862C22×C3—42no—
863C22×C3—41no—
864C22×C3—41no—
865C22×C3—41no—
866C22×C3—41no—
867C22×C3—41no—
868C22×C3—41no—
869C22×C3—41no—
870C22×C3—41no—
871C22×C3—41no—
872C22×C3—41no—
873C22×C3—41no—
874C22×C3—41no—
875C22×C3—41no—
876C22×C3—41no—
877C22×C3—41no—
878C22×C3—41no—
879C22×C3—81no—
880C22×C3—81no—
881C22×C3—81no—
882C22×C3—81no—
883C22×C3C2×D3×D411yescharacteristic
884C22×C3C2×D3×D411yescharacteristic
885C22×C3C2×D3×D411yescharacteristic
886C22×C3#100411yescharacteristic
887C22×C3#100411yescharacteristic
888C22×C3#100411yescharacteristic
889C22×C3D3×#4111yescharacteristic
890C22×C3D3×#4111yescharacteristic
891C22×C3D3×#4111yescharacteristic
892C22×C3D3×#4111yescharacteristic
893C22×C3D3×#4111yescharacteristic
894C22×C3D3×#4111yescharacteristic
895C22×C3#100911yescharacteristic
896C22×C3C22×#6711yescharacteristic
897C2×D3—34no—
898C2×D3—34no—
899C2×D3—64no—
900C2×D3—62no—
901C2×D3—62no—
902C2×D3—62no—
903C2×D3—62no—
904C2×D3—62no—
905C2×D3—62no—
906C2×D3—62no—
907C2×D3—62no—
908C2×D3—62no—
909C2×D3—62no—
910C2×D3—62no—
911C2×D3—62no—
912C2×D3—64no—
913C2×D3—62no—
914C2×D3—62no—
915C2×D3—62no—
916C2×D3—62no—
917C2×D3—62no—
918C2×D3—62no—
919C2×D3—122no—
920C2×D3—122no—
921C2×D3—122no—
922C2×D3—122no—
923C2×D3—122no—
924C2×D3—122no—
925C2×D3—122no—
926C2×D3—122no—
927C2×D3—1216no—
928C2×D3—1216no—
929C2×D3—122no—
930C2×D3—122no—
931C2×D3—122no—
932C2×D3—122no—
933C2×D3—1232no—
934C2×D3—121no—
935C2×D3—121no—
936C2×D3—121no—
937C2×D3—121no—
938C2×D3—121no—
939C2×D3—121no—
940C2×D3—121no—
941C2×D3—121no—
942C3×C4—42no—
943C3×C4—41no—
944C3×C4—41no—
945C3×C4—62no—
946C3×C4—62no—
947C3×C4—121no—
948C3×C4—121no—
949C3×C4—121no—
950C3×C4—121no—
951C3×C4—121no—
952C3×C4—121no—
953Dic3—22no—
954Dic3—22no—
955Dic3—41no—
956Dic3—41no—
957Dic3—41no—
958Dic3—41no—
959Dic3—41no—
960Dic3—41no—
961Dic3—62no—
962Dic3—62no—
963Dic3—122no—
964Dic3—122no—
965Dic3—121no—
966Dic3—121no—
967C32#241811yescharacteristic, complemented, Sylow
968C23—21no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—21no—
974C23—21no—
975C23—21no—
976C23—21no—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—92no—
981C23—92no—
982C23—92no—
983C23—92no—
984C23—188no—
985C23—181no—
986C23—181no—
987C23—181no—
988C23—181no—
989C23—181no—
990C23—181no—
991C23—181no—
992C23—181no—
993C23—181no—
994C23—181no—
995C23—364no—
996C23—364no—
997C23—364no—
998C23—364no—
999C23—364no—
1000C23—364no—
1001C23D3×#6712yes—
1002C23#381112yes—
1003C23C22×D3211yescharacteristic
1004D4—44no—
1005D4—188no—
1006D4—364no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—32no—
1011C2×C4—32no—
1012C2×C4—61no—
1013C2×C4—61no—
1014C2×C4—61no—
1015C2×C4—61no—
1016C2×C4—61no—
1017C2×C4—61no—
1018C2×C4—61no—
1019C2×C4—61no—
1020C2×C4—61no—
1021C2×C4—61no—
1022C2×C4—61no—
1023C2×C4—61no—
1024C2×C4—61no—
1025C2×C4—61no—
1026C2×C4—61no—
1027C2×C4—61no—
1028C2×C4—61no—
1029C2×C4—61no—
1030C2×C4—61no—
1031C2×C4—61no—
1032C2×C4—61no—
1033C2×C4—61no—
1034C2×C4—92no—
1035C2×C4—124no—
1036C2×C4—181no—
1037C2×C4—181no—
1038C2×C4—181no—
1039C2×C4—181no—
1040C2×C4—181no—
1041C2×C4—364no—
1042C2×C4—364no—
1043C2×C3—21no—
1044C2×C3—21no—
1045C2×C3—21no—
1046C2×C3—21no—
1047C2×C3—21no—
1048C2×C3—21no—
1049C2×C3—21no—
1050C2×C3—44no—
1051C2×C3—42no—
1052C2×C3—42no—
1053C2×C3—42no—
1054C2×C3—42no—
1055C2×C3—82no—
1056C2×C3#559011yescharacteristic
1057C2×C3#561011yescharacteristic
1058C2×C3#561011yescharacteristic
1059C2×C3#561311yescharacteristic
1060C2×C3D3×#12311yescharacteristic
1061C2×C3D3×#12311yescharacteristic
1062C2×C3#565411yescharacteristic
1063C2×C3#565611yescharacteristic
1064C2×C3#565711yescharacteristic
1065C2×C3#565911yescharacteristic
1066C2×C3#567911yescharacteristic
1067C2×C3D4×#6711yescharacteristic
1068C2×C3#582811yescharacteristic
1069C2×C3#582911yescharacteristic
1070D3—64no—
1071D3—64no—
1072D3—124no—
1073D3—124no—
1074D3—122no—
1075D3—122no—
1076C22—22no—
1077C22—22no—
1078C22—22no—
1079C22—22no—
1080C22—22no—
1081C22—22no—
1082C22—41no—
1083C22—41no—
1084C22—41no—
1085C22—41no—
1086C22—41no—
1087C22—41no—
1088C22—41no—
1089C22—41no—
1090C22—94no—
1091C22—182no—
1092C22—182no—
1093C22—182no—
1094C22—182no—
1095C22—182no—
1096C22—182no—
1097C22—182no—
1098C22—182no—
1099C22—182no—
1100C22—3616no—
1101C22—361no—
1102C22—361no—
1103C22—361no—
1104C22—361no—
1105C22#6431211yescharacteristic
1106C22#6431211yescharacteristic
1107C22#6431211yescharacteristic
1108C22#6431411yescharacteristic
1109C22C2×D3×#6711yescharacteristic
1110C22C2×#381111yescharacteristic
1111C22#6433011yescharacteristic
1112C4—41no—
1113C4—62no—
1114C4—62no—
1115C4—121no—
1116C4—121no—
1117C4—121no—
1118C4—121no—
1119C4—121no—
1120C4—121no—
1121C4—182no—
1122C4—361no—
1123C3—21no—
1124C3#7711111yescharacteristic, complemented
1125C3#8289611yescharacteristic, complemented
1126C2—42no—
1127C2—42no—
1128C2—184no—
1129C2—362no—
1130C2#1059515911yescharacteristic
1131C2#1059516311yescharacteristic
1132C2#1059516911yescharacteristic
1133C2#1059520811yescharacteristic
1134C2#1059525511yescharacteristic
1135C2#1059530511yescharacteristic
1136C2#1059552611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
prime radicalC2×#64146C2
hypercenterC22×D4D32
hypocenterC32#2418
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#935C2semidirect
3. C2×#63974C2semidirect
4. C2×#63952C2semidirect
5. C3×#5222C2semidirect
6. #10591722C2semidirect
7. #10591714C2semidirect
8. #10591712C2semidirect
9. #10591711C2semidirect
10. #10591702C2semidirect
11. #10591694C2semidirect
12. #10591374C2semidirect
13. #10591367C2semidirect
14. #10591258C2semidirect
15. #10591203C2semidirect
22. C23×C3×Dic3C22semidirect
33. C2×C3×#217C22semidirect
34. C2×C3×#217C22semidirect
35. C2×C3×#217C22semidirect
37. C2×C3×Dic3⋊C4C22semidirect
38. C2×C3×Dic3⋊C4C22semidirect
39. C2×C3×Dic3⋊C4C22semidirect
41. C2×#3724C22semidirect
42. C2×Dic3⋊Dic3C22semidirect
49. C2×Dic32C22semidirect
51. C3×C3⋊#95C22semidirect
52. #63579C22semidirect
53. #63579C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
61. C2×#935D3semidirect
67. #5222D3semidirect
137. C3×#217D4semidirect
164. C23×Dic3C2×D3semidirect
187. C2×#217C2×D3semidirect
188. C2×#217C2×D3semidirect
189. C2×#217C2×D3semidirect
217. C2×Dic3⋊C4C2×D3semidirect
218. C2×Dic3⋊C4C2×D3semidirect
219. C2×Dic3⋊C4C2×D3semidirect
236. C3⋊#95C2×D3semidirect
449. #217#67semidirect
512. C2×C3⋊D3#123semidirect
967. C32#2418semidirect
1124. C3#77111semidirect
1125. C3#82896semidirect

Maximal subgroups

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

subgroupindex
C2×#641462
C2×C3×#9352
C2×#639742
C2×#639522
C3×#52222
#105917222
#105917142
#105917122
#105917112
#105917022
#105916942
#105913742
#105913672
#105912582
#105912032
#828963
#771113