Finite Group Databasebeta

← #11810320

Subgroups — #11810320

Order 1152.

1813 conjugacy classes of subgroups.

The subgroup lattice has 1102 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64090C211yesmaximal, characteristic, complemented
2C2×#63983C211yesmaximal, characteristic
3C2×#63962C211yesmaximal, characteristic, complemented
4C2×#63921C211yesmaximal, characteristic, complemented
5C3×#4959C211yesmaximal, characteristic, complemented
6C3×#4959C211yesmaximal, characteristic, complemented
7#10591722C211yesmaximal, characteristic, complemented
8#10591713C211yesmaximal, characteristic, complemented
9#10591399C211yesmaximal, characteristic, complemented
10#10591367C211yesmaximal, characteristic, complemented
11#10591303C211yesmaximal, characteristic, complemented
12#10591298C211yesmaximal, characteristic, complemented
13#10591290C211yesmaximal, characteristic, complemented
14#10591286C211yesmaximal, characteristic, complemented
15#10591283C211yesmaximal, characteristic, complemented
16#77112—31nomaximal
17#77111—31nomaximal
18C23×D32C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic, complemented
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic, complemented
26C2×#3752C2211yescharacteristic
27C2×#3750C2211yescharacteristic, complemented
28C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
29#64090—24no—
30C2×C3×#217C2211yescharacteristic, complemented
31C2×C3×#217C2211yescharacteristic, complemented
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
37C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
38#63983—24no—
39C2×Dic3⋊Dic3C2211yescharacteristic, complemented
40C2×Dic3⋊Dic3C2211yescharacteristic, complemented
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43#63962—24no—
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×(C2×D3)⋊Dic3C2211yescharacteristic
50#63921—24no—
51C3×C3⋊#95C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53#63579C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×#937—31no—
58C2×#937—31no—
59C2×#935—31no—
60C2×#886—31no—
61C2×#67⋊C4—31no—
62C2×#67⋊C4—31no—
63C2×#67⋊C4—61no—
64C2×D3×C22⋊C4—31no—
65C2×D3×C22⋊C4—31no—
66C3×#394—31no—
67C3×#394—31no—
68#5220—31no—
69#4993—31no—
70#4990—31no—
71#4989—31no—
72#4987—31no—
73#4959D311yescharacteristic, complemented
74#4959D311yescharacteristic, complemented
75#4958—31no—
76#4956—31no—
77#4956—31no—
78#4955—31no—
79#4955—31no—
80#4952—31no—
81#4951—31no—
82#4949—31no—
83#4945—31no—
84#4675—31no—
85#4669—31no—
86#4668—31no—
87#4667—31no—
88C24×C32C2311yescharacteristic
89C23×C3⋊D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C22×D32—22no—
93C22×D32—22no—
94C22×D32—22no—
95C22×D32—22no—
96C22×D32—22no—
97C22×D32—41no—
98C22×D32—41no—
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C2×#638—22no—
102C2×#638—22no—
103C2×#638D414yes—
104C22×C3⋊Dic3—22no—
105C22×C3⋊Dic3—22no—
106C22×C3⋊Dic3—41no—
107C22×C3⋊Dic3C2311yescharacteristic
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C2×C4×C3⋊D3—22no—
111C2×C4×C3⋊D3—22no—
112C2×C4×C3⋊D3—41no—
113C2×C3×#67—22no—
114C2×C3×#67—22no—
115C2×C3×#67—22no—
116C2×C3×#67—22no—
117C2×C3×#67—41no—
118C2×C3×#67—41no—
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C2×#624—22no—
126C2×#624—22no—
127C2×#624—41no—
128C32×C22⋊C4—22no—
129#3752—22no—
130#3750—22no—
131C4×C3⋊Dic3—22no—
132C3×#217—22no—
133C3×#217—41no—
134C3×(C2×D3)⋊C4—22no—
135C3×(C2×D3)⋊C4—22no—
136C3×(C2×D3)⋊C4—22no—
137C3×(C2×D3)⋊C4—41no—
138C3×Dic3⋊C4—41no—
139C3×Dic3⋊C4—41no—
140Dic3⋊Dic3—22no—
141Dic3⋊Dic3—22no—
142#3722—22no—
143#3722—22no—
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—22no—
147(C2×D3)⋊Dic3—22no—
148(C2×D3)⋊Dic3—41no—
149(C2×D3)⋊Dic3D414yescomplemented
150#2418—91noSylow
151C24×D3—31no—
152C24×D3—31no—
153C22×C3×D4—31no—
154C22×C3×D4—31no—
155C22×#67—31no—
156C22×#67—31no—
157C22×#67—61no—
158C22×#67C2×D311yescharacteristic
159C22×#67C2×D311yescharacteristic
160C23×Dic3—31no—
161C23×Dic3—31no—
162C23×Dic3—61no—
163C22×C4×D3—31no—
164C22×C4×D3—31no—
165C22×C4×D3—31no—
166C22×C4×D3—31no—
167C22×C4×D3—61no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C4⋊C4—31no—
170C2×C3×C22⋊C4—21no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊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⋊C4C2×D311yescharacteristic, complemented
178C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
179C2×#217—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—31no—
183C2×#217—31no—
184C2×#217—31no—
185C2×#217C2×D311yescharacteristic, complemented
186C2×#217C2×D311yescharacteristic, complemented
187#937—64no—
188#937—64no—
189#935—64no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—31no—
194C2×(C2×D3)⋊C4—31no—
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—61no—
203C2×(C2×D3)⋊C4C2×D311yescharacteristic
204C2×(C2×D3)⋊C4C2×D311yescharacteristic
205C2×(C2×D3)⋊C4C2×D311yescharacteristic
206C2×(C2×D3)⋊C4C2×D311yescharacteristic
207C2×C4⋊Dic3—31no—
208C2×C4⋊Dic3—31no—
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4—31no—
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—61no—
214C2×Dic3⋊C4C2×D311yescharacteristic, complemented
215C2×Dic3⋊C4C2×D311yescharacteristic, complemented
216C2×C4×Dic3—31no—
217C2×C4×Dic3—31no—
218C2×C4×Dic3—61no—
219#886—64no—
220#67⋊C4—64no—
221#67⋊C4—64no—
222#67⋊C4—68no—
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⋊#95C2×D311yescharacteristic, complemented
236C3⋊#95C2×D311yescharacteristic, complemented
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—21no—
243C23×C32C2×D412yes—
244C23×C32C2411yescharacteristic
245C22×C3⋊D3—21no—
246C22×C3⋊D3—21no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3—21no—
249C22×C3⋊D3C2×D412yes—
250C22×C3⋊D3#4112yes—
251C22×C3⋊D3#4112yes—
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—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—21no—
264C22×C3×D3C2×D412yes—
265C22×C3×D3#4112yes—
266C2×D32—28no—
267C2×D32—44no—
268C2×D32—44no—
269C2×D32—44no—
270C2×D32—44no—
271C2×D32—44no—
272C2×D32—44no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C32×C4—21no—
279#638—28no—
280C2×C3⋊Dic3—21no—
281C2×C3⋊Dic3—21no—
282C2×C3⋊Dic3—21no—
283C2×C3⋊Dic3—21no—
284C2×C3⋊Dic3—21no—
285C2×C3⋊Dic3—21no—
286C2×C3⋊Dic3—21no—
287C2×C3⋊Dic3—44no—
288C2×C3⋊Dic3C2×D412yes—
289C2×C3⋊Dic3C2×D412yes—
290C4×C3⋊D3—44no—
291C3×#67—44no—
292C3×#67—44no—
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—21no—
308C2×C3×Dic3—21no—
309C2×C3×Dic3—21no—
310C2×C3×Dic3C2×D412yes—
311#624—44no—
312C2×#123—91no—
313C2×#120—91no—
314C2×C4×D4—91no—
315C22×C22⋊C4—91no—
316#399—91no—
317#397—91no—
318#394—31no—
319#394—31no—
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—31no—
329C24×C3—31no—
330C24×C3C22×D311yescharacteristic
331C24×C3C22×D311yescharacteristic
332C23×D3—31no—
333C23×D3—31no—
334C23×D3—61no—
335C23×D3—62no—
336C23×D3—62no—
337C23×D3—62no—
338C23×D3—62no—
339C23×D3—62no—
340C23×D3—62no—
341C23×D3—62no—
342C23×D3—62no—
343C23×D3—62no—
344C23×D3—62no—
345C23×D3—121no—
346C23×D3—121no—
347C23×D3—121no—
348C23×D3—121no—
349C23×D3C22×D311yescharacteristic
350C23×D3C22×D311yescharacteristic
351C2×C3×D4—62no—
352C2×C3×D4—62no—
353C2×C3×D4—62no—
354C2×C3×D4—62no—
355C2×C3×D4—121no—
356C2×C3×D4—121no—
357C22×C3×C4—21no—
358C22×C3×C4—21no—
359C22×C3×C4—31no—
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4C22×D311yescharacteristic
366C22×C3×C4C22×D311yescharacteristic
367C22×C3×C4C22×D311yescharacteristic
368C22×C3×C4C22×D311yescharacteristic
369C2×#67—22no—
370C2×#67—22no—
371C2×#67—22no—
372C2×#67—22no—
373C2×#67—34no—
374C2×#67—34no—
375C2×#67—41no—
376C2×#67—41no—
377C2×#67—64no—
378C2×#67—62no—
379C2×#67—62no—
380C2×#67—62no—
381C2×#67—62no—
382C2×#67—64no—
383C2×#67—64no—
384C22×Dic3—31no—
385C22×Dic3—31no—
386C22×Dic3—31no—
387C22×Dic3—31no—
388C22×Dic3—31no—
389C22×Dic3—31no—
390C22×Dic3—61no—
391C22×Dic3—61no—
392C22×Dic3—61no—
393C22×Dic3—62no—
394C22×Dic3—62no—
395C22×Dic3—64no—
396C22×Dic3—62no—
397C22×Dic3—62no—
398C22×Dic3—122no—
399C22×Dic3—121no—
400C22×Dic3—121no—
401C22×Dic3—122no—
402C22×Dic3C22×D311yescharacteristic
403C22×Dic3C22×D311yescharacteristic
404C22×Dic3C22×D311yescharacteristic
405C22×Dic3C22×D311yescharacteristic
406C22×Dic3C22×D311yescharacteristic
407C22×Dic3C22×D311yescharacteristic
408C2×C4×D3—62no—
409C2×C4×D3—62no—
410C2×C4×D3—62no—
411C2×C4×D3—62no—
412C2×C4×D3—62no—
413C2×C4×D3—62no—
414C2×C4×D3—62no—
415C2×C4×D3—64no—
416C2×C4×D3—62no—
417C2×C4×D3—122no—
418C2×C4×D3—121no—
419C2×C4×D3—121no—
420C2×C4×D3—121no—
421C2×C4×D3—121no—
422C2×C4×D3—122no—
423C3×C4⋊C4—121no—
424C3×C4⋊C4—121no—
425C3×C22⋊C4—24no—
426C3×C22⋊C4—22no—
427C3×C22⋊C4—22no—
428C3×C22⋊C4—62no—
429C3×C22⋊C4—62no—
430C3×C22⋊C4—62no—
431C3×C22⋊C4—62no—
432C3×C22⋊C4—121no—
433C3×C22⋊C4—121no—
434#217—22no—
435#217—34no—
436#217—41no—
437#217—62no—
438#217—62no—
439#217—62no—
440#217—62no—
441#217—121no—
442(C2×D3)⋊C4—22no—
443(C2×D3)⋊C4—22no—
444(C2×D3)⋊C4—22no—
445(C2×D3)⋊C4—34no—
446(C2×D3)⋊C4—41no—
447(C2×D3)⋊C4—62no—
448(C2×D3)⋊C4—62no—
449(C2×D3)⋊C4—62no—
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—64no—
457(C2×D3)⋊C4—62no—
458(C2×D3)⋊C4—121no—
459C4⋊Dic3—62no—
460C4⋊Dic3—62no—
461Dic3⋊C4—41no—
462Dic3⋊C4—41no—
463Dic3⋊C4—62no—
464Dic3⋊C4—62no—
465Dic3⋊C4—62no—
466Dic3⋊C4—64no—
467Dic3⋊C4—62no—
468C4×Dic3—62no—
469C4×Dic3—62no—
470C4×Dic3—64no—
471C22×C32—22no—
472C22×C32—22no—
473C22×C32—22no—
474C22×C32—41no—
475C22×C32—41no—
476C22×C32—41no—
477C22×C32—41no—
478C22×C32C22×D411yescharacteristic
479C22×C32C22×D411yescharacteristic
480C22×C32C2×#4111yescharacteristic
481C22×C32C2×#4111yescharacteristic
482C22×C32C2×#4111yescharacteristic
483C22×C32H(5,𝔽2)11yescharacteristic
484C22×C32H(5,𝔽2)11yescharacteristic
485C2×C3⋊D3—22no—
486C2×C3⋊D3—22no—
487C2×C3⋊D3—22no—
488C2×C3⋊D3—22no—
489C2×C3⋊D3—22no—
490C2×C3⋊D3—22no—
491C2×C3⋊D3#12314yescomplemented
492C2×C3×D3—22no—
493C2×C3×D3—22no—
494C2×C3×D3—22no—
495C2×C3×D3—22no—
496C2×C3×D3—22no—
497C2×C3×D3—22no—
498C2×C3×D3—41no—
499C2×C3×D3—41no—
500C2×C3×D3—41no—
501C2×C3×D3—41no—
502C2×C3×D3—41no—
503C2×C3×D3—41no—
504C2×C3×D3—41no—
505C2×C3×D3—41no—
506D32—416no—
507C32×C4—41no—
508C32×C4—41no—
509C3⋊Dic3—22no—
510C3⋊Dic3—22no—
511C3⋊Dic3—41no—
512C3×Dic3—22no—
513C3×Dic3—41no—
514C3×Dic3—41no—
515C3×Dic3—41no—
516C3×Dic3—41no—
517C3×Dic3—41no—
518C25—91no—
519C22×D4—31no—
520C22×D4—31no—
521C22×D4—91no—
522C23×C4—91no—
523C23×C4—91no—
524C23×C4—91no—
525#123—184no—
526#120—184no—
527C4×D4—184no—
528C2×C4⋊C4—31no—
529C2×C4⋊C4—31no—
530C2×C4⋊C4—91no—
531C2×C4⋊C4—91no—
532C2×C4⋊C4—91no—
533C2×C22⋊C4—31no—
534C2×C22⋊C4—31no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
537C2×C22⋊C4—31no—
538C2×C22⋊C4—31no—
539C2×C22⋊C4—91no—
540C2×C22⋊C4—91no—
541C2×C22⋊C4—91no—
542C2×C22⋊C4—91no—
543C2×C22⋊C4—91no—
544C2×C22⋊C4—91no—
545C2×C22⋊C4—91no—
546C2×C22⋊C4—91no—
547C2×C22⋊C4—91no—
548C2×C22⋊C4—184no—
549C2×C22⋊C4D3211yescharacteristic, complemented
550C2×C42—91no—
551#95—31no—
552#95—31no—
553#95—91no—
554#95—91no—
555#95—91no—
556#95—91no—
557C23×C3—22no—
558C23×C3—22no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—21no—
562C23×C3—21no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—22no—
573C23×C3—32no—
574C23×C3—32no—
575C23×C3—41no—
576C23×C3—41no—
577C23×C3—41no—
578C23×C3—41no—
579C23×C3—61no—
580C23×C3—61no—
581C23×C3—61no—
582C23×C3—61no—
583C23×C3—61no—
584C23×C3—61no—
585C23×C3—61no—
586C23×C3—61no—
587C23×C3—61no—
588C23×C3—61no—
589C23×C3—61no—
590C23×C3—61no—
591C23×C3D3×D412yes—
592C23×C3D3×D412yes—
593C23×C3C23×D311yescharacteristic
594C23×C3C23×D311yescharacteristic
595C22×D3—21no—
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—21no—
600C22×D3—21no—
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—32no—
608C22×D3—32no—
609C22×D3—32no—
610C22×D3—32no—
611C22×D3—32no—
612C22×D3—32no—
613C22×D3—62no—
614C22×D3—62no—
615C22×D3—62no—
616C22×D3—68no—
617C22×D3—68no—
618C22×D3—61no—
619C22×D3—61no—
620C22×D3—61no—
621C22×D3—61no—
622C22×D3—61no—
623C22×D3—61no—
624C22×D3—61no—
625C22×D3—61no—
626C22×D3—121no—
627C22×D3—121no—
628C22×D3—121no—
629C22×D3—121no—
630C22×D3—124no—
631C22×D3—124no—
632C22×D3—124no—
633C22×D3—124no—
634C22×D3—124no—
635C22×D3—124no—
636C22×D3—124no—
637C22×D3—124no—
638C22×D3—124no—
639C22×D3—124no—
640C22×D3—124no—
641C22×D3—124no—
642C22×D3D3×D412yes—
643C22×D3#23712yes—
644C3×D4—124no—
645C3×D4—124no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—32no—
661C2×C3×C4—41no—
662C2×C3×C4—41no—
663C2×C3×C4—41no—
664C2×C3×C4—41no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4—61no—
674C2×C3×C4—61no—
675C2×C3×C4—61no—
676C2×C3×C4—61no—
677C2×C3×C4—61no—
678C2×C3×C4—61no—
679C2×C3×C4—61no—
680C2×C3×C4—61no—
681C2×C3×C4—61no—
682#67—44no—
683#67—44no—
684#67—68no—
685#67—68no—
686#67—616no—
687C2×Dic3—21no—
688C2×Dic3—21no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—21no—
695C2×Dic3—21no—
696C2×Dic3—21no—
697C2×Dic3—21no—
698C2×Dic3—21no—
699C2×Dic3—21no—
700C2×Dic3—21no—
701C2×Dic3—21no—
702C2×Dic3—21no—
703C2×Dic3—21no—
704C2×Dic3—32no—
705C2×Dic3—32no—
706C2×Dic3—32no—
707C2×Dic3—32no—
708C2×Dic3—62no—
709C2×Dic3—62no—
710C2×Dic3—62no—
711C2×Dic3—62no—
712C2×Dic3—62no—
713C2×Dic3—62no—
714C2×Dic3—61no—
715C2×Dic3—61no—
716C2×Dic3—61no—
717C2×Dic3—61no—
718C2×Dic3—61no—
719C2×Dic3—61no—
720C2×Dic3—61no—
721C2×Dic3—61no—
722C2×Dic3—62no—
723C2×Dic3—61no—
724C2×Dic3—61no—
725C2×Dic3—61no—
726C2×Dic3—61no—
727C2×Dic3—61no—
728C2×Dic3—61no—
729C2×Dic3—121no—
730C2×Dic3—121no—
731C2×Dic3—124no—
732C2×Dic3—124no—
733C2×Dic3—128no—
734C2×Dic3D3×D412yes—
735C4×D3—124no—
736C4×D3—124no—
737C4×D3—124no—
738C4×D3—124no—
739C4×D3—128no—
740C2×C32—42no—
741C2×C32C2×#12311yescharacteristic
742C2×C32#52511yescharacteristic
743C2×C32#53811yescharacteristic
744C2×C32D4211yescharacteristic
745C2×C32#54611yescharacteristic
746C2×C32#54611yescharacteristic
747C2×C32#55111yescharacteristic
748C3⋊D3—24no—
749C3×D3—42no—
750C3×D3—42no—
751C24—31no—
752C24—31no—
753C24—91no—
754C24—182no—
755C24—182no—
756C24—182no—
757C24—182no—
758C24—182no—
759C24—361no—
760C24—361no—
761C24C2×D3211yescharacteristic
762C2×D4—62no—
763C2×D4—62no—
764C2×D4—62no—
765C2×D4—62no—
766C2×D4—94no—
767C2×D4—121no—
768C2×D4—121no—
769C2×D4—182no—
770C2×D4—182no—
771C22×C4—31no—
772C22×C4—31no—
773C22×C4—31no—
774C22×C4—31no—
775C22×C4—31no—
776C22×C4—31no—
777C22×C4—91no—
778C22×C4—91no—
779C22×C4—91no—
780C22×C4—182no—
781C22×C4—182no—
782C22×C4—182no—
783C22×C4—182no—
784C22×C4—182no—
785C22×C4—182no—
786C22×C4—361no—
787C22×C4—361no—
788C22×C4—361no—
789C22×C4C2×D3211yescharacteristic
790C22×C4C2×D3211yescharacteristic
791C4⋊C4—121no—
792C4⋊C4—121no—
793C4⋊C4—182no—
794C4⋊C4—182no—
795C4⋊C4—182no—
796C22⋊C4—22no—
797C22⋊C4—62no—
798C22⋊C4—62no—
799C22⋊C4—62no—
800C22⋊C4—62no—
801C22⋊C4—94no—
802C22⋊C4—121no—
803C22⋊C4—121no—
804C22⋊C4—182no—
805C22⋊C4—182no—
806C22⋊C4—182no—
807C22⋊C4—182no—
808C22⋊C4—182no—
809C22⋊C4—182no—
810C22⋊C4—182no—
811C22⋊C4—361no—
812C42—182no—
813C22×C3—24no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—22no—
817C22×C3—22no—
818C22×C3—22no—
819C22×C3—22no—
820C22×C3—21no—
821C22×C3—21no—
822C22×C3—21no—
823C22×C3—21no—
824C22×C3—21no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—42no—
828C22×C3—42no—
829C22×C3—42no—
830C22×C3—42no—
831C22×C3—42no—
832C22×C3—42no—
833C22×C3—41no—
834C22×C3—41no—
835C22×C3—41no—
836C22×C3—41no—
837C22×C3—41no—
838C22×C3—41no—
839C22×C3—41no—
840C22×C3—41no—
841C22×C3—62no—
842C22×C3—62no—
843C22×C3—62no—
844C22×C3—62no—
845C22×C3—62no—
846C22×C3—62no—
847C22×C3—121no—
848C22×C3—121no—
849C22×C3—121no—
850C22×C3—121no—
851C22×C3—121no—
852C22×C3—121no—
853C22×C3—121no—
854C22×C3—121no—
855C22×C3C2×D3×D411yescharacteristic
856C22×C3C2×D3×D411yescharacteristic
857C22×C3C2×D3×D411yescharacteristic
858C22×C3C2×D3×D411yescharacteristic
859C22×C3C2×#23711yescharacteristic
860C22×C3#100411yescharacteristic
861C22×C3#100411yescharacteristic
862C22×C3#100411yescharacteristic
863C22×C3D3×#4111yescharacteristic
864C22×C3D3×#4111yescharacteristic
865C22×C3D3×#4111yescharacteristic
866C22×C3D3×#4111yescharacteristic
867C22×C3D3×#4111yescharacteristic
868C22×C3#100911yescharacteristic
869C2×D3—22no—
870C2×D3—22no—
871C2×D3—22no—
872C2×D3—22no—
873C2×D3—22no—
874C2×D3—22no—
875C2×D3—34no—
876C2×D3—34no—
877C2×D3—41no—
878C2×D3—41no—
879C2×D3—41no—
880C2×D3—41no—
881C2×D3—41no—
882C2×D3—41no—
883C2×D3—41no—
884C2×D3—41no—
885C2×D3—64no—
886C2×D3—62no—
887C2×D3—62no—
888C2×D3—62no—
889C2×D3—62no—
890C2×D3—62no—
891C2×D3—62no—
892C2×D3—62no—
893C2×D3—62no—
894C2×D3—62no—
895C2×D3—62no—
896C2×D3—62no—
897C2×D3—62no—
898C2×D3—122no—
899C2×D3—122no—
900C2×D3—122no—
901C2×D3—122no—
902C2×D3—122no—
903C2×D3—122no—
904C2×D3—1216no—
905C2×D3—1216no—
906C3×C4—42no—
907C3×C4—42no—
908C3×C4—41no—
909C3×C4—41no—
910C3×C4—41no—
911C3×C4—41no—
912C3×C4—62no—
913C3×C4—121no—
914C3×C4—121no—
915C3×C4—121no—
916C3×C4—121no—
917C3×C4—121no—
918Dic3—22no—
919Dic3—41no—
920Dic3—41no—
921Dic3—41no—
922Dic3—41no—
923Dic3—41no—
924Dic3—64no—
925Dic3—64no—
926Dic3—62no—
927Dic3—62no—
928Dic3—62no—
929Dic3—62no—
930Dic3—122no—
931Dic3—121no—
932Dic3—121no—
933C32#241811yescharacteristic, complemented, Sylow
934C23—21no—
935C23—21no—
936C23—21no—
937C23—21no—
938C23—21no—
939C23—21no—
940C23—32no—
941C23—32no—
942C23—61no—
943C23—61no—
944C23—61no—
945C23—61no—
946C23—61no—
947C23—61no—
948C23—61no—
949C23—61no—
950C23—61no—
951C23—61no—
952C23—61no—
953C23—61no—
954C23—92no—
955C23—92no—
956C23—92no—
957C23—188no—
958C23—181no—
959C23—181no—
960C23—181no—
961C23—181no—
962C23—364no—
963C23—364no—
964C23—364no—
965C23—364no—
966C23—364no—
967C23—364no—
968C23#381112yes—
969C23C22×D3211yescharacteristic
970D4—124no—
971D4—124no—
972D4—188no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—32no—
980C2×C4—61no—
981C2×C4—61no—
982C2×C4—61no—
983C2×C4—61no—
984C2×C4—61no—
985C2×C4—61no—
986C2×C4—61no—
987C2×C4—61no—
988C2×C4—61no—
989C2×C4—61no—
990C2×C4—61no—
991C2×C4—61no—
992C2×C4—61no—
993C2×C4—61no—
994C2×C4—61no—
995C2×C4—61no—
996C2×C4—61no—
997C2×C4—92no—
998C2×C4—92no—
999C2×C4—181no—
1000C2×C4—181no—
1001C2×C4—181no—
1002C2×C4—181no—
1003C2×C4—181no—
1004C2×C4—181no—
1005C2×C4—181no—
1006C2×C4—364no—
1007C2×C4—364no—
1008C2×C4—364no—
1009C2×C3—21no—
1010C2×C3—21no—
1011C2×C3—21no—
1012C2×C3—21no—
1013C2×C3—21no—
1014C2×C3—21no—
1015C2×C3—21no—
1016C2×C3—44no—
1017C2×C3—42no—
1018C2×C3—42no—
1019C2×C3—122no—
1020C2×C3—122no—
1021C2×C3#559011yescharacteristic
1022C2×C3#559111yescharacteristic
1023C2×C3#560611yescharacteristic
1024C2×C3#560911yescharacteristic
1025C2×C3#561011yescharacteristic
1026C2×C3#561011yescharacteristic
1027C2×C3#561011yescharacteristic
1028C2×C3#561311yescharacteristic
1029C2×C3D3×#12311yescharacteristic
1030C2×C3D3×#12311yescharacteristic
1031C2×C3#565611yescharacteristic
1032C2×C3#565811yescharacteristic
1033C2×C3#567811yescharacteristic
1034C2×C3#567911yescharacteristic
1035D3—42no—
1036D3—42no—
1037D3—64no—
1038D3—64no—
1039D3—124no—
1040C22—22no—
1041C22—22no—
1042C22—22no—
1043C22—41no—
1044C22—41no—
1045C22—41no—
1046C22—41no—
1047C22—62no—
1048C22—62no—
1049C22—62no—
1050C22—62no—
1051C22—62no—
1052C22—62no—
1053C22—94no—
1054C22—121no—
1055C22—121no—
1056C22—121no—
1057C22—121no—
1058C22—121no—
1059C22—121no—
1060C22—121no—
1061C22—121no—
1062C22—182no—
1063C22—182no—
1064C22—182no—
1065C22—182no—
1066C22—182no—
1067C22—182no—
1068C22—3616no—
1069C22#6430611yescharacteristic
1070C22#6430611yescharacteristic
1071C22D32×D411yescharacteristic
1072C22D3×#23711yescharacteristic
1073C22#6431311yescharacteristic
1074C22#6431411yescharacteristic
1075C22C2×#381111yescharacteristic
1076C4—41no—
1077C4—41no—
1078C4—62no—
1079C4—121no—
1080C4—121no—
1081C4—121no—
1082C4—121no—
1083C4—121no—
1084C4—182no—
1085C4—182no—
1086C4—361no—
1087C3—21no—
1088C3#7711111yescharacteristic, complemented
1089C3#7711211yescharacteristic, complemented
1090C2—42no—
1091C2—122no—
1092C2—122no—
1093C2—184no—
1094C2#1059426711yescharacteristic
1095C2#1059427611yescharacteristic
1096C2#1059430511yescharacteristic
1097C2#1059430611yescharacteristic
1098C2#1059507911yescharacteristic
1099C2#1059529211yescharacteristic
1100C2#1059530711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC2×#63983C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2418
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64090C2semidirect
3. C2×#63962C2semidirect
4. C2×#63921C2semidirect
5. C3×#4959C2semidirect
6. C3×#4959C2semidirect
7. #10591722C2semidirect
8. #10591713C2semidirect
9. #10591399C2semidirect
10. #10591367C2semidirect
11. #10591303C2semidirect
12. #10591298C2semidirect
13. #10591290C2semidirect
14. #10591286C2semidirect
15. #10591283C2semidirect
20. C23×C3⋊Dic3C22semidirect
25. C2×C32×C22⋊C4C22semidirect
27. C2×#3750C22semidirect
28. C2×C4×C3⋊Dic3C22semidirect
30. C2×C3×#217C22semidirect
31. C2×C3×#217C22semidirect
36. C2×C3×Dic3⋊C4C22semidirect
37. C2×C3×Dic3⋊C4C22semidirect
39. C2×Dic3⋊Dic3C22semidirect
40. C2×Dic3⋊Dic3C22semidirect
51. C3×C3⋊#95C22semidirect
52. C3×C3⋊#95C22semidirect
53. #63579C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
73. #4959D3semidirect
74. #4959D3semidirect
149. (C2×D3)⋊Dic3D4semidirect
177. C2×C3×C22⋊C4C2×D3semidirect
178. C2×C3×C22⋊C4C2×D3semidirect
185. C2×#217C2×D3semidirect
186. C2×#217C2×D3semidirect
214. C2×Dic3⋊C4C2×D3semidirect
215. C2×Dic3⋊C4C2×D3semidirect
235. C3⋊#95C2×D3semidirect
236. C3⋊#95C2×D3semidirect
491. C2×C3⋊D3#123semidirect
549. C2×C22⋊C4D32semidirect
933. C32#2418semidirect
1088. C3#77111semidirect
1089. C3#77112semidirect

Maximal subgroups

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

subgroupindex
C2×#640902
C2×#639832
C2×#639622
C2×#639212
C3×#49592
#105917222
#105917132
#105913992
#105913672
#105913032
#105912982
#105912902
#105912862
#105912832
#771123
#771113