Finite Group Databasebeta

← #11810326

Subgroups — #11810326

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×#64102C211yesmaximal, characteristic, complemented
2C2×#63923C211yesmaximal, characteristic
3C2×#63921C211yesmaximal, characteristic, complemented
4C2×#63853C211yesmaximal, characteristic, complemented
5C3×#4993C211yesmaximal, characteristic, complemented
6C3×#4992C211yesmaximal, characteristic, complemented
7#10591399C211yesmaximal, characteristic, complemented
8#10591387C211yesmaximal, characteristic, complemented
9#10591380C211yesmaximal, characteristic, complemented
10#10591367C211yesmaximal, characteristic, complemented
11#10591312C211yesmaximal, characteristic, complemented
12#10591291C211yesmaximal, characteristic, complemented
13#10591290C211yesmaximal, characteristic, complemented
14#10591287C211yesmaximal, characteristic, complemented
15#10591287C211yesmaximal, characteristic, complemented
16#78101—31nomaximal
17#77669—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic, complemented
22C22×#626C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic, complemented
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic, complemented
28C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
29#64102—24no—
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
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
38C2×Dic3⋊Dic3C2211yescharacteristic, complemented
39C2×Dic3⋊Dic3C2211yescharacteristic, complemented
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic, complemented
43C2×#3722C2211yescharacteristic, complemented
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48#63923—24no—
49#63921—24no—
50#63853—24no—
51C3×C3⋊#95C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×#894—31no—
58C2×#893—31no—
59C2×#893—31no—
60C2×#893—61no—
61C2×#883—31no—
62C2×#882—31no—
63C2×#882—31no—
64C2×D3×C22⋊C4—31no—
65C2×D3×C22⋊C4—31no—
66C3×#399—31no—
67C3×#397—31no—
68#4993D311yescharacteristic, complemented
69#4992D311yescharacteristic, complemented
70#4991—31no—
71#4989—31no—
72#4987—31no—
73#4961—31no—
74#4959—31no—
75#4956—31no—
76#4955—31no—
77#4955—31no—
78#4944—31no—
79#4944—31no—
80#4672—31no—
81#4670—31no—
82#4670—31no—
83#4668—31no—
84#4667—31no—
85#4665—31no—
86#4665—31no—
87#4665—31no—
88C23×C3⋊D3C2311yescharacteristic
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
101C22×C32×C4C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C2×C4⋊(C3⋊D3)—22no—
105C2×C4⋊(C3⋊D3)—22no—
106C2×C4⋊(C3⋊D3)D414yes—
107C2×C4×C3⋊D3—22no—
108C2×C4×C3⋊D3—22no—
109C2×C4×C3⋊D3—22no—
110C2×C4×C3⋊D3—22no—
111C2×C4×C3⋊D3—41no—
112C2×C4×C3⋊D3—41no—
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C2×#626—22no—
120C2×#626—22no—
121C2×#626—22no—
122C2×#626—22no—
123C2×#626—41no—
124C2×#626—41no—
125C2×#624—22no—
126C2×#624—22no—
127C2×#624—41no—
128C32×C4⋊C4—22no—
129#3752—22no—
130#3752—22no—
131C4×C3⋊Dic3—22no—
132C3×(C2×D3)⋊C4—22no—
133C3×(C2×D3)⋊C4—22no—
134C3×(C2×D3)⋊C4—22no—
135C3×(C2×D3)⋊C4—22no—
136C3×(C2×D3)⋊C4—22no—
137C3×(C2×D3)⋊C4—41no—
138C3×Dic3⋊C4—22no—
139C3×Dic3⋊C4—41no—
140Dic3⋊Dic3—22no—
141Dic3⋊Dic3—41no—
142#3722—22no—
143#3722—22no—
144#3722—22no—
145#3722—41no—
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×#67—31no—
154C22×#67—31no—
155C22×D12—31no—
156C22×D12—31no—
157C22×D12—31no—
158C22×D12—31no—
159C22×D12—61no—
160C22×C4×D3—31no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3—31no—
165C22×C4×D3—31no—
166C22×C4×D3—61no—
167C22×C4×D3—61no—
168C2×C3×C4⋊C4—21no—
169C2×C3×C4⋊C4—31no—
170C2×C3×C4⋊C4—31no—
171C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
172C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
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×#217—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—31no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—31no—
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—61no—
200C2×(C2×D3)⋊C4—61no—
201C2×(C2×D3)⋊C4C2×D311yescharacteristic
202C2×(C2×D3)⋊C4C2×D311yescharacteristic
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⋊C4C2×D311yescharacteristic, complemented
212C2×Dic3⋊C4C2×D311yescharacteristic, complemented
213C2×C4×Dic3—31no—
214C2×C4×Dic3—31no—
215C2×C4×Dic3—61no—
216#894—64no—
217#893—64no—
218#893—64no—
219#893—68no—
220#883—64no—
221#882—64no—
222#882—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⋊#95C2×D311yescharacteristic, complemented
234C3⋊#95C2×D311yescharacteristic, complemented
235C3⋊#95C2×D311yescharacteristic, complemented
236C3⋊#95C2×D311yescharacteristic, complemented
237C23×C32C2411yescharacteristic
238C22×C3⋊D3—21no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3—21no—
243C22×C3⋊D3—21no—
244C22×C3⋊D3—21no—
245C22×C3⋊D3—21no—
246C22×C3⋊D3—21no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3C2×D412yes—
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—
279C2×C32×C4—21no—
280C2×C32×C4—21no—
281C2×C32×C4C2×D412yes—
282C2×C3⋊Dic3—21no—
283C2×C3⋊Dic3—21no—
284C2×C3⋊Dic3—21no—
285C2×C3⋊Dic3—21no—
286C2×C3⋊Dic3—21no—
287C2×C3⋊Dic3C2×D412yes—
288C4⋊(C3⋊D3)—28no—
289C4×C3⋊D3—44no—
290C4×C3⋊D3—44no—
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—21no—
308C2×C3×Dic3C2×D412yes—
309#626—44no—
310#626—44no—
311#624—44no—
312C2×#123—91no—
313C2×#120—91no—
314C2×C4×D4—91no—
315C22×C22⋊C4—91no—
316#399—31no—
317#397—31no—
318#394—91no—
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—31no—
328C24×C3—31no—
329C23×D3—31no—
330C23×D3—31no—
331C23×D3—31no—
332C23×D3—31no—
333C23×D3—61no—
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
351C22×C3×C4—21no—
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4—31no—
360C22×C3×C4C22×D311yescharacteristic
361C22×C3×C4C22×D311yescharacteristic
362C22×C3×C4C22×D311yescharacteristic
363C22×C3×C4C22×D311yescharacteristic
364C22×C3×C4C22×D311yescharacteristic
365C22×C3×C4C22×D311yescharacteristic
366C2×#67—62no—
367C2×#67—62no—
368C2×#67—62no—
369C2×#67—62no—
370C2×#67—121no—
371C2×#67—121no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—31no—
375C22×Dic3—31no—
376C22×Dic3—61no—
377C22×Dic3—61no—
378C22×Dic3C22×D311yescharacteristic
379C22×Dic3C22×D311yescharacteristic
380C22×Dic3C22×D311yescharacteristic
381C22×Dic3C22×D311yescharacteristic
382C22×Dic3C22×D311yescharacteristic
383C22×Dic3C22×D311yescharacteristic
384C2×D12—34no—
385C2×D12—34no—
386C2×D12—64no—
387C2×D12—62no—
388C2×D12—62no—
389C2×D12—62no—
390C2×D12—62no—
391C2×D12—64no—
392C2×D12—64no—
393C2×D12—62no—
394C2×D12—62no—
395C2×D12—62no—
396C2×D12—62no—
397C2×D12—121no—
398C2×D12—121no—
399C2×C4×D3—62no—
400C2×C4×D3—62no—
401C2×C4×D3—62no—
402C2×C4×D3—62no—
403C2×C4×D3—62no—
404C2×C4×D3—62no—
405C2×C4×D3—62no—
406C2×C4×D3—62no—
407C2×C4×D3—62no—
408C2×C4×D3—62no—
409C2×C4×D3—62no—
410C2×C4×D3—64no—
411C2×C4×D3—64no—
412C2×C4×D3—62no—
413C2×C4×D3—122no—
414C2×C4×D3—122no—
415C2×C4×D3—121no—
416C2×C4×D3—121no—
417C2×C4×D3—121no—
418C2×C4×D3—121no—
419C2×C4×D3—121no—
420C2×C4×D3—121no—
421C2×C4×D3—122no—
422C2×C4×D3—122no—
423C3×C4⋊C4—24no—
424C3×C4⋊C4—22no—
425C3×C4⋊C4—22no—
426C3×C4⋊C4—62no—
427C3×C4⋊C4—121no—
428C3×C22⋊C4—62no—
429C3×C22⋊C4—62no—
430C3×C22⋊C4—62no—
431C3×C22⋊C4—62no—
432C3×C22⋊C4—62no—
433C3×C22⋊C4—121no—
434#217—34no—
435#217—62no—
436#217—62no—
437#217—121no—
438(C2×D3)⋊C4—22no—
439(C2×D3)⋊C4—22no—
440(C2×D3)⋊C4—22no—
441(C2×D3)⋊C4—22no—
442(C2×D3)⋊C4—22no—
443(C2×D3)⋊C4—34no—
444(C2×D3)⋊C4—41no—
445(C2×D3)⋊C4—62no—
446(C2×D3)⋊C4—62no—
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—64no—
456(C2×D3)⋊C4—64no—
457(C2×D3)⋊C4—62no—
458(C2×D3)⋊C4—62no—
459(C2×D3)⋊C4—121no—
460(C2×D3)⋊C4—121no—
461(C2×D3)⋊C4—121no—
462C4⋊Dic3—62no—
463C4⋊Dic3—121no—
464Dic3⋊C4—22no—
465Dic3⋊C4—41no—
466Dic3⋊C4—62no—
467Dic3⋊C4—121no—
468C4×Dic3—64no—
469C4×Dic3—62no—
470C4×Dic3—62no—
471C22×C32C22×D411yescharacteristic
472C22×C32C22×D411yescharacteristic
473C22×C32C2×#4111yescharacteristic
474C22×C32C2×#4111yescharacteristic
475C22×C32C2×#4111yescharacteristic
476C22×C32H(5,𝔽2)11yescharacteristic
477C22×C32H(5,𝔽2)11yescharacteristic
478C2×C3⋊D3—22no—
479C2×C3⋊D3—22no—
480C2×C3⋊D3—22no—
481C2×C3⋊D3—22no—
482C2×C3⋊D3—22no—
483C2×C3⋊D3—22no—
484C2×C3⋊D3—22no—
485C2×C3⋊D3—22no—
486C2×C3⋊D3—22no—
487C2×C3⋊D3—41no—
488C2×C3⋊D3—41no—
489C2×C3⋊D3—41no—
490C2×C3⋊D3—41no—
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—22no—
508C32×C4—41no—
509C32×C4—41no—
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—91no—
520C22×D4—91no—
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⋊C4D3211yescharacteristic, complemented
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—91no—
549C2×C22⋊C4—184no—
550C2×C42—91no—
551#95—31no—
552#95—31no—
553#95—31no—
554#95—31no—
555#95—91no—
556#95—91no—
557C23×C3—21no—
558C23×C3—32no—
559C23×C3—32no—
560C23×C3—61no—
561C23×C3—61no—
562C23×C3—61no—
563C23×C3—61no—
564C23×C3—61no—
565C23×C3—61no—
566C23×C3—61no—
567C23×C3—61no—
568C23×C3—61no—
569C23×C3—61no—
570C23×C3—61no—
571C23×C3—61no—
572C23×C3C23×D311yescharacteristic
573C23×C3C23×D311yescharacteristic
574C22×D3—21no—
575C22×D3—21no—
576C22×D3—21no—
577C22×D3—21no—
578C22×D3—21no—
579C22×D3—21no—
580C22×D3—21no—
581C22×D3—21no—
582C22×D3—21no—
583C22×D3—21no—
584C22×D3—21no—
585C22×D3—21no—
586C22×D3—32no—
587C22×D3—32no—
588C22×D3—32no—
589C22×D3—32no—
590C22×D3—32no—
591C22×D3—32no—
592C22×D3—32no—
593C22×D3—32no—
594C22×D3—62no—
595C22×D3—62no—
596C22×D3—62no—
597C22×D3—62no—
598C22×D3—68no—
599C22×D3—68no—
600C22×D3—61no—
601C22×D3—61no—
602C22×D3—61no—
603C22×D3—61no—
604C22×D3—61no—
605C22×D3—61no—
606C22×D3—61no—
607C22×D3—61no—
608C22×D3—62no—
609C22×D3—62no—
610C22×D3—61no—
611C22×D3—61no—
612C22×D3—61no—
613C22×D3—61no—
614C22×D3—61no—
615C22×D3—61no—
616C22×D3—61no—
617C22×D3—61no—
618C22×D3—61no—
619C22×D3—61no—
620C22×D3—61no—
621C22×D3—61no—
622C22×D3—121no—
623C22×D3—121no—
624C22×D3—121no—
625C22×D3—121no—
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#23912yes—
644C2×C3×C4—22no—
645C2×C3×C4—22no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
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—21no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—22no—
665C2×C3×C4—32no—
666C2×C3×C4—41no—
667C2×C3×C4—41no—
668C2×C3×C4—41no—
669C2×C3×C4—41no—
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—
682C2×C3×C4—61no—
683C2×C3×C4—61no—
684C2×C3×C4—61no—
685C2×C3×C4—61no—
686C2×C3×C4—61no—
687C2×C3×C4D3×D412yes—
688C2×C3×C4D3×D412yes—
689#67—124no—
690#67—124no—
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—21no—
705C2×Dic3—21no—
706C2×Dic3—21no—
707C2×Dic3—21no—
708C2×Dic3—32no—
709C2×Dic3—32no—
710C2×Dic3—62no—
711C2×Dic3—62no—
712C2×Dic3—62no—
713C2×Dic3—61no—
714C2×Dic3—61no—
715C2×Dic3—61no—
716C2×Dic3—61no—
717C2×Dic3—62no—
718C2×Dic3—61no—
719C2×Dic3—61no—
720C2×Dic3—61no—
721C2×Dic3—61no—
722C2×Dic3—61no—
723C2×Dic3—61no—
724C2×Dic3—121no—
725C2×Dic3—121no—
726C2×Dic3D3×D412yes—
727D12—68no—
728D12—68no—
729D12—616no—
730D12—124no—
731D12—124no—
732C4×D3—124no—
733C4×D3—124no—
734C4×D3—124no—
735C4×D3—124no—
736C4×D3—124no—
737C4×D3—124no—
738C4×D3—128no—
739C4×D3—128no—
740C2×C32C2×#12311yescharacteristic
741C2×C32#52511yescharacteristic
742C2×C32#53811yescharacteristic
743C2×C32D4211yescharacteristic
744C2×C32#54611yescharacteristic
745C2×C32#54611yescharacteristic
746C2×C32#55111yescharacteristic
747C3⋊D3—24no—
748C3⋊D3—42no—
749C3×D3—42no—
750C3×D3—42no—
751C24—31no—
752C24—31no—
753C24—91no—
754C24—91no—
755C24—182no—
756C24—182no—
757C24—182no—
758C24—182no—
759C24—182no—
760C24—361no—
761C24—361no—
762C2×D4—94no—
763C2×D4—182no—
764C2×D4—182no—
765C2×D4—182no—
766C2×D4—182no—
767C2×D4—182no—
768C2×D4—182no—
769C2×D4—361no—
770C2×D4—361no—
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—182no—
780C22×C4—182no—
781C22×C4—182no—
782C22×C4—182no—
783C22×C4—182no—
784C22×C4—182no—
785C22×C4—361no—
786C22×C4—361no—
787C22×C4—361no—
788C22×C4C2×D3211yescharacteristic
789C22×C4C2×D3211yescharacteristic
790C22×C4C2×D3211yescharacteristic
791C4⋊C4—22no—
792C4⋊C4—62no—
793C4⋊C4—121no—
794C4⋊C4—182no—
795C4⋊C4—361no—
796C22⋊C4—62no—
797C22⋊C4—62no—
798C22⋊C4—62no—
799C22⋊C4—62no—
800C22⋊C4—62no—
801C22⋊C4—94no—
802C22⋊C4—121no—
803C22⋊C4—182no—
804C22⋊C4—182no—
805C22⋊C4—182no—
806C22⋊C4—182no—
807C22⋊C4—182no—
808C22⋊C4—182no—
809C22⋊C4—182no—
810C22⋊C4—361no—
811C22⋊C4—361no—
812C42—182no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—21no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—62no—
821C22×C3—62no—
822C22×C3—62no—
823C22×C3—62no—
824C22×C3—62no—
825C22×C3—62no—
826C22×C3—121no—
827C22×C3—121no—
828C22×C3—121no—
829C22×C3—121no—
830C22×C3—121no—
831C22×C3—121no—
832C22×C3—121no—
833C22×C3—121no—
834C22×C3C2×D3×D411yescharacteristic
835C22×C3C2×D3×D411yescharacteristic
836C22×C3C2×D3×D411yescharacteristic
837C22×C3C2×D3×D411yescharacteristic
838C22×C3#100411yescharacteristic
839C22×C3C2×#23911yescharacteristic
840C22×C3D3×#4111yescharacteristic
841C22×C3D3×#4111yescharacteristic
842C22×C3D3×#4111yescharacteristic
843C22×C3D3×#4111yescharacteristic
844C22×C3D3×#4111yescharacteristic
845C22×C3#100911yescharacteristic
846C22×C3#100911yescharacteristic
847C22×C3#100911yescharacteristic
848C2×D3—22no—
849C2×D3—22no—
850C2×D3—22no—
851C2×D3—22no—
852C2×D3—22no—
853C2×D3—22no—
854C2×D3—34no—
855C2×D3—34no—
856C2×D3—41no—
857C2×D3—41no—
858C2×D3—41no—
859C2×D3—41no—
860C2×D3—41no—
861C2×D3—41no—
862C2×D3—41no—
863C2×D3—41no—
864C2×D3—64no—
865C2×D3—62no—
866C2×D3—62no—
867C2×D3—62no—
868C2×D3—62no—
869C2×D3—62no—
870C2×D3—62no—
871C2×D3—62no—
872C2×D3—62no—
873C2×D3—62no—
874C2×D3—62no—
875C2×D3—62no—
876C2×D3—62no—
877C2×D3—64no—
878C2×D3—62no—
879C2×D3—62no—
880C2×D3—62no—
881C2×D3—62no—
882C2×D3—62no—
883C2×D3—62no—
884C2×D3—122no—
885C2×D3—122no—
886C2×D3—122no—
887C2×D3—122no—
888C2×D3—122no—
889C2×D3—122no—
890C2×D3—122no—
891C2×D3—122no—
892C2×D3—1216no—
893C2×D3—1216no—
894C2×D3—122no—
895C2×D3—122no—
896C2×D3—122no—
897C2×D3—122no—
898C2×D3—121no—
899C2×D3—121no—
900C2×D3—121no—
901C2×D3—121no—
902C2×D3—121no—
903C2×D3—121no—
904C2×D3—121no—
905C2×D3—121no—
906C3×C4—24no—
907C3×C4—22no—
908C3×C4—22no—
909C3×C4—42no—
910C3×C4—42no—
911C3×C4—41no—
912C3×C4—41no—
913C3×C4—41no—
914C3×C4—41no—
915C3×C4—62no—
916C3×C4—121no—
917C3×C4—121no—
918C3×C4—121no—
919C3×C4—121no—
920C3×C4—121no—
921Dic3—22no—
922Dic3—41no—
923Dic3—41no—
924Dic3—41no—
925Dic3—41no—
926Dic3—41no—
927Dic3—64no—
928Dic3—62no—
929Dic3—62no—
930Dic3—122no—
931Dic3—121no—
932Dic3—121no—
933C32#241811yescharacteristic, complemented, Sylow
934C23—32no—
935C23—32no—
936C23—61no—
937C23—61no—
938C23—61no—
939C23—61no—
940C23—61no—
941C23—61no—
942C23—61no—
943C23—61no—
944C23—61no—
945C23—61no—
946C23—61no—
947C23—61no—
948C23—92no—
949C23—92no—
950C23—92no—
951C23—92no—
952C23—188no—
953C23—181no—
954C23—181no—
955C23—181no—
956C23—181no—
957C23—181no—
958C23—181no—
959C23—181no—
960C23—181no—
961C23—181no—
962C23—181no—
963C23—364no—
964C23—364no—
965C23—364no—
966C23—364no—
967C23—364no—
968C23—364no—
969C23C22×D3211yescharacteristic
970D4—188no—
971D4—364no—
972D4—364no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—32no—
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—61no—
998C2×C4—61no—
999C2×C4—92no—
1000C2×C4—181no—
1001C2×C4—181no—
1002C2×C4—181no—
1003C2×C4—181no—
1004C2×C4—181no—
1005C2×C4—364no—
1006C2×C4—364no—
1007C2×C4—364no—
1008C2×C4#381112yes—
1009C2×C3—21no—
1010C2×C3—21no—
1011C2×C3—21no—
1012C2×C3—21no—
1013C2×C3—21no—
1014C2×C3—21no—
1015C2×C3—21no—
1016C2×C3—122no—
1017C2×C3—122no—
1018C2×C3#560911yescharacteristic
1019C2×C3#562711yescharacteristic
1020C2×C3#563011yescharacteristic
1021C2×C3#563711yescharacteristic
1022C2×C3D3×#12311yescharacteristic
1023C2×C3D3×#12311yescharacteristic
1024C2×C3#565411yescharacteristic
1025C2×C3#565411yescharacteristic
1026C2×C3#565611yescharacteristic
1027C2×C3#565711yescharacteristic
1028C2×C3#567611yescharacteristic
1029C2×C3#570411yescharacteristic
1030C2×C3#570511yescharacteristic
1031C2×C3#571711yescharacteristic
1032D3—42no—
1033D3—42no—
1034D3—64no—
1035D3—64no—
1036D3—124no—
1037D3—124no—
1038D3—122no—
1039D3—122no—
1040C22—62no—
1041C22—62no—
1042C22—62no—
1043C22—62no—
1044C22—62no—
1045C22—62no—
1046C22—94no—
1047C22—121no—
1048C22—121no—
1049C22—121no—
1050C22—121no—
1051C22—121no—
1052C22—121no—
1053C22—121no—
1054C22—121no—
1055C22—182no—
1056C22—182no—
1057C22—182no—
1058C22—182no—
1059C22—182no—
1060C22—182no—
1061C22—182no—
1062C22—182no—
1063C22—182no—
1064C22—3616no—
1065C22—361no—
1066C22—361no—
1067C22—361no—
1068C22—361no—
1069C22#6430611yescharacteristic
1070C22#6430611yescharacteristic
1071C22D32×D411yescharacteristic
1072C22#6431411yescharacteristic
1073C22D3×#23911yescharacteristic
1074C22#6432011yescharacteristic
1075C22C2×#381111yescharacteristic
1076C4—22no—
1077C4—41no—
1078C4—41no—
1079C4—62no—
1080C4—121no—
1081C4—121no—
1082C4—121no—
1083C4—121no—
1084C4—121no—
1085C4—182no—
1086C4—361no—
1087C3—21no—
1088C3#7766911yescharacteristic, complemented
1089C3#7810111yescharacteristic, complemented
1090C2—122no—
1091C2—122no—
1092C2—184no—
1093C2—362no—
1094C2#1059461511yescharacteristic
1095C2#1059461611yescharacteristic
1096C2#1059465511yescharacteristic
1097C2#1059465711yescharacteristic
1098C2#1059507911yescharacteristic
1099C2#1059529711yescharacteristic
1100C2#1059543111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC2×#63923C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2418
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64102C2semidirect
3. C2×#63921C2semidirect
4. C2×#63853C2semidirect
5. C3×#4993C2semidirect
6. C3×#4992C2semidirect
7. #10591399C2semidirect
8. #10591387C2semidirect
9. #10591380C2semidirect
10. #10591367C2semidirect
11. #10591312C2semidirect
12. #10591291C2semidirect
13. #10591290C2semidirect
14. #10591287C2semidirect
15. #10591287C2semidirect
21. C22×C4×C3⋊D3C22semidirect
25. C2×C32×C4⋊C4C22semidirect
27. C2×#3752C22semidirect
28. C2×C4×C3⋊Dic3C22semidirect
36. C2×C3×Dic3⋊C4C22semidirect
37. C2×C3×Dic3⋊C4C22semidirect
38. C2×Dic3⋊Dic3C22semidirect
39. C2×Dic3⋊Dic3C22semidirect
42. C2×#3722C22semidirect
43. C2×#3722C22semidirect
51. C3×C3⋊#95C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. C3×C3⋊#95C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
68. #4993D3semidirect
69. #4992D3semidirect
149. (C2×D3)⋊Dic3D4semidirect
171. C2×C3×C4⋊C4C2×D3semidirect
172. C2×C3×C4⋊C4C2×D3semidirect
211. C2×Dic3⋊C4C2×D3semidirect
212. C2×Dic3⋊C4C2×D3semidirect
233. C3⋊#95C2×D3semidirect
234. C3⋊#95C2×D3semidirect
235. C3⋊#95C2×D3semidirect
236. C3⋊#95C2×D3semidirect
491. C2×C3⋊D3#123semidirect
532. C2×C4⋊C4D32semidirect
933. C32#2418semidirect
1088. C3#77669semidirect
1089. C3#78101semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
C2×#639232
C2×#639212
C2×#638532
C3×#49932
C3×#49922
#105913992
#105913872
#105913802
#105913672
#105913122
#105912912
#105912902
#105912872
#781013
#776693