Finite Group Databasebeta

← #11836003

Subgroups — #11836003

Order 1152.

1845 conjugacy classes of subgroups.

The subgroup lattice has 1196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64104C211yesmaximal, characteristic, complemented
2C2×#63923C211yesmaximal, characteristic, complemented
3C2×#63923C211yesmaximal, characteristic, complemented
4C2×#63910C211yesmaximal, characteristic, complemented
5C3×#4993C211yesmaximal, characteristic, complemented
6C3×#4992C211yesmaximal, characteristic, complemented
7#10591399C211yesmaximal, characteristic, complemented
8#10591395C211yesmaximal, characteristic, complemented
9#10591387C211yesmaximal, characteristic, complemented
10#10591387C211yesmaximal, characteristic, complemented
11#10591380C211yesmaximal, characteristic, complemented
12#10591321C211yesmaximal, characteristic, complemented
13#10591291C211yesmaximal, characteristic, complemented
14#10591275C211yesmaximal, characteristic, complemented
15#10591204C211yesmaximal, characteristic, complemented
16#78112—31nomaximal
17#77689—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
22C22×C4×C3⋊D3C2211yescharacteristic, complemented
23C22×#626C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#626C2211yescharacteristic
27C22×#624C2211yescharacteristic, complemented
28C2×C32×C4⋊C4C2211yescharacteristic, complemented
29C2×#3752C2211yescharacteristic
30C2×#3752C2211yescharacteristic, complemented
31#64104—24no—
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
39C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic, complemented
44C2×#3722C2211yescharacteristic, complemented
45C2×#3722C2211yescharacteristic, complemented
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48#63923—24no—
49#63923—24no—
50#63910—24no—
51C3×C3⋊#95C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×#895—31no—
58C2×#895—31no—
59C2×#895—31no—
60C2×#895—61no—
61C2×#884—31no—
62C2×#882—31no—
63C2×#882—31no—
64C2×#882—31no—
65C2×#882—31no—
66C3×#399—31no—
67C3×#397—31no—
68#4993D311yescharacteristic, complemented
69#4992—31no—
70#4992D311yescharacteristic, complemented
71#4991—31no—
72#4991—31no—
73#4960—31no—
74#4959—31no—
75#4956—31no—
76#4956—31no—
77#4956—31no—
78#4955—31no—
79#4955—31no—
80#4675—31no—
81#4672—31no—
82#4671—31no—
83#4665—31no—
84#4665—31no—
85#4665—31no—
86#4665—31no—
87#4665—31no—
88C23×C3⋊D3C2311yescharacteristic
89C23×C3⋊D3C2311yescharacteristic
90C23×C3⋊D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C23×C3×D3C2311yescharacteristic
93C22×D32—22no—
94C22×D32—22no—
95C22×D32—22no—
96C22×D32—41no—
97C22×D32—41no—
98C22×D32—41no—
99C22×D32—41no—
100C22×C32×C4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C22×C32×C4C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C2×C4⋊(C3⋊D3)—22no—
105C2×C4⋊(C3⋊D3)—22no—
106C2×C4⋊(C3⋊D3)—22no—
107C2×C4⋊(C3⋊D3)—22no—
108C2×C4⋊(C3⋊D3)—41no—
109C2×C4⋊(C3⋊D3)—41no—
110C2×C4⋊(C3⋊D3)—41no—
111C2×C4⋊(C3⋊D3)—41no—
112C2×C4⋊(C3⋊D3)D414yescomplemented
113C2×C4×C3⋊D3—22no—
114C2×C4×C3⋊D3—41no—
115C2×C4×C3⋊D3—41no—
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C2×#626—22no—
123C2×#626—22no—
124C2×#626—22no—
125C2×#626—22no—
126C2×#626—22no—
127C2×#626—22no—
128C2×#626—41no—
129C2×#626—41no—
130C2×#626—41no—
131C2×#626—41no—
132C2×#626—41no—
133C2×#626D414yescomplemented
134C2×#624—22no—
135C2×#624—41no—
136C2×#624—41no—
137C32×C4⋊C4—22no—
138#3752—22no—
139#3752—22no—
140C3×(C2×D3)⋊C4—22no—
141C3×(C2×D3)⋊C4—22no—
142C3×(C2×D3)⋊C4—22no—
143C3×(C2×D3)⋊C4—22no—
144C3×(C2×D3)⋊C4—22no—
145C3×(C2×D3)⋊C4—41no—
146C3×Dic3⋊C4—22no—
147C3×Dic3⋊C4—41no—
148#3722—22no—
149#3722—22no—
150#3722—22no—
151#3722—41no—
152#3722—41no—
153#3722—41no—
154(C2×D3)⋊Dic3—41no—
155(C2×D3)⋊Dic3—41no—
156#2668—91noSylow
157C24×D3—31no—
158C24×D3—31no—
159C22×#67—31no—
160C22×#67—31no—
161C22×#67—31no—
162C22×#67—31no—
163C22×D12—31no—
164C22×D12—31no—
165C22×D12—31no—
166C22×D12—31no—
167C22×D12—31no—
168C22×D12—31no—
169C22×D12—31no—
170C22×D12—31no—
171C22×D12—31no—
172C22×D12—31no—
173C22×D12—61no—
174C22×D12—61no—
175C22×D12—61no—
176C22×C4×D3—31no—
177C22×C4×D3—31no—
178C22×C4×D3—31no—
179C22×C4×D3—31no—
180C22×C4×D3—61no—
181C2×C3×C4⋊C4—21no—
182C2×C3×C4⋊C4—31no—
183C2×C3×C4⋊C4—31no—
184C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
185C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
186C2×C3×C22⋊C4—31no—
187C2×C3×C22⋊C4—31no—
188C2×C3×C22⋊C4—31no—
189C2×C3×C22⋊C4—31no—
190C2×C3×C22⋊C4—31no—
191C2×C3×C22⋊C4—31no—
192C2×#217—31no—
193C2×#217—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—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—31no—
212C2×(C2×D3)⋊C4—61no—
213C2×(C2×D3)⋊C4—61no—
214C2×(C2×D3)⋊C4C2×D311yescharacteristic
215C2×(C2×D3)⋊C4C2×D311yescharacteristic
216C2×(C2×D3)⋊C4C2×D311yescharacteristic
217C2×(C2×D3)⋊C4C2×D311yescharacteristic
218C2×(C2×D3)⋊C4C2×D311yescharacteristic
219C2×(C2×D3)⋊C4C2×D311yescharacteristic
220C2×Dic3⋊C4C2×D311yescharacteristic, complemented
221C2×Dic3⋊C4C2×D311yescharacteristic, complemented
222#895—64no—
223#895—64no—
224#895—64no—
225#895—68no—
226#884—64no—
227#882—64no—
228#882—64no—
229#882—64no—
230#882—64no—
231C3×#95—31no—
232C3×#95—31no—
233C3×#95—31no—
234C3×#95—31no—
235C3⋊#95—31no—
236C3⋊#95—31no—
237C3⋊#95—31no—
238C3⋊#95—31no—
239C3⋊#95C2×D311yescharacteristic, complemented
240C3⋊#95C2×D311yescharacteristic, complemented
241C3⋊#95C2×D311yescharacteristic, complemented
242C3⋊#95C2×D311yescharacteristic, complemented
243C23×C32C2411yescharacteristic
244C22×C3⋊D3—21no—
245C22×C3⋊D3—21no—
246C22×C3⋊D3—21no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3—21no—
249C22×C3⋊D3—21no—
250C22×C3⋊D3—21no—
251C22×C3⋊D3—21no—
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⋊D3C2×D412yes—
263C22×C3⋊D3C2×D412yes—
264C22×C3⋊D3C2×D412yes—
265C22×C3×D3—21no—
266C22×C3×D3—21no—
267C22×C3×D3—21no—
268C22×C3×D3—21no—
269C22×C3×D3—21no—
270C22×C3×D3—21no—
271C22×C3×D3—21no—
272C22×C3×D3—21no—
273C22×C3×D3—21no—
274C22×C3×D3—21no—
275C22×C3×D3—21no—
276C22×C3×D3—21no—
277C22×C3×D3C2×D412yes—
278C22×C3×D3#4112yes—
279C2×D32—44no—
280C2×D32—44no—
281C2×D32—44no—
282C2×D32—44no—
283C2×D32—44no—
284C2×D32—44no—
285C2×D32—44no—
286C2×C32×C4—21no—
287C2×C32×C4—21no—
288C2×C32×C4—21no—
289C2×C32×C4—21no—
290C2×C32×C4—21no—
291C2×C32×C4—21no—
292C2×C32×C4—21no—
293C2×C32×C4—21no—
294C2×C32×C4C2×D412yes—
295C2×C3⋊Dic3—21no—
296C2×C3⋊Dic3—21no—
297C2×C3⋊Dic3—21no—
298C4⋊(C3⋊D3)—44no—
299C4⋊(C3⋊D3)—44no—
300C4⋊(C3⋊D3)—44no—
301C4×C3⋊D3—44no—
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×Dic3—21no—
311C2×C3×Dic3—21no—
312C2×C3×Dic3—21no—
313C2×C3×Dic3—21no—
314C2×C3×Dic3—21no—
315C2×C3×Dic3—21no—
316C2×C3×Dic3—21no—
317C2×C3×Dic3—21no—
318C2×C3×Dic3—21no—
319C2×C3×Dic3C2×D412yes—
320#626—44no—
321#626—44no—
322#626—44no—
323#626—44no—
324#624—44no—
325C2×#121—91no—
326C2×#121—91no—
327C2×#120—91no—
328C2×#120—91no—
329#399—31no—
330#397—31no—
331#397—91no—
332#394—91no—
333#394—91no—
334#392—91no—
335#386—91no—
336#386—91no—
337#386—91no—
338#386—91no—
339#379—91no—
340C24×C3—31no—
341C24×C3—31no—
342C23×D3—31no—
343C23×D3—31no—
344C23×D3—31no—
345C23×D3—31no—
346C23×D3—31no—
347C23×D3—31no—
348C23×D3—61no—
349C23×D3—61no—
350C23×D3—61no—
351C23×D3—62no—
352C23×D3—62no—
353C23×D3—62no—
354C23×D3—62no—
355C23×D3—62no—
356C23×D3—62no—
357C23×D3—121no—
358C23×D3—121no—
359C23×D3—121no—
360C23×D3—121no—
361C23×D3—121no—
362C23×D3—121no—
363C23×D3—121no—
364C23×D3—121no—
365C23×D3C22×D311yescharacteristic
366C23×D3C22×D311yescharacteristic
367C22×C3×C4—21no—
368C22×C3×C4—21no—
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×C4C22×D311yescharacteristic
377C22×C3×C4C22×D311yescharacteristic
378C22×C3×C4C22×D311yescharacteristic
379C22×C3×C4C22×D311yescharacteristic
380C22×C3×C4C22×D311yescharacteristic
381C22×C3×C4C22×D311yescharacteristic
382C2×#67—34no—
383C2×#67—62no—
384C2×#67—62no—
385C2×#67—62no—
386C2×#67—62no—
387C2×#67—62no—
388C2×#67—62no—
389C2×#67—121no—
390C2×#67—121no—
391C2×#67—121no—
392C2×#67—121no—
393C2×#67—121no—
394C22×Dic3—31no—
395C22×Dic3—31no—
396C22×Dic3—61no—
397C22×Dic3C22×D311yescharacteristic
398C22×Dic3C22×D311yescharacteristic
399C22×Dic3C22×D311yescharacteristic
400C22×Dic3C22×D311yescharacteristic
401C22×Dic3C22×D311yescharacteristic
402C22×Dic3C22×D311yescharacteristic
403C2×D12—34no—
404C2×D12—34no—
405C2×D12—34no—
406C2×D12—64no—
407C2×D12—62no—
408C2×D12—62no—
409C2×D12—62no—
410C2×D12—62no—
411C2×D12—62no—
412C2×D12—62no—
413C2×D12—62no—
414C2×D12—62no—
415C2×D12—64no—
416C2×D12—64no—
417C2×D12—62no—
418C2×D12—62no—
419C2×D12—62no—
420C2×D12—62no—
421C2×D12—62no—
422C2×D12—62no—
423C2×D12—122no—
424C2×D12—122no—
425C2×D12—121no—
426C2×D12—121no—
427C2×D12—121no—
428C2×D12—121no—
429C2×D12—121no—
430C2×D12—121no—
431C2×D12—121no—
432C2×D12—121no—
433C2×D12—122no—
434C2×D12—122no—
435C2×D12—122no—
436C2×D12—122no—
437C2×D12—121no—
438C2×D12—121no—
439C2×D12—121no—
440C2×D12—121no—
441C2×D12—121no—
442C2×C4×D3—62no—
443C2×C4×D3—64no—
444C2×C4×D3—62no—
445C2×C4×D3—62no—
446C2×C4×D3—62no—
447C2×C4×D3—121no—
448C2×C4×D3—121no—
449C2×C4×D3—121no—
450C2×C4×D3—121no—
451C2×C4×D3—121no—
452C2×C4×D3—121no—
453C2×C4×D3—121no—
454C2×C4×D3—121no—
455C2×C4×D3—122no—
456C2×C4×D3—122no—
457C3×C4⋊C4—24no—
458C3×C4⋊C4—22no—
459C3×C4⋊C4—22no—
460C3×C4⋊C4—62no—
461C3×C4⋊C4—121no—
462C3×C22⋊C4—62no—
463C3×C22⋊C4—62no—
464C3×C22⋊C4—62no—
465C3×C22⋊C4—62no—
466C3×C22⋊C4—62no—
467C3×C22⋊C4—121no—
468#217—121no—
469#217—121no—
470(C2×D3)⋊C4—22no—
471(C2×D3)⋊C4—22no—
472(C2×D3)⋊C4—22no—
473(C2×D3)⋊C4—22no—
474(C2×D3)⋊C4—22no—
475(C2×D3)⋊C4—41no—
476(C2×D3)⋊C4—62no—
477(C2×D3)⋊C4—62no—
478(C2×D3)⋊C4—62no—
479(C2×D3)⋊C4—62no—
480(C2×D3)⋊C4—62no—
481(C2×D3)⋊C4—62no—
482(C2×D3)⋊C4—62no—
483(C2×D3)⋊C4—62no—
484(C2×D3)⋊C4—62no—
485(C2×D3)⋊C4—64no—
486(C2×D3)⋊C4—64no—
487(C2×D3)⋊C4—62no—
488(C2×D3)⋊C4—121no—
489(C2×D3)⋊C4—121no—
490(C2×D3)⋊C4—121no—
491(C2×D3)⋊C4—121no—
492(C2×D3)⋊C4—121no—
493(C2×D3)⋊C4—121no—
494(C2×D3)⋊C4—121no—
495(C2×D3)⋊C4—121no—
496Dic3⋊C4—22no—
497Dic3⋊C4—41no—
498C22×C32C22×D411yescharacteristic
499C22×C32C22×D411yescharacteristic
500C22×C32C2×#4111yescharacteristic
501C22×C32H(5,𝔽2)11yescharacteristic
502C22×C32H(5,𝔽2)11yescharacteristic
503C22×C32H(5,𝔽2)11yescharacteristic
504C22×C32H(5,𝔽2)11yescharacteristic
505C2×C3⋊D3—22no—
506C2×C3⋊D3—22no—
507C2×C3⋊D3—22no—
508C2×C3⋊D3—22no—
509C2×C3⋊D3—22no—
510C2×C3⋊D3—22no—
511C2×C3⋊D3—22no—
512C2×C3⋊D3—22no—
513C2×C3⋊D3—22no—
514C2×C3⋊D3—41no—
515C2×C3⋊D3—41no—
516C2×C3⋊D3—41no—
517C2×C3⋊D3—41no—
518C2×C3⋊D3—41no—
519C2×C3⋊D3—41no—
520C2×C3⋊D3—41no—
521C2×C3⋊D3—41no—
522C2×C3⋊D3—41no—
523C2×C3⋊D3—41no—
524C2×C3⋊D3—41no—
525C2×C3⋊D3—41no—
526C2×C3×D3—22no—
527C2×C3×D3—22no—
528C2×C3×D3—22no—
529C2×C3×D3—22no—
530C2×C3×D3—22no—
531C2×C3×D3—22no—
532C2×C3×D3—41no—
533C2×C3×D3—41no—
534C2×C3×D3—41no—
535C2×C3×D3—41no—
536C2×C3×D3—41no—
537C2×C3×D3—41no—
538C2×C3×D3—41no—
539C2×C3×D3—41no—
540D32—416no—
541C32×C4—22no—
542C32×C4—41no—
543C32×C4—41no—
544C3⋊Dic3—41no—
545C3×Dic3—22no—
546C3×Dic3—41no—
547C3×Dic3—41no—
548C3×Dic3—41no—
549C3×Dic3—41no—
550C3×Dic3—41no—
551C25—91no—
552C22×D4—91no—
553C22×D4—91no—
554C22×D4—91no—
555C22×D4—91no—
556C22×D4—91no—
557C22×D4—91no—
558C22×D4—91no—
559C23×C4—91no—
560C23×C4—91no—
561#121—184no—
562#121—184no—
563#120—184no—
564#120—184no—
565C2×C4⋊C4—31no—
566C2×C4⋊C4—31no—
567C2×C4⋊C4D3211yescharacteristic, complemented
568C2×C22⋊C4—31no—
569C2×C22⋊C4—31no—
570C2×C22⋊C4—31no—
571C2×C22⋊C4—31no—
572C2×C22⋊C4—31no—
573C2×C22⋊C4—31no—
574C2×C22⋊C4—91no—
575C2×C22⋊C4—91no—
576C2×C22⋊C4—91no—
577C2×C22⋊C4—91no—
578C2×C22⋊C4—91no—
579C2×C22⋊C4—91no—
580C2×C22⋊C4—91no—
581C2×C22⋊C4—91no—
582C2×C22⋊C4—91no—
583C2×C22⋊C4—91no—
584#95—31no—
585#95—31no—
586#95—31no—
587#95—31no—
588#95—91no—
589#95—91no—
590C23×C3—21no—
591C23×C3—32no—
592C23×C3—32no—
593C23×C3—61no—
594C23×C3—61no—
595C23×C3—61no—
596C23×C3—61no—
597C23×C3—61no—
598C23×C3—61no—
599C23×C3—61no—
600C23×C3—61no—
601C23×C3—61no—
602C23×C3—61no—
603C23×C3—61no—
604C23×C3—61no—
605C23×C3C23×D311yescharacteristic
606C23×C3C23×D311yescharacteristic
607C22×D3—21no—
608C22×D3—21no—
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—21no—
613C22×D3—21no—
614C22×D3—21no—
615C22×D3—21no—
616C22×D3—21no—
617C22×D3—21no—
618C22×D3—21no—
619C22×D3—32no—
620C22×D3—32no—
621C22×D3—32no—
622C22×D3—32no—
623C22×D3—32no—
624C22×D3—32no—
625C22×D3—62no—
626C22×D3—62no—
627C22×D3—62no—
628C22×D3—62no—
629C22×D3—62no—
630C22×D3—61no—
631C22×D3—61no—
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—61no—
645C22×D3—61no—
646C22×D3—61no—
647C22×D3—61no—
648C22×D3—61no—
649C22×D3—61no—
650C22×D3—61no—
651C22×D3—61no—
652C22×D3—61no—
653C22×D3—61no—
654C22×D3—61no—
655C22×D3—61no—
656C22×D3—61no—
657C22×D3—61no—
658C22×D3—61no—
659C22×D3—61no—
660C22×D3—61no—
661C22×D3—61no—
662C22×D3—61no—
663C22×D3—61no—
664C22×D3—61no—
665C22×D3—61no—
666C22×D3—121no—
667C22×D3—121no—
668C22×D3—121no—
669C22×D3—121no—
670C22×D3—121no—
671C22×D3—121no—
672C22×D3—121no—
673C22×D3—121no—
674C22×D3—121no—
675C22×D3—121no—
676C22×D3—121no—
677C22×D3—121no—
678C22×D3—121no—
679C22×D3—121no—
680C22×D3—121no—
681C22×D3—121no—
682C22×D3—124no—
683C22×D3—124no—
684C22×D3—124no—
685C22×D3—124no—
686C22×D3—124no—
687C22×D3—124no—
688C22×D3—124no—
689C22×D3—124no—
690C22×D3—124no—
691C22×D3—124no—
692C22×D3—124no—
693C22×D3—124no—
694C22×D3—124no—
695C22×D3—124no—
696C22×D3D3×D412yes—
697C22×D3#23912yes—
698C2×C3×C4—22no—
699C2×C3×C4—22no—
700C2×C3×C4—21no—
701C2×C3×C4—21no—
702C2×C3×C4—21no—
703C2×C3×C4—21no—
704C2×C3×C4—22no—
705C2×C3×C4—22no—
706C2×C3×C4—21no—
707C2×C3×C4—21no—
708C2×C3×C4—21no—
709C2×C3×C4—21no—
710C2×C3×C4—21no—
711C2×C3×C4—21no—
712C2×C3×C4—21no—
713C2×C3×C4—21no—
714C2×C3×C4—21no—
715C2×C3×C4—21no—
716C2×C3×C4—21no—
717C2×C3×C4—21no—
718C2×C3×C4—22no—
719C2×C3×C4—32no—
720C2×C3×C4—41no—
721C2×C3×C4—41no—
722C2×C3×C4—41no—
723C2×C3×C4—41no—
724C2×C3×C4—61no—
725C2×C3×C4—61no—
726C2×C3×C4—61no—
727C2×C3×C4—61no—
728C2×C3×C4—61no—
729C2×C3×C4—61no—
730C2×C3×C4—61no—
731C2×C3×C4—61no—
732C2×C3×C4—61no—
733C2×C3×C4—61no—
734C2×C3×C4—61no—
735C2×C3×C4—61no—
736C2×C3×C4—61no—
737C2×C3×C4—61no—
738C2×C3×C4—61no—
739C2×C3×C4—61no—
740C2×C3×C4—61no—
741C2×C3×C4D3×D412yes—
742C2×C3×C4D3×D412yes—
743#67—124no—
744#67—124no—
745#67—124no—
746#67—124no—
747C2×Dic3—21no—
748C2×Dic3—21no—
749C2×Dic3—21no—
750C2×Dic3—21no—
751C2×Dic3—21no—
752C2×Dic3—21no—
753C2×Dic3—21no—
754C2×Dic3—21no—
755C2×Dic3—21no—
756C2×Dic3—21no—
757C2×Dic3—21no—
758C2×Dic3—21no—
759C2×Dic3—21no—
760C2×Dic3—21no—
761C2×Dic3—21no—
762C2×Dic3—21no—
763C2×Dic3—21no—
764C2×Dic3—62no—
765C2×Dic3—61no—
766C2×Dic3—61no—
767C2×Dic3—61no—
768C2×Dic3—61no—
769C2×Dic3—61no—
770C2×Dic3—61no—
771C2×Dic3—121no—
772C2×Dic3—121no—
773C2×Dic3D3×D412yes—
774D12—124no—
775D12—124no—
776D12—128no—
777D12—124no—
778D12—124no—
779D12—124no—
780D12—124no—
781D12—128no—
782D12—128no—
783D12—124no—
784D12—124no—
785D12—124no—
786D12—124no—
787C4×D3—124no—
788C4×D3—124no—
789C4×D3—128no—
790C4×D3—124no—
791C4×D3—124no—
792C2×C32#53411yescharacteristic
793C2×C32#53411yescharacteristic
794C2×C32#53811yescharacteristic
795C2×C32D4211yescharacteristic
796C2×C32#54611yescharacteristic
797C2×C32#54611yescharacteristic
798C2×C32#56011yescharacteristic
799C3⋊D3—42no—
800C3⋊D3—42no—
801C3⋊D3—42no—
802C3×D3—42no—
803C3×D3—42no—
804C24—31no—
805C24—31no—
806C24—91no—
807C24—91no—
808C24—91no—
809C24—182no—
810C24—182no—
811C24—182no—
812C24—361no—
813C24—361no—
814C24—361no—
815C24—361no—
816C2×D4—94no—
817C2×D4—94no—
818C2×D4—182no—
819C2×D4—182no—
820C2×D4—182no—
821C2×D4—182no—
822C2×D4—182no—
823C2×D4—182no—
824C2×D4—182no—
825C2×D4—182no—
826C2×D4—182no—
827C2×D4—182no—
828C2×D4—361no—
829C2×D4—361no—
830C2×D4—361no—
831C2×D4—361no—
832C2×D4—361no—
833C2×D4—361no—
834C2×D4—361no—
835C2×D4—361no—
836C2×D4—361no—
837C22×C4—31no—
838C22×C4—31no—
839C22×C4—31no—
840C22×C4—31no—
841C22×C4—31no—
842C22×C4—31no—
843C22×C4—91no—
844C22×C4—182no—
845C22×C4—182no—
846C22×C4—361no—
847C22×C4—361no—
848C22×C4—361no—
849C22×C4—361no—
850C22×C4C2×D3211yescharacteristic
851C22×C4C2×D3211yescharacteristic
852C22×C4C2×D3211yescharacteristic
853C4⋊C4—22no—
854C4⋊C4—62no—
855C4⋊C4—121no—
856C22⋊C4—62no—
857C22⋊C4—62no—
858C22⋊C4—62no—
859C22⋊C4—62no—
860C22⋊C4—62no—
861C22⋊C4—121no—
862C22⋊C4—182no—
863C22⋊C4—182no—
864C22⋊C4—182no—
865C22⋊C4—182no—
866C22⋊C4—182no—
867C22⋊C4—361no—
868C22⋊C4—361no—
869C22⋊C4—361no—
870C22⋊C4—361no—
871C22⋊C4—361no—
872C22×C3—21no—
873C22×C3—21no—
874C22×C3—21no—
875C22×C3—21no—
876C22×C3—21no—
877C22×C3—21no—
878C22×C3—21no—
879C22×C3—62no—
880C22×C3—62no—
881C22×C3—62no—
882C22×C3—62no—
883C22×C3—62no—
884C22×C3—62no—
885C22×C3—121no—
886C22×C3—121no—
887C22×C3—121no—
888C22×C3—121no—
889C22×C3—121no—
890C22×C3—121no—
891C22×C3—121no—
892C22×C3—121no—
893C22×C3C2×D3×D411yescharacteristic
894C22×C3C2×D3×D411yescharacteristic
895C22×C3C2×D3×D411yescharacteristic
896C22×C3C2×D3×D411yescharacteristic
897C22×C3#100411yescharacteristic
898C22×C3C2×#23911yescharacteristic
899C22×C3D3×#4111yescharacteristic
900C22×C3#100911yescharacteristic
901C22×C3#100911yescharacteristic
902C22×C3#100911yescharacteristic
903C22×C3#100911yescharacteristic
904C22×C3#100911yescharacteristic
905C22×C3#100911yescharacteristic
906C22×C3#100911yescharacteristic
907C2×D3—22no—
908C2×D3—22no—
909C2×D3—22no—
910C2×D3—22no—
911C2×D3—22no—
912C2×D3—22no—
913C2×D3—41no—
914C2×D3—41no—
915C2×D3—41no—
916C2×D3—41no—
917C2×D3—41no—
918C2×D3—41no—
919C2×D3—41no—
920C2×D3—41no—
921C2×D3—64no—
922C2×D3—62no—
923C2×D3—62no—
924C2×D3—62no—
925C2×D3—62no—
926C2×D3—62no—
927C2×D3—62no—
928C2×D3—62no—
929C2×D3—62no—
930C2×D3—62no—
931C2×D3—62no—
932C2×D3—62no—
933C2×D3—62no—
934C2×D3—62no—
935C2×D3—62no—
936C2×D3—62no—
937C2×D3—62no—
938C2×D3—62no—
939C2×D3—62no—
940C2×D3—122no—
941C2×D3—122no—
942C2×D3—122no—
943C2×D3—122no—
944C2×D3—122no—
945C2×D3—122no—
946C2×D3—122no—
947C2×D3—122no—
948C2×D3—1216no—
949C2×D3—1216no—
950C2×D3—122no—
951C2×D3—122no—
952C2×D3—122no—
953C2×D3—122no—
954C2×D3—121no—
955C2×D3—121no—
956C2×D3—121no—
957C2×D3—121no—
958C2×D3—121no—
959C2×D3—121no—
960C2×D3—121no—
961C2×D3—121no—
962C2×D3—121no—
963C2×D3—121no—
964C2×D3—121no—
965C2×D3—121no—
966C2×D3—121no—
967C2×D3—121no—
968C2×D3—121no—
969C2×D3—121no—
970C2×D3—121no—
971C2×D3—121no—
972C2×D3—121no—
973C2×D3—121no—
974C2×D3—121no—
975C2×D3—121no—
976C2×D3—121no—
977C2×D3—121no—
978C2×D3—241no—
979C2×D3—241no—
980C2×D3—241no—
981C2×D3—241no—
982C2×D3—241no—
983C2×D3—241no—
984C2×D3—241no—
985C2×D3—241no—
986C3×C4—24no—
987C3×C4—22no—
988C3×C4—22no—
989C3×C4—42no—
990C3×C4—42no—
991C3×C4—41no—
992C3×C4—41no—
993C3×C4—41no—
994C3×C4—41no—
995C3×C4—62no—
996C3×C4—121no—
997C3×C4—121no—
998C3×C4—121no—
999C3×C4—121no—
1000C3×C4—121no—
1001Dic3—22no—
1002Dic3—41no—
1003Dic3—41no—
1004Dic3—41no—
1005Dic3—41no—
1006Dic3—41no—
1007Dic3—122no—
1008Dic3—121no—
1009Dic3—121no—
1010C32#266811yescharacteristic, complemented, Sylow
1011C23—32no—
1012C23—32no—
1013C23—61no—
1014C23—61no—
1015C23—61no—
1016C23—61no—
1017C23—61no—
1018C23—61no—
1019C23—61no—
1020C23—61no—
1021C23—61no—
1022C23—61no—
1023C23—61no—
1024C23—61no—
1025C23—92no—
1026C23—92no—
1027C23—92no—
1028C23—181no—
1029C23—181no—
1030C23—181no—
1031C23—181no—
1032C23—181no—
1033C23—181no—
1034C23—181no—
1035C23—181no—
1036C23—181no—
1037C23—181no—
1038C23—181no—
1039C23—181no—
1040C23—181no—
1041C23—181no—
1042C23—181no—
1043C23—181no—
1044C23—181no—
1045C23—181no—
1046C23—364no—
1047C23—364no—
1048C23—364no—
1049C23—364no—
1050C23—364no—
1051C23—364no—
1052C23—364no—
1053C23C22×D3211yescharacteristic
1054D4—364no—
1055D4—364no—
1056D4—364no—
1057D4—364no—
1058D4—364no—
1059D4—364no—
1060D4—364no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—32no—
1070C2×C4—61no—
1071C2×C4—61no—
1072C2×C4—61no—
1073C2×C4—61no—
1074C2×C4—61no—
1075C2×C4—61no—
1076C2×C4—61no—
1077C2×C4—61no—
1078C2×C4—61no—
1079C2×C4—61no—
1080C2×C4—61no—
1081C2×C4—61no—
1082C2×C4—61no—
1083C2×C4—61no—
1084C2×C4—61no—
1085C2×C4—61no—
1086C2×C4—61no—
1087C2×C4—181no—
1088C2×C4—181no—
1089C2×C4—181no—
1090C2×C4—364no—
1091C2×C4—364no—
1092C2×C4#381112yes—
1093C2×C3—21no—
1094C2×C3—21no—
1095C2×C3—21no—
1096C2×C3—21no—
1097C2×C3—21no—
1098C2×C3—21no—
1099C2×C3—21no—
1100C2×C3—122no—
1101C2×C3—122no—
1102C2×C3#560911yescharacteristic
1103C2×C3#563011yescharacteristic
1104C2×C3#563011yescharacteristic
1105C2×C3#564411yescharacteristic
1106C2×C3#565311yescharacteristic
1107C2×C3#565311yescharacteristic
1108C2×C3#565311yescharacteristic
1109C2×C3#565311yescharacteristic
1110C2×C3#565411yescharacteristic
1111C2×C3#566611yescharacteristic
1112C2×C3#567611yescharacteristic
1113C2×C3#570411yescharacteristic
1114C2×C3#571111yescharacteristic
1115C2×C3#571711yescharacteristic
1116D3—42no—
1117D3—42no—
1118D3—124no—
1119D3—122no—
1120D3—122no—
1121D3—122no—
1122D3—122no—
1123D3—122no—
1124D3—122no—
1125D3—242no—
1126D3—242no—
1127C22—62no—
1128C22—62no—
1129C22—62no—
1130C22—62no—
1131C22—62no—
1132C22—62no—
1133C22—121no—
1134C22—121no—
1135C22—121no—
1136C22—121no—
1137C22—121no—
1138C22—121no—
1139C22—121no—
1140C22—121no—
1141C22—182no—
1142C22—182no—
1143C22—182no—
1144C22—182no—
1145C22—182no—
1146C22—182no—
1147C22—182no—
1148C22—182no—
1149C22—182no—
1150C22—3616no—
1151C22—361no—
1152C22—361no—
1153C22—361no—
1154C22—361no—
1155C22—361no—
1156C22—361no—
1157C22—361no—
1158C22—361no—
1159C22—361no—
1160C22—361no—
1161C22—361no—
1162C22—361no—
1163C22#6430811yescharacteristic
1164C22#6430811yescharacteristic
1165C22D32×D411yescharacteristic
1166C22#6431411yescharacteristic
1167C22D3×#23911yescharacteristic
1168C22#6432011yescharacteristic
1169C22C2×#381111yescharacteristic
1170C4—22no—
1171C4—41no—
1172C4—41no—
1173C4—62no—
1174C4—121no—
1175C4—121no—
1176C4—121no—
1177C4—121no—
1178C4—121no—
1179C4—361no—
1180C3—21no—
1181C3#7768911yescharacteristic, complemented
1182C3#7811211yescharacteristic, complemented
1183C2—122no—
1184C2—122no—
1185C2—362no—
1186C2—362no—
1187C2—362no—
1188C2#1059461011yescharacteristic
1189C2#1059462011yescharacteristic
1190C2#1059465211yescharacteristic
1191C2#1059466311yescharacteristic
1192C2#1059508011yescharacteristic
1193C2#1059529711yescharacteristic
1194C2#1059543111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2668
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×#64104C2semidirect
2. C2×#63923C2semidirect
3. C2×#63923C2semidirect
4. C2×#63910C2semidirect
5. C3×#4993C2semidirect
6. C3×#4992C2semidirect
7. #10591399C2semidirect
8. #10591395C2semidirect
9. #10591387C2semidirect
10. #10591387C2semidirect
11. #10591380C2semidirect
12. #10591321C2semidirect
13. #10591291C2semidirect
14. #10591275C2semidirect
15. #10591204C2semidirect
21. C22×C4⋊(C3⋊D3)C22semidirect
22. C22×C4×C3⋊D3C22semidirect
27. C22×#624C22semidirect
28. C2×C32×C4⋊C4C22semidirect
30. C2×#3752C22semidirect
38. C2×C3×Dic3⋊C4C22semidirect
39. C2×C3×Dic3⋊C4C22semidirect
43. C2×#3722C22semidirect
44. C2×#3722C22semidirect
45. C2×#3722C22semidirect
51. C3×C3⋊#95C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. C3×C3⋊#95C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
68. #4993D3semidirect
70. #4992D3semidirect
112. C2×C4⋊(C3⋊D3)D4semidirect
133. C2×#626D4semidirect
184. C2×C3×C4⋊C4C2×D3semidirect
185. C2×C3×C4⋊C4C2×D3semidirect
220. C2×Dic3⋊C4C2×D3semidirect
221. C2×Dic3⋊C4C2×D3semidirect
239. C3⋊#95C2×D3semidirect
240. C3⋊#95C2×D3semidirect
241. C3⋊#95C2×D3semidirect
242. C3⋊#95C2×D3semidirect
567. C2×C4⋊C4D32semidirect
1010. C32#2668semidirect
1181. C3#77689semidirect
1182. C3#78112semidirect

Maximal subgroups

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

subgroupindex
C2×#641042
C2×#639232
C2×#639102
C3×#49932
C3×#49922
#105913992
#105913952
#105913872
#105913802
#105913212
#105912912
#105912752
#105912042
#781123
#776893