Finite Group Databasebeta

← #11835995

Subgroups — #11835995

Order 1152.

1717 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63922C211yesmaximal, characteristic, complemented
2C2×#63922C211yesmaximal, characteristic, complemented
3C2×#63908C211yesmaximal, characteristic, complemented
4C2×#63906C211yesmaximal, characteristic, complemented
5#10592373C211yesmaximal, characteristic, complemented
6C3×#4665C211yesmaximal, characteristic, complemented
7C3×#4665C211yesmaximal, characteristic, complemented
8#10591399C211yesmaximal, characteristic, complemented
9#10591390C211yesmaximal, characteristic, complemented
10#10591389C211yesmaximal, characteristic, complemented
11#10591382C211yesmaximal, characteristic, complemented
12#10591381C211yesmaximal, characteristic, complemented
13#10591317C211yesmaximal, characteristic, complemented
14#10591312C211yesmaximal, characteristic, complemented
15#10591297C211yesmaximal, characteristic, complemented
16#74911—31nomaximal
17#74910—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic, complemented
22C22×C3×C4×D3C2211yescharacteristic, complemented
23C22×#626C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#625C2211yescharacteristic
26C22×#625C2211yescharacteristic
27C22×#625C2211yescharacteristic, complemented
28C2×#3752C2211yescharacteristic
29C2×#3752C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
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, complemented
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
38C2×Dic3⋊Dic3C2211yescharacteristic, complemented
39C2×Dic3⋊Dic3C2211yescharacteristic, complemented
40C2×#3722C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
46C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
47#63922—24no—
48#63922—24no—
49#63908—24no—
50#63906—24no—
51C32×#95C2211yescharacteristic, complemented
52#63658C2211yescharacteristic, complemented
53#63658C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55C3×C3⋊#95C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×#938—31no—
58C2×#937—31no—
59C2×#937—31no—
60C2×#930—31no—
61C2×#930—31no—
62C2×#884—31no—
63C2×#882—31no—
64C2×#882—31no—
65C3×#386—31no—
66C3×#386—31no—
67#5223—31no—
68#5213—31no—
69#5213—31no—
70#4961—31no—
71#4961—31no—
72#4960—31no—
73#4959—31no—
74#4956—31no—
75#4955—31no—
76#4955—31no—
77#4953—31no—
78#4949—31no—
79#4677—31no—
80#4675—31no—
81#4674—31no—
82#4674—31no—
83#4674—61no—
84#4672—31no—
85#4665—31no—
86#4665D311yescharacteristic, complemented
87#4665D311yescharacteristic, complemented
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
104C22×C3⋊Dic3C2311yescharacteristic
105C22×C3⋊Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C2×C3×D12—22no—
111C2×C3×D12—22no—
112C2×C3×D12—41no—
113C2×C3×D12—41no—
114C2×C3×D12—41no—
115C2×C3×D12D414yescomplemented
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—22no—
118C2×C3×C4×D3—41no—
119C2×C3×C4×D3—41no—
120C2×C3×C4×D3—41no—
121C2×C3×C4×D3—41no—
122C2×#626—22no—
123C2×#626—22no—
124C2×#626—41no—
125C2×#626—41no—
126C2×#626—41no—
127C2×#626D414yescomplemented
128C2×#625—22no—
129C2×#625—22no—
130C2×#625—22no—
131C2×#625—22no—
132C2×#625—22no—
133C2×#625—22no—
134C2×#625—41no—
135C2×#625—41no—
136C2×#625—41no—
137#3752—22no—
138#3752—22no—
139#3752—22no—
140C4⋊(C3⋊Dic3)—22no—
141C3×(C2×D3)⋊C4—22no—
142C3×(C2×D3)⋊C4—22no—
143C3×(C2×D3)⋊C4—22no—
144C3×(C2×D3)⋊C4—41no—
145C3×(C2×D3)⋊C4—41no—
146C3×(C2×D3)⋊C4—41no—
147Dic3⋊Dic3—22no—
148Dic3⋊Dic3—41no—
149#3722—41no—
150(C2×D3)⋊Dic3—22no—
151(C2×D3)⋊Dic3—22no—
152(C2×D3)⋊Dic3—22no—
153(C2×D3)⋊Dic3—22no—
154(C2×D3)⋊Dic3—41no—
155(C2×D3)⋊Dic3—41no—
156#2668—91noSylow
157C24×D3—31no—
158C24×D3—31no—
159C22×C3×D4—31no—
160C22×C3×D4—31no—
161C23×C3×C4—31no—
162C23×C3×C4—31no—
163C22×#67—31no—
164C22×#67—31no—
165C22×#67—31no—
166C22×#67—31no—
167C22×#67—31no—
168C22×#67—31no—
169C22×#67—31no—
170C22×#67—31no—
171C22×D12—31no—
172C22×D12—31no—
173C22×D12C2×D311yescharacteristic
174C22×D12C2×D311yescharacteristic
175C22×C4×D3C2×D311yescharacteristic, complemented
176C22×C4×D3C2×D311yescharacteristic, complemented
177C2×C3×C22⋊C4—31no—
178C2×C3×C22⋊C4—31no—
179C2×C3×C22⋊C4—31no—
180C2×C3×C22⋊C4—31no—
181C2×C3×C22⋊C4—31no—
182C2×C3×C22⋊C4—31no—
183C2×#217—31no—
184C2×#217—31no—
185C2×#217—31no—
186C2×#217—31no—
187C2×#217—31no—
188C2×#217—31no—
189#938—64no—
190#937—64no—
191#937—64no—
192#930—64no—
193#930—64no—
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—61no—
209C2×(C2×D3)⋊C4—61no—
210C2×(C2×D3)⋊C4—61no—
211C2×(C2×D3)⋊C4C2×D311yescharacteristic
212C2×(C2×D3)⋊C4C2×D311yescharacteristic
213C2×(C2×D3)⋊C4C2×D311yescharacteristic
214C2×(C2×D3)⋊C4C2×D311yescharacteristic
215C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
216C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
217C2×C4⋊Dic3—31no—
218C2×C4⋊Dic3—31no—
219C2×C4⋊Dic3—31no—
220C2×C4⋊Dic3—31no—
221C2×C4⋊Dic3—61no—
222C2×Dic3⋊C4—31no—
223C2×Dic3⋊C4—31no—
224#884—64no—
225#882—64no—
226#882—64no—
227C3×#95—21no—
228C3×#95—31no—
229C3×#95—31no—
230C3×#95C2×D311yescharacteristic, complemented
231C3×#95C2×D311yescharacteristic, complemented
232C3⋊#95—31no—
233C3⋊#95—31no—
234C3⋊#95—31no—
235C3⋊#95—31no—
236C3⋊#95—31no—
237C3⋊#95—31no—
238C3⋊#95—61no—
239C3⋊#95—61no—
240C3⋊#95C2×D311yescharacteristic, complemented
241C3⋊#95C2×D311yescharacteristic, complemented
242C23×C32C2411yescharacteristic
243C22×C3⋊D3—21no—
244C22×C3⋊D3—21no—
245C22×C3⋊D3—21no—
246C22×C3⋊D3—21no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3—21no—
249C22×C3⋊D3C2×D412yes—
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×D3—21no—
263C22×C3×D3—21no—
264C22×C3×D3—21no—
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×D3C2×D412yes—
275C22×C3×D3C2×D412yes—
276C22×C3×D3C2×D412yes—
277C22×C3×D3#4112yes—
278C2×D32—44no—
279C2×D32—44no—
280C2×D32—44no—
281C2×D32—44no—
282C2×D32—44no—
283C2×D32—44no—
284C2×D32—44no—
285C2×C32×C4—21no—
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×C4C2×D412yes—
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×Dic3—21no—
311C2×C3×Dic3—21no—
312C2×C3×Dic3—21no—
313C2×C3×Dic3—21no—
314C2×C3×Dic3C2×D412yes—
315C3×D12—44no—
316C3×D12—44no—
317C3×C4×D3—44no—
318C3×C4×D3—44no—
319#626—44no—
320#626—44no—
321#625—44no—
322#625—44no—
323#625—44no—
324C2×#121—91no—
325C2×#121—91no—
326C2×#120—91no—
327C2×#120—91no—
328#399—91no—
329#397—91no—
330#397—91no—
331#394—91no—
332#394—91no—
333#392—91no—
334#386—31no—
335#386—31no—
336#386—91no—
337#386—91no—
338#379—91no—
339C24×C3—31no—
340C24×C3—31no—
341C24×C3—31no—
342C24×C3—31no—
343C23×D3—31no—
344C23×D3—31no—
345C23×D3—61no—
346C23×D3—62no—
347C23×D3—62no—
348C23×D3—62no—
349C23×D3—62no—
350C23×D3—62no—
351C23×D3—62no—
352C23×D3—121no—
353C23×D3—121no—
354C23×D3—121no—
355C23×D3—121no—
356C23×D3—121no—
357C23×D3—121no—
358C23×D3—121no—
359C23×D3—121no—
360C23×D3C22×D311yescharacteristic
361C23×D3C22×D311yescharacteristic
362C23×D3C22×D311yescharacteristic
363C23×D3C22×D311yescharacteristic
364C2×C3×D4—34no—
365C2×C3×D4—62no—
366C2×C3×D4—62no—
367C2×C3×D4—121no—
368C2×C3×D4—121no—
369C2×C3×D4—121no—
370C22×C3×C4—21no—
371C22×C3×C4—21no—
372C22×C3×C4—21no—
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—62no—
378C22×C3×C4—62no—
379C22×C3×C4—121no—
380C22×C3×C4—121no—
381C22×C3×C4—121no—
382C22×C3×C4—121no—
383C22×C3×C4C22×D311yescharacteristic
384C22×C3×C4C22×D311yescharacteristic
385C22×C3×C4C22×D311yescharacteristic
386C22×C3×C4C22×D311yescharacteristic
387C22×C3×C4C22×D311yescharacteristic
388C22×C3×C4C22×D311yescharacteristic
389C2×#67—34no—
390C2×#67—62no—
391C2×#67—62no—
392C2×#67—62no—
393C2×#67—62no—
394C2×#67—62no—
395C2×#67—62no—
396C2×#67—62no—
397C2×#67—62no—
398C2×#67—62no—
399C2×#67—62no—
400C2×#67—62no—
401C2×#67—62no—
402C2×#67—62no—
403C2×#67—62no—
404C2×#67—121no—
405C2×#67—121no—
406C2×#67—121no—
407C2×#67—121no—
408C2×#67—121no—
409C2×#67—121no—
410C2×#67—121no—
411C2×#67—121no—
412C2×#67—121no—
413C22×Dic3—31no—
414C22×Dic3—31no—
415C22×Dic3—31no—
416C22×Dic3—31no—
417C22×Dic3—31no—
418C22×Dic3—31no—
419C22×Dic3—61no—
420C22×Dic3—61no—
421C22×Dic3—61no—
422C22×Dic3C22×D311yescharacteristic
423C22×Dic3C22×D311yescharacteristic
424C22×Dic3C22×D311yescharacteristic
425C22×Dic3C22×D311yescharacteristic
426C2×D12—22no—
427C2×D12—22no—
428C2×D12—34no—
429C2×D12—41no—
430C2×D12—41no—
431C2×D12—41no—
432C2×D12—62no—
433C2×D12—62no—
434C2×D12—121no—
435C2×D12—121no—
436C2×D12—121no—
437C2×D12D1214yescomplemented
438C2×C4×D3—22no—
439C2×C4×D3—22no—
440C2×C4×D3—41no—
441C2×C4×D3—41no—
442C2×C4×D3—41no—
443C2×C4×D3—41no—
444C3×C22⋊C4—62no—
445C3×C22⋊C4—62no—
446C3×C22⋊C4—62no—
447C3×C22⋊C4—121no—
448C3×C22⋊C4—121no—
449C3×C22⋊C4—121no—
450#217—62no—
451#217—62no—
452#217—62no—
453#217—62no—
454#217—121no—
455#217—121no—
456(C2×D3)⋊C4—22no—
457(C2×D3)⋊C4—22no—
458(C2×D3)⋊C4—22no—
459(C2×D3)⋊C4—41no—
460(C2×D3)⋊C4—41no—
461(C2×D3)⋊C4—41no—
462(C2×D3)⋊C4—62no—
463(C2×D3)⋊C4—62no—
464(C2×D3)⋊C4—62no—
465(C2×D3)⋊C4—62no—
466(C2×D3)⋊C4—62no—
467(C2×D3)⋊C4—62no—
468(C2×D3)⋊C4—62no—
469(C2×D3)⋊C4—62no—
470(C2×D3)⋊C4—62no—
471(C2×D3)⋊C4—62no—
472(C2×D3)⋊C4—122no—
473(C2×D3)⋊C4—122no—
474(C2×D3)⋊C4—122no—
475(C2×D3)⋊C4—121no—
476(C2×D3)⋊C4—121no—
477(C2×D3)⋊C4—121no—
478(C2×D3)⋊C4—121no—
479C4⋊Dic3—62no—
480C4⋊Dic3—62no—
481C4⋊Dic3—62no—
482C4⋊Dic3—122no—
483C4⋊Dic3—121no—
484Dic3⋊C4—62no—
485Dic3⋊C4—121no—
486C22×C32C22×D411yescharacteristic
487C22×C32C22×D411yescharacteristic
488C22×C32C2×#4111yescharacteristic
489C22×C32H(5,𝔽2)11yescharacteristic
490C22×C32H(5,𝔽2)11yescharacteristic
491C22×C32H(5,𝔽2)11yescharacteristic
492C22×C32H(5,𝔽2)11yescharacteristic
493C2×C3⋊D3—22no—
494C2×C3⋊D3—22no—
495C2×C3⋊D3—22no—
496C2×C3⋊D3—41no—
497C2×C3⋊D3—41no—
498C2×C3⋊D3—41no—
499C2×C3⋊D3—41no—
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—22no—
508C2×C3×D3—22no—
509C2×C3×D3—22no—
510C2×C3×D3—22no—
511C2×C3×D3—22no—
512C2×C3×D3—41no—
513C2×C3×D3—41no—
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—41no—
527C2×C3×D3—41no—
528D32—416no—
529C32×C4—22no—
530C32×C4—41no—
531C32×C4—41no—
532C3⋊Dic3—41no—
533C3⋊Dic3—41no—
534C3⋊Dic3—41no—
535C3×Dic3—22no—
536C3×Dic3—41no—
537C3×Dic3—41no—
538C3×Dic3—41no—
539C25—91no—
540C22×D4—31no—
541C22×D4—31no—
542C22×D4—91no—
543C22×D4—91no—
544C22×D4—91no—
545C22×D4—91no—
546C22×D4—91no—
547C23×C4—31no—
548C23×C4—31no—
549#121—184no—
550#121—184no—
551#120—184no—
552#120—184no—
553C2×C4⋊C4—91no—
554C2×C4⋊C4—91no—
555C2×C4⋊C4—91no—
556C2×C22⋊C4—31no—
557C2×C22⋊C4—31no—
558C2×C22⋊C4—31no—
559C2×C22⋊C4—31no—
560C2×C22⋊C4—31no—
561C2×C22⋊C4—31no—
562C2×C22⋊C4—91no—
563C2×C22⋊C4—91no—
564C2×C22⋊C4—91no—
565C2×C22⋊C4—91no—
566C2×C22⋊C4—91no—
567C2×C22⋊C4—91no—
568C2×C22⋊C4—91no—
569C2×C22⋊C4—91no—
570C2×C22⋊C4—91no—
571C2×C22⋊C4—91no—
572#95—31no—
573#95—31no—
574#95—91no—
575#95—91no—
576#95—91no—
577#95D3211yescharacteristic, complemented
578C23×C3—21no—
579C23×C3—32no—
580C23×C3—32no—
581C23×C3—32no—
582C23×C3—32no—
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×C3—61no—
592C23×C3—61no—
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×C3—61no—
606C23×C3—61no—
607C23×C3C23×D311yescharacteristic
608C23×C3C23×D311yescharacteristic
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—21no—
620C22×D3—21no—
621C22×D3—21no—
622C22×D3—21no—
623C22×D3—21no—
624C22×D3—21no—
625C22×D3—21no—
626C22×D3—21no—
627C22×D3—21no—
628C22×D3—21no—
629C22×D3—21no—
630C22×D3—21no—
631C22×D3—21no—
632C22×D3—21no—
633C22×D3—32no—
634C22×D3—32no—
635C22×D3—62no—
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—121no—
649C22×D3—121no—
650C22×D3—121no—
651C22×D3—121no—
652C22×D3—121no—
653C22×D3—121no—
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—124no—
664C22×D3—124no—
665C22×D3—124no—
666C22×D3—124no—
667C22×D3—124no—
668C22×D3C2×D1212yes—
669C22×D3C2×D1212yes—
670C22×D3#23512yes—
671C22×D3D3×D412yes—
672C3×D4—124no—
673C3×D4—124no—
674C2×C3×C4—21no—
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—21no—
682C2×C3×C4—21no—
683C2×C3×C4—21no—
684C2×C3×C4—21no—
685C2×C3×C4—21no—
686C2×C3×C4—21no—
687C2×C3×C4—21no—
688C2×C3×C4—21no—
689C2×C3×C4—21no—
690C2×C3×C4—22no—
691C2×C3×C4—32no—
692C2×C3×C4—41no—
693C2×C3×C4—41no—
694C2×C3×C4—41no—
695C2×C3×C4—41no—
696C2×C3×C4—41no—
697C2×C3×C4—41no—
698C2×C3×C4—41no—
699C2×C3×C4—41no—
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—61no—
708C2×C3×C4—61no—
709C2×C3×C4—61no—
710C2×C3×C4—61no—
711C2×C3×C4—124no—
712C2×C3×C4—124no—
713C2×C3×C4C2×D1212yes—
714C2×C3×C4D3×D412yes—
715#67—124no—
716#67—124no—
717#67—124no—
718#67—124no—
719#67—124no—
720#67—124no—
721#67—124no—
722#67—124no—
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—61no—
735C2×Dic3—61no—
736C2×Dic3—61no—
737C2×Dic3—61no—
738C2×Dic3—61no—
739C2×Dic3—61no—
740C2×Dic3—61no—
741C2×Dic3—61no—
742C2×Dic3—61no—
743C2×Dic3—61no—
744C2×Dic3—61no—
745C2×Dic3—61no—
746C2×Dic3—61no—
747C2×Dic3—61no—
748C2×Dic3—61no—
749C2×Dic3—61no—
750C2×Dic3—61no—
751C2×Dic3—61no—
752C2×Dic3—121no—
753C2×Dic3—121no—
754C2×Dic3—121no—
755C2×Dic3—121no—
756C2×Dic3—121no—
757C2×Dic3—121no—
758C2×Dic3—121no—
759C2×Dic3—121no—
760C2×Dic3—121no—
761C2×Dic3D3×D412yes—
762D12—44no—
763D12—44no—
764D12—124no—
765D12—124no—
766C4×D3—44no—
767C4×D3—44no—
768C2×C32#53411yescharacteristic
769C2×C32#53411yescharacteristic
770C2×C32#53811yescharacteristic
771C2×C32D4211yescharacteristic
772C2×C32#54611yescharacteristic
773C2×C32#54611yescharacteristic
774C2×C32#56011yescharacteristic
775C3⋊D3—42no—
776C3×D3—42no—
777C3×D3—42no—
778C3×D3—42no—
779C3×D3—42no—
780C24—31no—
781C24—31no—
782C24—31no—
783C24—31no—
784C24—91no—
785C24—182no—
786C24—182no—
787C24—182no—
788C24—361no—
789C24—361no—
790C24—361no—
791C24—361no—
792C2×D4—34no—
793C2×D4—62no—
794C2×D4—62no—
795C2×D4—94no—
796C2×D4—121no—
797C2×D4—121no—
798C2×D4—121no—
799C2×D4—182no—
800C2×D4—182no—
801C2×D4—182no—
802C2×D4—182no—
803C2×D4—182no—
804C2×D4—182no—
805C2×D4—182no—
806C2×D4—182no—
807C2×D4—361no—
808C2×D4—361no—
809C2×D4—361no—
810C2×D4—361no—
811C2×D4—361no—
812C2×D4—361no—
813C22×C4—31no—
814C22×C4—31no—
815C22×C4—31no—
816C22×C4—31no—
817C22×C4—62no—
818C22×C4—62no—
819C22×C4—91no—
820C22×C4—91no—
821C22×C4—91no—
822C22×C4—121no—
823C22×C4—121no—
824C22×C4—121no—
825C22×C4—121no—
826C22×C4C2×D3211yescharacteristic
827C22×C4C2×D3211yescharacteristic
828C22×C4C2×D3211yescharacteristic
829C4⋊C4—182no—
830C4⋊C4—182no—
831C4⋊C4—361no—
832C22⋊C4—62no—
833C22⋊C4—62no—
834C22⋊C4—62no—
835C22⋊C4—121no—
836C22⋊C4—121no—
837C22⋊C4—121no—
838C22⋊C4—182no—
839C22⋊C4—182no—
840C22⋊C4—182no—
841C22⋊C4—182no—
842C22⋊C4—182no—
843C22⋊C4—182no—
844C22⋊C4—182no—
845C22⋊C4—361no—
846C22⋊C4—361no—
847C22⋊C4—361no—
848C22×C3—21no—
849C22×C3—21no—
850C22×C3—21no—
851C22×C3—21no—
852C22×C3—21no—
853C22×C3—21no—
854C22×C3—21no—
855C22×C3—62no—
856C22×C3—62no—
857C22×C3—62no—
858C22×C3—62no—
859C22×C3—62no—
860C22×C3—62no—
861C22×C3—62no—
862C22×C3—62no—
863C22×C3—62no—
864C22×C3—62no—
865C22×C3—62no—
866C22×C3—62no—
867C22×C3—121no—
868C22×C3—121no—
869C22×C3—121no—
870C22×C3—121no—
871C22×C3—121no—
872C22×C3—121no—
873C22×C3—121no—
874C22×C3—121no—
875C22×C3—121no—
876C22×C3—121no—
877C22×C3—121no—
878C22×C3—121no—
879C22×C3—121no—
880C22×C3—121no—
881C22×C3—121no—
882C22×C3—121no—
883C22×C3C22×D1211yescharacteristic
884C22×C3C2×#23511yescharacteristic
885C22×C3C2×D3×D411yescharacteristic
886C22×C3C2×D3×D411yescharacteristic
887C22×C3C2×D3×D411yescharacteristic
888C22×C3#100411yescharacteristic
889C22×C3#100411yescharacteristic
890C22×C3#100411yescharacteristic
891C22×C3#100411yescharacteristic
892C22×C3#100411yescharacteristic
893C22×C3D3×#4111yescharacteristic
894C22×C3#100911yescharacteristic
895C22×C3#100911yescharacteristic
896C22×C3#100911yescharacteristic
897C2×D3—22no—
898C2×D3—22no—
899C2×D3—22no—
900C2×D3—22no—
901C2×D3—22no—
902C2×D3—22no—
903C2×D3—22no—
904C2×D3—22no—
905C2×D3—22no—
906C2×D3—22no—
907C2×D3—22no—
908C2×D3—22no—
909C2×D3—41no—
910C2×D3—41no—
911C2×D3—41no—
912C2×D3—41no—
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—41no—
922C2×D3—41no—
923C2×D3—41no—
924C2×D3—41no—
925C2×D3—62no—
926C2×D3—62no—
927C2×D3—62no—
928C2×D3—62no—
929C2×D3—62no—
930C2×D3—62no—
931C2×D3—122no—
932C2×D3—122no—
933C2×D3—122no—
934C2×D3—1216no—
935C2×D3—1216no—
936C2×D3—121no—
937C2×D3—121no—
938C2×D3—121no—
939C2×D3—121no—
940C2×D3—121no—
941C2×D3—121no—
942C2×D3—121no—
943C2×D3—121no—
944C2×D3—241no—
945C2×D3—241no—
946C2×D3—241no—
947C2×D3—241no—
948C3×C4—22no—
949C3×C4—22no—
950C3×C4—42no—
951C3×C4—41no—
952C3×C4—41no—
953C3×C4—41no—
954C3×C4—41no—
955C3×C4—62no—
956C3×C4—81no—
957C3×C4—81no—
958C3×C4—121no—
959C3×C4—121no—
960C3×C4—121no—
961Dic3—22no—
962Dic3—41no—
963Dic3—41no—
964Dic3—41no—
965Dic3—121no—
966Dic3—121no—
967Dic3—121no—
968Dic3—121no—
969Dic3—121no—
970Dic3—121no—
971Dic3—241no—
972Dic3—241no—
973Dic3—241no—
974C32#266811yescharacteristic, complemented, Sylow
975C23—32no—
976C23—32no—
977C23—32no—
978C23—32no—
979C23—61no—
980C23—61no—
981C23—61no—
982C23—61no—
983C23—61no—
984C23—61no—
985C23—61no—
986C23—61no—
987C23—61no—
988C23—61no—
989C23—61no—
990C23—61no—
991C23—61no—
992C23—61no—
993C23—61no—
994C23—61no—
995C23—61no—
996C23—61no—
997C23—61no—
998C23—61no—
999C23—61no—
1000C23—61no—
1001C23—61no—
1002C23—61no—
1003C23—92no—
1004C23—181no—
1005C23—181no—
1006C23—181no—
1007C23—181no—
1008C23—181no—
1009C23—181no—
1010C23—364no—
1011C23—364no—
1012C23—364no—
1013C23—364no—
1014C23—364no—
1015C23—364no—
1016C23—364no—
1017C23C22×D3211yescharacteristic
1018D4—124no—
1019D4—124no—
1020D4—364no—
1021D4—364no—
1022D4—364no—
1023D4—364no—
1024D4—364no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—32no—
1034C2×C4—61no—
1035C2×C4—61no—
1036C2×C4—61no—
1037C2×C4—61no—
1038C2×C4—61no—
1039C2×C4—61no—
1040C2×C4—61no—
1041C2×C4—61no—
1042C2×C4—61no—
1043C2×C4—61no—
1044C2×C4—61no—
1045C2×C4—124no—
1046C2×C4—124no—
1047C2×C4—181no—
1048C2×C4—181no—
1049C2×C4—181no—
1050C2×C4—181no—
1051C2×C4—181no—
1052C2×C4—181no—
1053C2×C4—181no—
1054C2×C4—181no—
1055C2×C4—181no—
1056C2×C4D3×D1212yes—
1057C2×C3—21no—
1058C2×C3—21no—
1059C2×C3—21no—
1060C2×C3—21no—
1061C2×C3—21no—
1062C2×C3—21no—
1063C2×C3—21no—
1064C2×C3—122no—
1065C2×C3—122no—
1066C2×C3—122no—
1067C2×C3—122no—
1068C2×C3#549011yescharacteristic
1069C2×C3#549311yescharacteristic
1070C2×C3D4×D1211yescharacteristic
1071C2×C3#555011yescharacteristic
1072C2×C3#555411yescharacteristic
1073C2×C3#556011yescharacteristic
1074C2×C3#558911yescharacteristic
1075C2×C3#558911yescharacteristic
1076C2×C3#560511yescharacteristic
1077C2×C3#560911yescharacteristic
1078C2×C3#561211yescharacteristic
1079C2×C3#562011yescharacteristic
1080C2×C3#565711yescharacteristic
1081C2×C3#566611yescharacteristic
1082D3—42no—
1083D3—42no—
1084D3—42no—
1085D3—42no—
1086D3—122no—
1087D3—122no—
1088D3—242no—
1089C22—62no—
1090C22—62no—
1091C22—62no—
1092C22—62no—
1093C22—62no—
1094C22—62no—
1095C22—62no—
1096C22—62no—
1097C22—62no—
1098C22—62no—
1099C22—62no—
1100C22—62no—
1101C22—121no—
1102C22—121no—
1103C22—121no—
1104C22—121no—
1105C22—121no—
1106C22—121no—
1107C22—121no—
1108C22—121no—
1109C22—121no—
1110C22—121no—
1111C22—121no—
1112C22—121no—
1113C22—121no—
1114C22—121no—
1115C22—121no—
1116C22—121no—
1117C22—182no—
1118C22—182no—
1119C22—182no—
1120C22—3616no—
1121C22—361no—
1122C22—361no—
1123C22—361no—
1124C22—361no—
1125C22C2×D3×D1211yescharacteristic
1126C22D3×#23511yescharacteristic
1127C22#6430711yescharacteristic
1128C22D32×D411yescharacteristic
1129C22#6431311yescharacteristic
1130C22#6431311yescharacteristic
1131C22#6432011yescharacteristic
1132C4—22no—
1133C4—41no—
1134C4—41no—
1135C4—62no—
1136C4—121no—
1137C4—121no—
1138C4—121no—
1139C4—361no—
1140C4—361no—
1141C4—361no—
1142C3—21no—
1143C3#7491011yescharacteristic, complemented
1144C3#7491111yescharacteristic, complemented
1145C2—122no—
1146C2—122no—
1147C2—122no—
1148C2—122no—
1149C2—362no—
1150C2#1059400311yescharacteristic
1151C2#1059426311yescharacteristic
1152C2#1059427811yescharacteristic
1153C2#1059429011yescharacteristic
1154C2#1059462111yescharacteristic
1155C2#1059463911yescharacteristic
1156C2#1059466211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
hypercenter#95D32
hypocenterC32#2668
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. C2×#63922C2semidirect
2. C2×#63922C2semidirect
3. C2×#63908C2semidirect
4. C2×#63906C2semidirect
5. #10592373C2semidirect
6. C3×#4665C2semidirect
7. C3×#4665C2semidirect
8. #10591399C2semidirect
9. #10591390C2semidirect
10. #10591389C2semidirect
11. #10591382C2semidirect
12. #10591381C2semidirect
13. #10591317C2semidirect
14. #10591312C2semidirect
15. #10591297C2semidirect
21. C22×C3×C4×D3C22semidirect
22. C22×C3×C4×D3C22semidirect
27. C22×#625C22semidirect
31. C2×C4⋊(C3⋊Dic3)C22semidirect
36. C2×C3×(C2×D3)⋊C4C22semidirect
37. C2×C3×(C2×D3)⋊C4C22semidirect
38. C2×Dic3⋊Dic3C22semidirect
39. C2×Dic3⋊Dic3C22semidirect
45. C2×(C2×D3)⋊Dic3C22semidirect
46. C2×(C2×D3)⋊Dic3C22semidirect
51. C32×#95C22semidirect
52. #63658C22semidirect
53. #63658C22semidirect
54. C3×C3⋊#95C22semidirect
55. C3×C3⋊#95C22semidirect
56. #63579C22semidirect
86. #4665D3semidirect
87. #4665D3semidirect
115. C2×C3×D12D4semidirect
127. C2×#626D4semidirect
175. C22×C4×D3C2×D3semidirect
176. C22×C4×D3C2×D3semidirect
215. C2×(C2×D3)⋊C4C2×D3semidirect
216. C2×(C2×D3)⋊C4C2×D3semidirect
230. C3×#95C2×D3semidirect
231. C3×#95C2×D3semidirect
240. C3⋊#95C2×D3semidirect
241. C3⋊#95C2×D3semidirect
437. C2×D12D12semidirect
577. #95D32semidirect
974. C32#2668semidirect
1143. C3#74910semidirect
1144. C3#74911semidirect

Maximal subgroups

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

subgroupindex
C2×#639222
C2×#639082
C2×#639062
#105923732
C3×#46652
#105913992
#105913902
#105913892
#105913822
#105913812
#105913172
#105913122
#105912972
#749113
#749103