Finite Group Databasebeta

← #11836000

Subgroups — #11836000

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×#64093C211yesmaximal, characteristic, complemented
2C2×#63983C211yesmaximal, characteristic, complemented
3C2×#63978C211yesmaximal, characteristic, complemented
4C2×#63923C211yesmaximal, characteristic, complemented
5C3×#4959C211yesmaximal, characteristic, complemented
6C3×#4958C211yesmaximal, characteristic, complemented
7#10591724C211yesmaximal, characteristic, complemented
8#10591711C211yesmaximal, characteristic, complemented
9#10591399C211yesmaximal, characteristic, complemented
10#10591387C211yesmaximal, characteristic, complemented
11#10591387C211yesmaximal, characteristic, complemented
12#10591321C211yesmaximal, characteristic, complemented
13#10591303C211yesmaximal, characteristic, complemented
14#10591298C211yesmaximal, characteristic, complemented
15#10591208C211yesmaximal, characteristic, complemented
16#77127—31nomaximal
17#74911—31nomaximal
18C23×D32C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×#638C2211yescharacteristic, complemented
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic, complemented
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C23×C3×Dic3C2211yescharacteristic, complemented
26C22×#626C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic, complemented
29C2×#3752C2211yescharacteristic
30C2×#3750C2211yescharacteristic, complemented
31#64093—24no—
32C2×C3×#217C2211yescharacteristic, complemented
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
38#63983—24no—
39#63978—24no—
40C2×Dic3⋊Dic3C2211yescharacteristic, complemented
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×#3722C2211yescharacteristic, complemented
45C2×#3722C2211yescharacteristic, complemented
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×(C2×D3)⋊Dic3C2211yescharacteristic
50#63923—24no—
51C3×C3⋊#95C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×#939—31no—
58C2×#937—31no—
59C2×#937—31no—
60C2×#930—31no—
61C2×#884—31no—
62C2×#884—31no—
63C2×#884—61no—
64C2×#882—31no—
65C2×#882—31no—
66C3×#394—31no—
67C3×#386—31no—
68#5223—31no—
69#5213—31no—
70#4993—31no—
71#4991—31no—
72#4960—31no—
73#4959D311yescharacteristic, complemented
74#4958—31no—
75#4958D311yescharacteristic, complemented
76#4956—31no—
77#4956—31no—
78#4955—31no—
79#4955—31no—
80#4952—31no—
81#4949—31no—
82#4675—31no—
83#4675—31no—
84#4674—31no—
85#4672—31no—
86#4665—31no—
87#4665—31no—
88C24×C32C2311yescharacteristic
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
102C2×#638—22no—
103C2×#638—22no—
104C2×#638—41no—
105C2×#638—41no—
106C2×#638—41no—
107C2×#638D414yescomplemented
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C2×C4⋊(C3⋊D3)—22no—
111C2×C4⋊(C3⋊D3)—22no—
112C2×C4⋊(C3⋊D3)—41no—
113C2×C4×C3⋊D3—22no—
114C2×C4×C3⋊D3—41no—
115C2×C4×C3⋊D3—41no—
116C2×C3×#67—22no—
117C2×C3×#67—22no—
118C2×C3×#67—22no—
119C2×C3×#67—22no—
120C2×C3×#67—41no—
121C2×C3×#67—41no—
122C22×C3×Dic3—22no—
123C22×C3×Dic3—41no—
124C22×C3×Dic3—41no—
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C2×#626—22no—
132C2×#626—22no—
133C2×#626—41no—
134C2×#626—41no—
135C2×#626—41no—
136C2×#626D414yescomplemented
137C32×C22⋊C4—22no—
138#3752—22no—
139#3750—22no—
140C3×#217—41no—
141C3×(C2×D3)⋊C4—22no—
142C3×(C2×D3)⋊C4—22no—
143C3×(C2×D3)⋊C4—41no—
144C3×(C2×D3)⋊C4—41no—
145C3×Dic3⋊C4—41no—
146Dic3⋊Dic3—22no—
147#3722—22no—
148#3722—22no—
149#3722—22no—
150#3722—41no—
151#3722—41no—
152(C2×D3)⋊Dic3—22no—
153(C2×D3)⋊Dic3—22no—
154(C2×D3)⋊Dic3—22no—
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—
162C22×#67—31no—
163C22×#67—31no—
164C22×#67—31no—
165C22×#67—31no—
166C22×#67—31no—
167C22×#67—31no—
168C22×#67—61no—
169C22×#67—61no—
170C22×#67C2×D311yescharacteristic
171C22×#67C2×D311yescharacteristic
172C23×Dic3C2×D311yescharacteristic, complemented
173C22×D12—31no—
174C22×D12—31no—
175C22×D12—31no—
176C22×D12—31no—
177C22×D12—61no—
178C22×C4×D3—31no—
179C22×C4×D3—31no—
180C22×C4×D3—61no—
181C2×C3×C4⋊C4—31no—
182C2×C3×C22⋊C4—21no—
183C2×C3×C22⋊C4—31no—
184C2×C3×C22⋊C4—31no—
185C2×C3×C22⋊C4—31no—
186C2×C3×C22⋊C4—31no—
187C2×C3×C22⋊C4—31no—
188C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
189C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
190C2×#217—31no—
191C2×#217—31no—
192C2×#217—31no—
193C2×#217—31no—
194C2×#217C2×D311yescharacteristic, complemented
195#939—64no—
196#937—64no—
197#937—64no—
198#930—64no—
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—31no—
213C2×(C2×D3)⋊C4—31no—
214C2×(C2×D3)⋊C4—31no—
215C2×(C2×D3)⋊C4—61no—
216C2×(C2×D3)⋊C4C2×D311yescharacteristic
217C2×(C2×D3)⋊C4C2×D311yescharacteristic
218C2×(C2×D3)⋊C4C2×D311yescharacteristic
219C2×(C2×D3)⋊C4C2×D311yescharacteristic
220C2×C4⋊Dic3—31no—
221C2×Dic3⋊C4—31no—
222C2×Dic3⋊C4—31no—
223C2×Dic3⋊C4—31no—
224C2×Dic3⋊C4—61no—
225C2×Dic3⋊C4C2×D311yescharacteristic, complemented
226#884—64no—
227#884—64no—
228#884—68no—
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⋊#95—31no—
240C3⋊#95C2×D311yescharacteristic, complemented
241C3⋊#95C2×D311yescharacteristic, complemented
242C3⋊#95C2×D311yescharacteristic, complemented
243C23×C32—21no—
244C23×C32—21no—
245C23×C32—21no—
246C23×C32—21no—
247C23×C32—21no—
248C23×C32—21no—
249C23×C32C2×D412yes—
250C23×C32C2411yescharacteristic
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⋊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—
292#638—44no—
293#638—44no—
294C2×C3⋊Dic3—21no—
295C2×C3⋊Dic3—21no—
296C2×C3⋊Dic3—21no—
297C2×C3⋊Dic3—21no—
298C2×C3⋊Dic3—21no—
299C2×C3⋊Dic3C2×D412yes—
300C4⋊(C3⋊D3)—44no—
301C4×C3⋊D3—44no—
302C3×#67—44no—
303C3×#67—44no—
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×Dic3—21no—
320C2×C3×Dic3—21no—
321C2×C3×Dic3—44no—
322C2×C3×Dic3C2×D412yes—
323#626—44no—
324#626—44no—
325C2×#121—91no—
326C2×#121—91no—
327C2×#120—91no—
328C2×#120—91no—
329#399—91no—
330#397—91no—
331#397—91no—
332#394—31no—
333#394—91no—
334#392—91no—
335#386—31no—
336#386—91no—
337#386—91no—
338#386—91no—
339#379—91no—
340C24×C3—21no—
341C24×C3—31no—
342C24×C3—31no—
343C24×C3C22×D311yescharacteristic
344C24×C3C22×D311yescharacteristic
345C23×D3—31no—
346C23×D3—31no—
347C23×D3—31no—
348C23×D3—31no—
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
367C2×C3×D4—62no—
368C2×C3×D4—62no—
369C2×C3×D4—62no—
370C2×C3×D4—62no—
371C2×C3×D4—121no—
372C2×C3×D4—121no—
373C22×C3×C4—21no—
374C22×C3×C4—21no—
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—62no—
382C22×C3×C4—121no—
383C22×C3×C4—121no—
384C22×C3×C4C22×D311yescharacteristic
385C22×C3×C4C22×D311yescharacteristic
386C22×C3×C4C22×D311yescharacteristic
387C22×C3×C4C22×D311yescharacteristic
388C2×#67—22no—
389C2×#67—22no—
390C2×#67—22no—
391C2×#67—22no—
392C2×#67—34no—
393C2×#67—34no—
394C2×#67—34no—
395C2×#67—41no—
396C2×#67—41no—
397C2×#67—64no—
398C2×#67—62no—
399C2×#67—62no—
400C2×#67—62no—
401C2×#67—62no—
402C2×#67—64no—
403C2×#67—62no—
404C2×#67—62no—
405C2×#67—122no—
406C2×#67—121no—
407C2×#67—121no—
408C2×#67—121no—
409C2×#67—121no—
410C2×#67—121no—
411C2×#67—121no—
412C2×#67—121no—
413C2×#67—121no—
414C2×#67—121no—
415C2×#67—122no—
416C2×#67—122no—
417C2×#67—122no—
418C22×Dic3—22no—
419C22×Dic3—31no—
420C22×Dic3—31no—
421C22×Dic3—31no—
422C22×Dic3—31no—
423C22×Dic3—41no—
424C22×Dic3—41no—
425C22×Dic3—61no—
426C22×Dic3—61no—
427C22×Dic3C22×D311yescharacteristic
428C22×Dic3C22×D311yescharacteristic
429C22×Dic3C22×D311yescharacteristic
430C22×Dic3C22×D311yescharacteristic
431C22×Dic3C22×D311yescharacteristic
432C22×Dic3C22×D311yescharacteristic
433C2×D12—34no—
434C2×D12—62no—
435C2×D12—62no—
436C2×D12—62no—
437C2×D12—62no—
438C2×D12—64no—
439C2×D12—62no—
440C2×D12—62no—
441C2×D12—122no—
442C2×D12—121no—
443C2×D12—121no—
444C2×D12—122no—
445C2×D12—121no—
446C2×D12—121no—
447C2×D12—121no—
448C2×C4×D3—62no—
449C2×C4×D3—62no—
450C2×C4×D3—64no—
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—121no—
458C3×C22⋊C4—24no—
459C3×C22⋊C4—22no—
460C3×C22⋊C4—22no—
461C3×C22⋊C4—62no—
462C3×C22⋊C4—62no—
463C3×C22⋊C4—121no—
464C3×C22⋊C4—121no—
465C3×C22⋊C4—121no—
466#217—41no—
467#217—62no—
468#217—62no—
469#217—62no—
470#217—121no—
471(C2×D3)⋊C4—22no—
472(C2×D3)⋊C4—22no—
473(C2×D3)⋊C4—41no—
474(C2×D3)⋊C4—41no—
475(C2×D3)⋊C4—62no—
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—64no—
485(C2×D3)⋊C4—62no—
486(C2×D3)⋊C4—62no—
487(C2×D3)⋊C4—121no—
488(C2×D3)⋊C4—121no—
489(C2×D3)⋊C4—121no—
490(C2×D3)⋊C4—121no—
491(C2×D3)⋊C4—121no—
492C4⋊Dic3—62no—
493Dic3⋊C4—41no—
494Dic3⋊C4—62no—
495Dic3⋊C4—62no—
496Dic3⋊C4—64no—
497Dic3⋊C4—62no—
498C22×C32—22no—
499C22×C32—22no—
500C22×C32—22no—
501C22×C32—41no—
502C22×C32—41no—
503C22×C32—41no—
504C22×C32—41no—
505C22×C32C22×D411yescharacteristic
506C22×C32C22×D411yescharacteristic
507C22×C32C2×#4111yescharacteristic
508C22×C32H(5,𝔽2)11yescharacteristic
509C22×C32H(5,𝔽2)11yescharacteristic
510C22×C32H(5,𝔽2)11yescharacteristic
511C22×C32H(5,𝔽2)11yescharacteristic
512C2×C3⋊D3—22no—
513C2×C3⋊D3—22no—
514C2×C3⋊D3—22no—
515C2×C3⋊D3—22no—
516C2×C3⋊D3—22no—
517C2×C3⋊D3—22no—
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—41no—
542C32×C4—41no—
543C3⋊Dic3—22no—
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—31no—
553C22×D4—31no—
554C22×D4—91no—
555C22×D4—91no—
556C22×D4—91no—
557C22×D4—91no—
558C22×D4—91no—
559C23×C4—31no—
560C23×C4—91no—
561#121—184no—
562#121—184no—
563#120—184no—
564#120—184no—
565C2×C4⋊C4—31no—
566C2×C4⋊C4—91no—
567C2×C4⋊C4—91no—
568C2×C22⋊C4—31no—
569C2×C22⋊C4—31no—
570C2×C22⋊C4—31no—
571C2×C22⋊C4—31no—
572C2×C22⋊C4—31no—
573C2×C22⋊C4—91no—
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⋊C4D3211yescharacteristic, complemented
584#95—31no—
585#95—31no—
586#95—31no—
587#95—91no—
588#95—91no—
589#95—91no—
590C23×C3—21no—
591C23×C3—21no—
592C23×C3—21no—
593C23×C3—21no—
594C23×C3—21no—
595C23×C3—21no—
596C23×C3—21no—
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—21no—
600C23×C3—21no—
601C23×C3—21no—
602C23×C3—21no—
603C23×C3—22no—
604C23×C3—32no—
605C23×C3—32no—
606C23×C3—41no—
607C23×C3—41no—
608C23×C3—41no—
609C23×C3—41no—
610C23×C3—41no—
611C23×C3—41no—
612C23×C3—61no—
613C23×C3—61no—
614C23×C3—61no—
615C23×C3—61no—
616C23×C3—61no—
617C23×C3—61no—
618C23×C3—61no—
619C23×C3—61no—
620C23×C3—61no—
621C23×C3—61no—
622C23×C3—61no—
623C23×C3—61no—
624C23×C3D3×D412yes—
625C23×C3D3×D412yes—
626C23×C3C23×D311yescharacteristic
627C23×C3C23×D311yescharacteristic
628C22×D3—21no—
629C22×D3—21no—
630C22×D3—21no—
631C22×D3—21no—
632C22×D3—21no—
633C22×D3—21no—
634C22×D3—21no—
635C22×D3—21no—
636C22×D3—21no—
637C22×D3—21no—
638C22×D3—21no—
639C22×D3—21no—
640C22×D3—32no—
641C22×D3—32no—
642C22×D3—32no—
643C22×D3—32no—
644C22×D3—62no—
645C22×D3—62no—
646C22×D3—62no—
647C22×D3—62no—
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—61no—
667C22×D3—61no—
668C22×D3—61no—
669C22×D3—61no—
670C22×D3—61no—
671C22×D3—61no—
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×D3#23512yes—
697C22×D3D3×D412yes—
698C3×D4—124no—
699C3×D4—124no—
700C2×C3×C4—22no—
701C2×C3×C4—22no—
702C2×C3×C4—21no—
703C2×C3×C4—21no—
704C2×C3×C4—21no—
705C2×C3×C4—21no—
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—32no—
715C2×C3×C4—41no—
716C2×C3×C4—41no—
717C2×C3×C4—41no—
718C2×C3×C4—41no—
719C2×C3×C4—61no—
720C2×C3×C4—61no—
721C2×C3×C4—61no—
722C2×C3×C4—61no—
723C2×C3×C4—61no—
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—124no—
737#67—44no—
738#67—44no—
739#67—124no—
740#67—124no—
741#67—124no—
742#67—124no—
743#67—128no—
744#67—124no—
745#67—124no—
746#67—128no—
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—32no—
765C2×Dic3—32no—
766C2×Dic3—44no—
767C2×Dic3—62no—
768C2×Dic3—62no—
769C2×Dic3—62no—
770C2×Dic3—61no—
771C2×Dic3—61no—
772C2×Dic3—61no—
773C2×Dic3—61no—
774C2×Dic3—62no—
775C2×Dic3—61no—
776C2×Dic3—61no—
777C2×Dic3—61no—
778C2×Dic3—61no—
779C2×Dic3—61no—
780C2×Dic3—61no—
781C2×Dic3—121no—
782C2×Dic3—121no—
783C2×Dic3D3×D412yes—
784D12—124no—
785D12—124no—
786D12—128no—
787D12—124no—
788D12—124no—
789C4×D3—128no—
790C4×D3—124no—
791C4×D3—124no—
792C2×C32—42no—
793C2×C32#53411yescharacteristic
794C2×C32#53411yescharacteristic
795C2×C32#53811yescharacteristic
796C2×C32D4211yescharacteristic
797C2×C32#54611yescharacteristic
798C2×C32#54611yescharacteristic
799C2×C32#56011yescharacteristic
800C3⋊D3—42no—
801C3⋊D3—42no—
802C3×D3—42no—
803C3×D3—42no—
804C24—31no—
805C24—31no—
806C24—91no—
807C24—91no—
808C24—182no—
809C24—182no—
810C24—182no—
811C24—361no—
812C24—361no—
813C24—361no—
814C24—361no—
815C24C2×D3211yescharacteristic
816C2×D4—62no—
817C2×D4—62no—
818C2×D4—62no—
819C2×D4—62no—
820C2×D4—94no—
821C2×D4—94no—
822C2×D4—121no—
823C2×D4—121no—
824C2×D4—182no—
825C2×D4—182no—
826C2×D4—182no—
827C2×D4—182no—
828C2×D4—182no—
829C2×D4—182no—
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—62no—
844C22×C4—91no—
845C22×C4—91no—
846C22×C4—121no—
847C22×C4—121no—
848C22×C4—182no—
849C22×C4—361no—
850C22×C4—361no—
851C22×C4C2×D3211yescharacteristic
852C22×C4C2×D3211yescharacteristic
853C4⋊C4—121no—
854C4⋊C4—182no—
855C4⋊C4—182no—
856C22⋊C4—22no—
857C22⋊C4—62no—
858C22⋊C4—62no—
859C22⋊C4—121no—
860C22⋊C4—121no—
861C22⋊C4—121no—
862C22⋊C4—182no—
863C22⋊C4—182no—
864C22⋊C4—182no—
865C22⋊C4—182no—
866C22⋊C4—182no—
867C22⋊C4—182no—
868C22⋊C4—182no—
869C22⋊C4—361no—
870C22⋊C4—361no—
871C22⋊C4—361no—
872C22×C3—22no—
873C22×C3—22no—
874C22×C3—22no—
875C22×C3—22no—
876C22×C3—22no—
877C22×C3—22no—
878C22×C3—21no—
879C22×C3—21no—
880C22×C3—21no—
881C22×C3—21no—
882C22×C3—21no—
883C22×C3—21no—
884C22×C3—21no—
885C22×C3—42no—
886C22×C3—42no—
887C22×C3—42no—
888C22×C3—41no—
889C22×C3—41no—
890C22×C3—41no—
891C22×C3—41no—
892C22×C3—41no—
893C22×C3—41no—
894C22×C3—41no—
895C22×C3—41no—
896C22×C3—62no—
897C22×C3—62no—
898C22×C3—62no—
899C22×C3—62no—
900C22×C3—62no—
901C22×C3—62no—
902C22×C3—81no—
903C22×C3—81no—
904C22×C3—81no—
905C22×C3—81no—
906C22×C3—121no—
907C22×C3—121no—
908C22×C3—121no—
909C22×C3—121no—
910C22×C3—121no—
911C22×C3—121no—
912C22×C3—121no—
913C22×C3—121no—
914C22×C3C2×#23511yescharacteristic
915C22×C3C2×D3×D411yescharacteristic
916C22×C3C2×D3×D411yescharacteristic
917C22×C3C2×D3×D411yescharacteristic
918C22×C3C2×D3×D411yescharacteristic
919C22×C3#100411yescharacteristic
920C22×C3#100411yescharacteristic
921C22×C3#100411yescharacteristic
922C22×C3#100411yescharacteristic
923C22×C3D3×#4111yescharacteristic
924C22×C3#100911yescharacteristic
925C22×C3#100911yescharacteristic
926C22×C3#100911yescharacteristic
927C22×C3#100911yescharacteristic
928C2×D3—22no—
929C2×D3—22no—
930C2×D3—22no—
931C2×D3—22no—
932C2×D3—22no—
933C2×D3—22no—
934C2×D3—41no—
935C2×D3—41no—
936C2×D3—41no—
937C2×D3—41no—
938C2×D3—41no—
939C2×D3—41no—
940C2×D3—41no—
941C2×D3—41no—
942C2×D3—64no—
943C2×D3—62no—
944C2×D3—62no—
945C2×D3—62no—
946C2×D3—62no—
947C2×D3—62no—
948C2×D3—62no—
949C2×D3—62no—
950C2×D3—62no—
951C2×D3—62no—
952C2×D3—62no—
953C2×D3—62no—
954C2×D3—62no—
955C2×D3—122no—
956C2×D3—122no—
957C2×D3—122no—
958C2×D3—122no—
959C2×D3—122no—
960C2×D3—1216no—
961C2×D3—1216no—
962C2×D3—122no—
963C2×D3—122no—
964C2×D3—122no—
965C2×D3—122no—
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—121no—
979C2×D3—121no—
980C2×D3—121no—
981C2×D3—121no—
982C2×D3—241no—
983C2×D3—241no—
984C2×D3—241no—
985C2×D3—241no—
986C3×C4—42no—
987C3×C4—42no—
988C3×C4—41no—
989C3×C4—41no—
990C3×C4—41no—
991C3×C4—41no—
992C3×C4—62no—
993C3×C4—121no—
994C3×C4—121no—
995C3×C4—121no—
996C3×C4—121no—
997C3×C4—121no—
998Dic3—22no—
999Dic3—41no—
1000Dic3—41no—
1001Dic3—41no—
1002Dic3—41no—
1003Dic3—41no—
1004Dic3—64no—
1005Dic3—62no—
1006Dic3—62no—
1007Dic3—122no—
1008Dic3—121no—
1009Dic3—121no—
1010C32#266811yescharacteristic, complemented, Sylow
1011C23—21no—
1012C23—21no—
1013C23—21no—
1014C23—21no—
1015C23—21no—
1016C23—21no—
1017C23—32no—
1018C23—32no—
1019C23—61no—
1020C23—61no—
1021C23—61no—
1022C23—61no—
1023C23—61no—
1024C23—61no—
1025C23—61no—
1026C23—61no—
1027C23—61no—
1028C23—61no—
1029C23—61no—
1030C23—61no—
1031C23—92no—
1032C23—92no—
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—364no—
1046C23—364no—
1047C23—364no—
1048C23—364no—
1049C23—364no—
1050C23—364no—
1051C23—364no—
1052C23#381112yes—
1053C23C22×D3211yescharacteristic
1054D4—124no—
1055D4—124no—
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—32no—
1068C2×C4—61no—
1069C2×C4—61no—
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—92no—
1086C2×C4—124no—
1087C2×C4—181no—
1088C2×C4—181no—
1089C2×C4—181no—
1090C2×C4—181no—
1091C2×C4—181no—
1092C2×C4—364no—
1093C2×C3—21no—
1094C2×C3—21no—
1095C2×C3—21no—
1096C2×C3—21no—
1097C2×C3—21no—
1098C2×C3—21no—
1099C2×C3—21no—
1100C2×C3—42no—
1101C2×C3—42no—
1102C2×C3—82no—
1103C2×C3—122no—
1104C2×C3—122no—
1105C2×C3#549011yescharacteristic
1106C2×C3#555011yescharacteristic
1107C2×C3#556011yescharacteristic
1108C2×C3#558911yescharacteristic
1109C2×C3#559011yescharacteristic
1110C2×C3#560511yescharacteristic
1111C2×C3#560511yescharacteristic
1112C2×C3#560911yescharacteristic
1113C2×C3#561011yescharacteristic
1114C2×C3#562011yescharacteristic
1115C2×C3#565311yescharacteristic
1116C2×C3#565411yescharacteristic
1117C2×C3#566611yescharacteristic
1118C2×C3#567811yescharacteristic
1119D3—42no—
1120D3—42no—
1121D3—124no—
1122D3—122no—
1123D3—122no—
1124D3—122no—
1125D3—122no—
1126D3—242no—
1127C22—22no—
1128C22—22no—
1129C22—22no—
1130C22—41no—
1131C22—41no—
1132C22—41no—
1133C22—41no—
1134C22—62no—
1135C22—62no—
1136C22—62no—
1137C22—62no—
1138C22—62no—
1139C22—62no—
1140C22—121no—
1141C22—121no—
1142C22—121no—
1143C22—121no—
1144C22—121no—
1145C22—121no—
1146C22—121no—
1147C22—121no—
1148C22—182no—
1149C22—182no—
1150C22—182no—
1151C22—182no—
1152C22—182no—
1153C22—182no—
1154C22—3616no—
1155C22—361no—
1156C22—361no—
1157C22—361no—
1158C22—361no—
1159C22—361no—
1160C22—361no—
1161C22—361no—
1162C22—361no—
1163C22D3×#23511yescharacteristic
1164C22#6430711yescharacteristic
1165C22D32×D411yescharacteristic
1166C22#6431411yescharacteristic
1167C22#6431411yescharacteristic
1168C22#6431411yescharacteristic
1169C22C2×#381111yescharacteristic
1170C4—41no—
1171C4—41no—
1172C4—62no—
1173C4—121no—
1174C4—121no—
1175C4—121no—
1176C4—121no—
1177C4—121no—
1178C4—182no—
1179C4—361no—
1180C3—21no—
1181C3#7491111yescharacteristic, complemented
1182C3#7712711yescharacteristic, complemented
1183C2—42no—
1184C2—122no—
1185C2—122no—
1186C2—362no—
1187C2—362no—
1188C2#1059426211yescharacteristic
1189C2#1059428311yescharacteristic
1190C2#1059429811yescharacteristic
1191C2#1059430811yescharacteristic
1192C2#1059507711yescharacteristic
1193C2#1059529211yescharacteristic
1194C2#1059530811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2668
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×#64093C2semidirect
2. C2×#63983C2semidirect
3. C2×#63978C2semidirect
4. C2×#63923C2semidirect
5. C3×#4959C2semidirect
6. C3×#4958C2semidirect
7. #10591724C2semidirect
8. #10591711C2semidirect
9. #10591399C2semidirect
10. #10591387C2semidirect
11. #10591387C2semidirect
12. #10591321C2semidirect
13. #10591303C2semidirect
14. #10591298C2semidirect
15. #10591208C2semidirect
20. C22×#638C22semidirect
22. C22×C4×C3⋊D3C22semidirect
25. C23×C3×Dic3C22semidirect
28. C2×C32×C22⋊C4C22semidirect
30. C2×#3750C22semidirect
32. C2×C3×#217C22semidirect
37. C2×C3×Dic3⋊C4C22semidirect
40. C2×Dic3⋊Dic3C22semidirect
44. C2×#3722C22semidirect
45. C2×#3722C22semidirect
51. C3×C3⋊#95C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
73. #4959D3semidirect
75. #4958D3semidirect
107. C2×#638D4semidirect
136. C2×#626D4semidirect
172. C23×Dic3C2×D3semidirect
188. C2×C3×C22⋊C4C2×D3semidirect
189. C2×C3×C22⋊C4C2×D3semidirect
194. C2×#217C2×D3semidirect
225. C2×Dic3⋊C4C2×D3semidirect
240. C3⋊#95C2×D3semidirect
241. C3⋊#95C2×D3semidirect
242. C3⋊#95C2×D3semidirect
583. C2×C22⋊C4D32semidirect
1010. C32#2668semidirect
1181. C3#74911semidirect
1182. C3#77127semidirect

Maximal subgroups

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

subgroupindex
C2×#640932
C2×#639832
C2×#639782
C2×#639232
C3×#49592
C3×#49582
#105917242
#105917112
#105913992
#105913872
#105913212
#105913032
#105912982
#105912082
#771273
#749113