Finite Group Databasebeta

← #11804850

Subgroups — #11804850

Order 1152.

1999 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3799C211yesmaximal, characteristic
2C2×#63904C211yesmaximal, characteristic, complemented
3C2×C4×#626C211yesmaximal, characteristic, complemented
4#10592364C211yesmaximal, characteristic, complemented
5C3×D3×#95C211yesmaximal, characteristic, complemented
6C3×#4646C211yesmaximal, characteristic, complemented
7#10591382C211yesmaximal, characteristic, complemented
8#10591382C211yesmaximal, characteristic, complemented
9#10591380C211yesmaximal, characteristic, complemented
10#10591371C211yesmaximal, characteristic, complemented
11#10591370C211yesmaximal, characteristic, complemented
12#10591367C211yesmaximal, characteristic, complemented
13#10591294C211yesmaximal, characteristic, complemented
14#10591261C211yesmaximal, characteristic, complemented
15#10591233C211yesmaximal, characteristic, complemented
16#76613—31nomaximal
17#73368—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×Dic6C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#624C2211yescharacteristic
27C22×#624C2211yescharacteristic
28C22×#624C2211yescharacteristic
29C2×#3799—24no—
30C2×#3799—24no—
31C2×#3799C418yescomplemented
32C2×#3752C2211yescharacteristic
33C2×#3752C2211yescharacteristic
34C2×#3752C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44#63904—24no—
45C4×#626—24no—
46C32×#95C2211yescharacteristic
47#63658C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57#63579C2211yescharacteristic
58C22×#239—31no—
59C22×#235—31no—
60C2×C4×#67—31no—
61C2×C4×#67—31no—
62C2×#893—31no—
63C2×C4×D12—31no—
64C3×#391—31no—
65C2×C3×#95—31no—
66#5229—31no—
67#5213—31no—
68#5213—31no—
69#5211—31no—
70#4987—31no—
71C4×(C2×D3)⋊C4—31no—
72#4667—31no—
73#4666—31no—
74#4665—31no—
75#4665—31no—
76#4665—31no—
77#4665—31no—
78#4665—31no—
79#4665—31no—
80#4665—61no—
81#4664—31no—
82#4664—31no—
83#4664—31no—
84D3×#95—31no—
85D3×#95—31no—
86D3×#95D311yescharacteristic, complemented
87#4646—31no—
88#4646D311yescharacteristic, complemented
89C23×C3⋊D3C2311yescharacteristic
90C23×C3⋊D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C2×C4⋊(C3⋊D3)—22no—
98C2×C4⋊(C3⋊D3)—22no—
99C2×C4⋊(C3⋊D3)C2×C414yescomplemented
100C2×C4×C3⋊D3—22no—
101C2×C4×C3⋊D3—22no—
102C2×C4×C3⋊D3—41no—
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C2×C3×C4×D3—22no—
111C2×C3×C4×D3—22no—
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3—41no—
117C2×C3×C4×D3—41no—
118C2×C3×C4×D3C2×C414yescomplemented
119C2×C3×Dic6—22no—
120C2×C3×Dic6—22no—
121C2×C3×Dic6C2×C414yescomplemented
122C2×#626—22no—
123C2×#626—22no—
124C2×#626C2×C414yes—
125C2×#626C2×C414yescomplemented
126C2×#626D414yes—
127C2×#626D414yes—
128C2×#624—22no—
129C2×#624—22no—
130C2×#624—22no—
131C2×#624—22no—
132C2×#624—22no—
133C2×#624—22no—
134C2×#624—41no—
135C2×#624C2×C414yescomplemented
136C2×#624C2×C414yescomplemented
137#3799—232no—
138#3752—22no—
139#3752—22no—
140#3752—41no—
141C3×Dic3⋊C4—22no—
142C3×C4×Dic3—22no—
143Dic3⋊Dic3—22no—
144#3722—22no—
145#3722—22no—
146#3722—41no—
147(C2×D3)⋊Dic3—22no—
148(C2×D3)⋊Dic3—22no—
149Dic32—22no—
150#2339—91noSylow
151C22×C3×Q8—31no—
152C23×C3×C4—31no—
153C23×C3×C4—31no—
154C23×C3×C4—31no—
155C22×#67—31no—
156C22×#67—31no—
157C2×#239—38no—
158C2×#239—64no—
159C2×#239—64no—
160C2×#235—38no—
161C2×#235—64no—
162C2×#235—64no—
163C22×D12—31no—
164C22×D12—31no—
165C22×D12—31no—
166C22×D12—31no—
167C22×D12—61no—
168C22×C4×D3—31no—
169C22×C4×D3—31no—
170C22×C4×D3—31no—
171C22×C4×D3—31no—
172C22×C4×D3—31no—
173C22×C4×D3—31no—
174C22×C4×D3—31no—
175C22×C4×D3—31no—
176C22×C4×D3—61no—
177C22×C4×D3C2×D311yescharacteristic
178C22×C4×D3C2×D311yescharacteristic
179C22×C4×D3C2×D311yescharacteristic
180C22×Dic6C2×D311yescharacteristic
181C2×C3×C4⋊C4—31no—
182C2×C3×C42—31no—
183C2×#217—31no—
184C2×#217—31no—
185C4×#67—64no—
186C4×#67—64no—
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—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—61no—
202C2×(C2×D3)⋊C4—61no—
203C2×(C2×D3)⋊C4—61no—
204C2×C4⋊Dic3—31no—
205C2×Dic3⋊C4—31no—
206C2×Dic3⋊C4C2×D311yescharacteristic
207C2×C4×Dic3—31no—
208C2×C4×Dic3—31no—
209C2×C4×Dic3C2×D311yescharacteristic
210#893—64no—
211C4×D12—64no—
212C3×#95—21no—
213C3×#95—31no—
214C3×#95—31no—
215C3×#95—31no—
216C3×#95—31no—
217C3×#95—31no—
218C3×#95—31no—
219C3×#95C2×D311yescharacteristic
220C3×#95C2×D311yescharacteristic
221C3⋊#95—31no—
222C3⋊#95—31no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95—61no—
232C3⋊#95C2×D311yescharacteristic
233C3⋊#95C2×D311yescharacteristic
234C3⋊#95C2×D311yescharacteristic
235C3⋊#95C2×D311yescharacteristic
236C3⋊#95C2×D311yescharacteristic
237C3⋊#95C2×D311yescharacteristic
238C23×C32C2411yescharacteristic
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⋊D3—21no—
249C22×C3⋊D3C22×C412yes—
250C22×C3⋊D3C22×C412yes—
251C22×C3⋊D3C2×D412yes—
252C22×C3⋊D3C2×D412yes—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3C22×C412yes—
258C22×C3×D3C2×D412yes—
259C22×C3×D3C2×D412yes—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C22×C412yes—
268C2×C32×C4#4112yescomplemented
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3—21no—
275C4⋊(C3⋊D3)—28no—
276C4×C3⋊D3—44no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3C22×C412yes—
293C2×C3×Dic3C22×C412yes—
294C2×C3×Dic3C22×C412yes—
295C2×C3×Dic3C2×D412yes—
296C2×C3×Dic3C2×D412yes—
297C2×C3×Dic3#4112yescomplemented
298C3×C4×D3—28no—
299C3×C4×D3—44no—
300C3×C4×D3—44no—
301C3×Dic6—28no—
302#626—28no—
303#626C22⋊C4116yescomplemented
304#624—28no—
305#624—28no—
306#624—44no—
307C22×#41—91no—
308C2×C4×D4—91no—
309C2×C4×D4—91no—
310#391—31no—
311#391—91no—
312#386—91no—
313#386—91no—
314#386—91no—
315#386—91no—
316#381—91no—
317#381—91no—
318#380—91no—
319C4×C22⋊C4—91no—
320C2×#95—31no—
321C2×#95—91no—
322C24×C3—31no—
323C23×D3—31no—
324C23×D3—31no—
325C23×D3—31no—
326C23×D3—31no—
327C23×D3—61no—
328C23×D3—61no—
329C23×D3C22×D311yescharacteristic
330C2×C3×Q8—34no—
331C2×C3×Q8—62no—
332C2×C3×Q8—62no—
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—34no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—62no—
345C22×C3×C4—62no—
346C22×C3×C4—62no—
347C22×C3×C4—62no—
348C22×C3×C4—62no—
349C22×C3×C4—62no—
350C22×C3×C4—121no—
351C22×C3×C4—121no—
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C22×C3×C4C22×D311yescharacteristic
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C22×D311yescharacteristic
358C2×#67—34no—
359C2×#67—34no—
360C2×#67—34no—
361C2×#67—34no—
362C2×#67—62no—
363C2×#67—62no—
364C22×Dic3—31no—
365C22×Dic3—31no—
366C22×Dic3—31no—
367C22×Dic3—31no—
368C22×Dic3—61no—
369C22×Dic3—61no—
370C22×Dic3C22×D311yescharacteristic
371C22×Dic3C22×D311yescharacteristic
372C22×Dic3C22×D311yescharacteristic
373C22×Dic3C22×D311yescharacteristic
374C22×Dic3C22×D311yescharacteristic
375C22×Dic3C22×D311yescharacteristic
376C22×Dic3C22×D311yescharacteristic
377#239—632no—
378#235—632no—
379C2×D12—34no—
380C2×D12—34no—
381C2×D12—34no—
382C2×D12—34no—
383C2×D12—34no—
384C2×D12—34no—
385C2×D12—64no—
386C2×D12—62no—
387C2×D12—62no—
388C2×D12—62no—
389C2×D12—62no—
390C2×D12—62no—
391C2×D12—62no—
392C2×D12—122no—
393C2×D12—122no—
394C2×C4×D3—22no—
395C2×C4×D3—22no—
396C2×C4×D3—22no—
397C2×C4×D3—22no—
398C2×C4×D3—22no—
399C2×C4×D3—22no—
400C2×C4×D3—34no—
401C2×C4×D3—34no—
402C2×C4×D3—34no—
403C2×C4×D3—34no—
404C2×C4×D3—41no—
405C2×C4×D3—41no—
406C2×C4×D3—62no—
407C2×C4×D3—62no—
408C2×C4×D3—62no—
409C2×C4×D3—62no—
410C2×C4×D3—62no—
411C2×C4×D3—62no—
412C2×C4×D3—62no—
413C2×C4×D3—62no—
414C2×C4×D3—62no—
415C2×C4×D3—62no—
416C2×C4×D3—62no—
417C2×C4×D3—62no—
418C2×C4×D3—62no—
419C2×C4×D3—62no—
420C2×C4×D3—62no—
421C2×C4×D3—62no—
422C2×C4×D3—122no—
423C2×C4×D3—122no—
424C2×C4×D3—121no—
425C2×C4×D3—121no—
426C2×C4×D3—121no—
427C2×C4×D3—121no—
428C2×C4×D3—122no—
429C2×C4×D3C4×D314yescomplemented
430C2×Dic6—22no—
431C2×Dic6—22no—
432C2×Dic6C4×D314yescomplemented
433C3×C4⋊C4—62no—
434C3×C42—62no—
435#217—62no—
436#217—62no—
437(C2×D3)⋊C4—62no—
438(C2×D3)⋊C4—62no—
439(C2×D3)⋊C4—62no—
440(C2×D3)⋊C4—62no—
441(C2×D3)⋊C4—62no—
442(C2×D3)⋊C4—62no—
443(C2×D3)⋊C4—62no—
444(C2×D3)⋊C4—62no—
445(C2×D3)⋊C4—62no—
446(C2×D3)⋊C4—62no—
447(C2×D3)⋊C4—122no—
448(C2×D3)⋊C4—122no—
449(C2×D3)⋊C4—121no—
450(C2×D3)⋊C4—121no—
451(C2×D3)⋊C4—121no—
452(C2×D3)⋊C4—121no—
453(C2×D3)⋊C4—122no—
454C4⋊Dic3—62no—
455Dic3⋊C4—22no—
456Dic3⋊C4—62no—
457C4×Dic3—22no—
458C4×Dic3—62no—
459C4×Dic3—62no—
460C22×C32C23×C411yescharacteristic
461C22×C32C22×D411yescharacteristic
462C22×C32C22×D411yescharacteristic
463C22×C32C2×#4111yescharacteristic
464C22×C32C2×#4111yescharacteristic
465C22×C32H(5,𝔽2)11yescharacteristic
466C22×C322−1+411yescharacteristic
467C2×C3⋊D3—22no—
468C2×C3⋊D3—22no—
469C2×C3⋊D3—22no—
470C2×C3⋊D3—22no—
471C2×C3⋊D3—22no—
472C2×C3⋊D3—22no—
473C2×C3⋊D3—22no—
474C2×C3⋊D3—22no—
475C2×C3⋊D3—22no—
476C2×C3⋊D3—41no—
477C2×C3⋊D3—41no—
478C2×C3⋊D3—41no—
479C2×C3⋊D3—41no—
480C2×C3⋊D3C2×C22⋊C414yes—
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×D3C2×C22⋊C414yes—
488C32×C4—22no—
489C32×C4—22no—
490C32×C4—41no—
491C3⋊Dic3—41no—
492C3⋊Dic3—41no—
493C3×Dic3—22no—
494C3×Dic3—22no—
495C3×Dic3—22no—
496C3×Dic3—41no—
497C3×Dic3—41no—
498C3×Dic3—41no—
499C3×Dic3C2×C22⋊C414yes—
500C2×#41—98no—
501C2×#41—184no—
502C2×#41—184no—
503C22×Q8—31no—
504C22×D4—91no—
505C22×D4—91no—
506C22×D4—91no—
507C23×C4—31no—
508C23×C4—31no—
509C23×C4—31no—
510C23×C4—91no—
511C23×C4—91no—
512C23×C4—91no—
513C23×C4—91no—
514C4×D4—184no—
515C4×D4—184no—
516C2×C4⋊C4—31no—
517C2×C4⋊C4—91no—
518C2×C22⋊C4—91no—
519C2×C22⋊C4—91no—
520C2×C22⋊C4—91no—
521C2×C22⋊C4—91no—
522C2×C22⋊C4—91no—
523C2×C22⋊C4—91no—
524C2×C22⋊C4—91no—
525C2×C22⋊C4—91no—
526C2×C42—31no—
527C2×C42—91no—
528#95—31no—
529#95—31no—
530#95—31no—
531#95—31no—
532#95—31no—
533#95—31no—
534#95—91no—
535#95—91no—
536#95—91no—
537#95—91no—
538#95—91no—
539#95D3211yescharacteristic
540C23×C3—21no—
541C23×C3—32no—
542C23×C3—32no—
543C23×C3—32no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—61no—
547C23×C3—61no—
548C23×C3C23×D311yescharacteristic
549C23×C3C23×D311yescharacteristic
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—21no—
553C22×D3—21no—
554C22×D3—32no—
555C22×D3—32no—
556C22×D3—32no—
557C22×D3—32no—
558C22×D3—32no—
559C22×D3—32no—
560C22×D3—32no—
561C22×D3—32no—
562C22×D3—62no—
563C22×D3—62no—
564C22×D3—62no—
565C22×D3—62no—
566C22×D3—61no—
567C22×D3—61no—
568C22×D3—61no—
569C22×D3—61no—
570C22×D3—61no—
571C22×D3—61no—
572C22×D3—61no—
573C22×D3—61no—
574C22×D3—61no—
575C22×D3—61no—
576C22×D3—61no—
577C22×D3—61no—
578C22×D3—61no—
579C22×D3—61no—
580C22×D3—61no—
581C22×D3—61no—
582C22×D3—61no—
583C22×D3—61no—
584C22×D3—61no—
585C22×D3—61no—
586C22×D3—121no—
587C22×D3—121no—
588C22×D3—121no—
589C22×D3—121no—
590C22×D3—121no—
591C22×D3—121no—
592C22×D3—121no—
593C22×D3—121no—
594C22×D3—121no—
595C22×D3—121no—
596C22×D3C2×C4×D312yes—
597C22×D3D3×D412yes—
598C22×D3D3×D412yes—
599C3×Q8—68no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—32no—
617C2×C3×C4—32no—
618C2×C3×C4—32no—
619C2×C3×C4—32no—
620C2×C3×C4—32no—
621C2×C3×C4—32no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—41no—
626C2×C3×C4—41no—
627C2×C3×C4—41no—
628C2×C3×C4—41no—
629C2×C3×C4—68no—
630C2×C3×C4—61no—
631C2×C3×C4—61no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—61no—
635C2×C3×C4—61no—
636C2×C3×C4—61no—
637C2×C3×C4—61no—
638C2×C3×C4—61no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4—61no—
645C2×C3×C4—124no—
646C2×C3×C4—124no—
647C2×C3×C4C2×C4×D312yes—
648C2×C3×C4C2×C4×D312yes—
649C2×C3×C4#23512yescomplemented
650C2×C3×C4#23912yescomplemented
651#67—316no—
652#67—68no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—21no—
656C2×Dic3—21no—
657C2×Dic3—21no—
658C2×Dic3—21no—
659C2×Dic3—21no—
660C2×Dic3—21no—
661C2×Dic3—21no—
662C2×Dic3—21no—
663C2×Dic3—21no—
664C2×Dic3—21no—
665C2×Dic3—21no—
666C2×Dic3—21no—
667C2×Dic3—21no—
668C2×Dic3—62no—
669C2×Dic3—61no—
670C2×Dic3—61no—
671C2×Dic3—61no—
672C2×Dic3—61no—
673C2×Dic3—61no—
674C2×Dic3—61no—
675C2×Dic3—61no—
676C2×Dic3—61no—
677C2×Dic3—61no—
678C2×Dic3—61no—
679C2×Dic3—61no—
680C2×Dic3—61no—
681C2×Dic3—121no—
682C2×Dic3—121no—
683C2×Dic3—121no—
684C2×Dic3—121no—
685C2×Dic3—121no—
686C2×Dic3C2×C4×D312yes—
687C2×Dic3C2×C4×D312yes—
688C2×Dic3C2×C4×D312yes—
689C2×Dic3#23512yescomplemented
690C2×Dic3D3×D412yes—
691C2×Dic3D3×D412yes—
692D12—316no—
693D12—68no—
694D12—68no—
695D12—68no—
696D12—128no—
697C4×D3—28no—
698C4×D3—44no—
699C4×D3—44no—
700C4×D3—68no—
701C4×D3—68no—
702C4×D3—68no—
703C4×D3—68no—
704C4×D3—124no—
705C4×D3—124no—
706C4×D3—124no—
707C4×D3—124no—
708C4×D3—128no—
709Dic6—28no—
710C2×C32C22×C22⋊C411yescharacteristic
711C2×C32C4×#4111yescharacteristic
712C2×C32#52011yescharacteristic
713C2×C32#54611yescharacteristic
714C2×C32#54611yescharacteristic
715C2×C32#54711yescharacteristic
716C2×C32#54711yescharacteristic
717C3⋊D3—24no—
718C3⋊D3—42no—
719C3×D3—24no—
720C24—31no—
721C24—91no—
722C24—91no—
723#41—1832no—
724C2×Q8—34no—
725C2×Q8—62no—
726C2×Q8—62no—
727C2×D4—94no—
728C2×D4—94no—
729C2×D4—94no—
730C2×D4—94no—
731C2×D4—94no—
732C2×D4—182no—
733C2×D4—182no—
734C2×D4—182no—
735C2×D4—182no—
736C22×C4—31no—
737C22×C4—31no—
738C22×C4—31no—
739C22×C4—31no—
740C22×C4—34no—
741C22×C4—31no—
742C22×C4—31no—
743C22×C4—31no—
744C22×C4—62no—
745C22×C4—62no—
746C22×C4—62no—
747C22×C4—62no—
748C22×C4—62no—
749C22×C4—62no—
750C22×C4—94no—
751C22×C4—94no—
752C22×C4—91no—
753C22×C4—91no—
754C22×C4—121no—
755C22×C4—121no—
756C22×C4—182no—
757C22×C4—182no—
758C22×C4—182no—
759C22×C4—182no—
760C22×C4—182no—
761C22×C4—182no—
762C22×C4—182no—
763C22×C4—182no—
764C22×C4—361no—
765C22×C4—361no—
766C22×C4C2×D3211yescharacteristic
767C22×C4C2×D3211yescharacteristic
768C22×C4C2×D3211yescharacteristic
769C4⋊C4—62no—
770C4⋊C4—182no—
771C22⋊C4—182no—
772C22⋊C4—182no—
773C22⋊C4—182no—
774C22⋊C4—182no—
775C22⋊C4—182no—
776C22⋊C4—182no—
777C22⋊C4—361no—
778C22⋊C4—361no—
779C42—62no—
780C42—182no—
781C22×C3—21no—
782C22×C3—21no—
783C22×C3—21no—
784C22×C3—21no—
785C22×C3—21no—
786C22×C3—21no—
787C22×C3—21no—
788C22×C3—34no—
789C22×C3—62no—
790C22×C3—62no—
791C22×C3—62no—
792C22×C3—62no—
793C22×C3—62no—
794C22×C3—62no—
795C22×C3C22×C4×D311yescharacteristic
796C22×C3C22×C4×D311yescharacteristic
797C22×C3C2×#23511yescharacteristic
798C22×C3C2×#23511yescharacteristic
799C22×C3C2×D3×D411yescharacteristic
800C22×C3C2×D3×D411yescharacteristic
801C22×C3C2×D3×D411yescharacteristic
802C22×C3C2×D3×D411yescharacteristic
803C22×C3#100411yescharacteristic
804C22×C3C2×#23911yescharacteristic
805C22×C3#100711yescharacteristic
806C22×C3#100711yescharacteristic
807C22×C3D3×#4111yescharacteristic
808C22×C3#100911yescharacteristic
809C2×D3—22no—
810C2×D3—22no—
811C2×D3—22no—
812C2×D3—22no—
813C2×D3—22no—
814C2×D3—22no—
815C2×D3—34no—
816C2×D3—34no—
817C2×D3—64no—
818C2×D3—62no—
819C2×D3—62no—
820C2×D3—62no—
821C2×D3—62no—
822C2×D3—62no—
823C2×D3—62no—
824C2×D3—62no—
825C2×D3—62no—
826C2×D3—62no—
827C2×D3—62no—
828C2×D3—62no—
829C2×D3—62no—
830C2×D3—62no—
831C2×D3—62no—
832C2×D3—62no—
833C2×D3—62no—
834C2×D3—62no—
835C2×D3—62no—
836C2×D3—122no—
837C2×D3—122no—
838C2×D3—122no—
839C2×D3—122no—
840C2×D3—122no—
841C2×D3—122no—
842C2×D3—122no—
843C2×D3—122no—
844C2×D3—122no—
845C2×D3—121no—
846C2×D3—121no—
847C2×D3—121no—
848C2×D3—121no—
849C2×D3—121no—
850C2×D3—121no—
851C2×D3—121no—
852C2×D3—121no—
853C2×D3—241no—
854C2×D3—241no—
855C2×D3—241no—
856C2×D3—241no—
857C2×D3D3×C22⋊C414yes—
858C3×C4—22no—
859C3×C4—22no—
860C3×C4—22no—
861C3×C4—22no—
862C3×C4—34no—
863C3×C4—42no—
864C3×C4—42no—
865C3×C4—41no—
866C3×C4—41no—
867C3×C4—62no—
868C3×C4—62no—
869C3×C4—62no—
870C3×C4—81no—
871C3×C4—121no—
872C3×C4—121no—
873C3×C4—121no—
874Dic3—22no—
875Dic3—22no—
876Dic3—22no—
877Dic3—41no—
878Dic3—41no—
879Dic3—41no—
880Dic3—122no—
881Dic3—121no—
882Dic3—121no—
883Dic3—121no—
884Dic3—121no—
885Dic3—241no—
886Dic3D3×C22⋊C414yes—
887C32#233911yescharacteristic, complemented, Sylow
888C23—32no—
889C23—32no—
890C23—32no—
891C23—61no—
892C23—61no—
893C23—61no—
894C23—61no—
895C23—92no—
896C23—92no—
897C23—92no—
898C23—92no—
899C23—181no—
900C23—181no—
901C23—181no—
902C23—181no—
903C23—181no—
904C23—181no—
905C23—181no—
906C23—181no—
907C23—181no—
908C23—181no—
909C23C22×D3211yescharacteristic
910Q8—68no—
911D4—916no—
912D4—188no—
913D4—188no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—32no—
922C2×C4—32no—
923C2×C4—32no—
924C2×C4—32no—
925C2×C4—32no—
926C2×C4—32no—
927C2×C4—68no—
928C2×C4—61no—
929C2×C4—61no—
930C2×C4—61no—
931C2×C4—61no—
932C2×C4—61no—
933C2×C4—61no—
934C2×C4—61no—
935C2×C4—61no—
936C2×C4—61no—
937C2×C4—61no—
938C2×C4—61no—
939C2×C4—61no—
940C2×C4—61no—
941C2×C4—61no—
942C2×C4—61no—
943C2×C4—124no—
944C2×C4—124no—
945C2×C4—188no—
946C2×C4—188no—
947C2×C4—181no—
948C2×C4—181no—
949C2×C4—181no—
950C2×C4—181no—
951C2×C4—181no—
952C2×C4—181no—
953C2×C4—364no—
954C2×C4—364no—
955C2×C4#379912yescomplemented
956C2×C4C4×D3212yes—
957C2×C3—21no—
958C2×C3—21no—
959C2×C3—21no—
960C2×C3—21no—
961C2×C3—21no—
962C2×C3—21no—
963C2×C3—21no—
964C2×C3—64no—
965C2×C3C4×#23511yescharacteristic
966C2×C3C2×D3×C22⋊C411yescharacteristic
967C2×C3C2×D3×C22⋊C411yescharacteristic
968C2×C3#549011yescharacteristic
969C2×C3#549011yescharacteristic
970C2×C3#550411yescharacteristic
971C2×C3#550711yescharacteristic
972C2×C3#550711yescharacteristic
973C2×C3C4×#23911yescharacteristic
974C2×C3#557411yescharacteristic
975C2×C3#563011yescharacteristic
976C2×C3#563111yescharacteristic
977C2×C3#567611yescharacteristic
978C2×C3#572611yescharacteristic
979D3—24no—
980D3—64no—
981D3—64no—
982D3—124no—
983D3—122no—
984D3—122no—
985D3—242no—
986C22—34no—
987C22—62no—
988C22—62no—
989C22—62no—
990C22—62no—
991C22—62no—
992C22—62no—
993C22—94no—
994C22—182no—
995C22—182no—
996C22—182no—
997C22—182no—
998C22—182no—
999C22—182no—
1000C22—182no—
1001C22—182no—
1002C22—182no—
1003C22—361no—
1004C22—361no—
1005C22—361no—
1006C22—361no—
1007C22C2×#379911yescharacteristic
1008C22C2×C4×D3211yescharacteristic
1009C22D3×#23511yescharacteristic
1010C22D32×D411yescharacteristic
1011C22D32×D411yescharacteristic
1012C22#6431411yescharacteristic
1013C22#6431611yescharacteristic
1014C4—22no—
1015C4—22no—
1016C4—34no—
1017C4—41no—
1018C4—62no—
1019C4—62no—
1020C4—62no—
1021C4—121no—
1022C4—121no—
1023C4—121no—
1024C4—361no—
1025C4—361no—
1026C3—21no—
1027C3#7336811yescharacteristic, complemented
1028C3#7661311yescharacteristic, complemented
1029C2—64no—
1030C2—184no—
1031C2—362no—
1032C2C4×#379911yescharacteristic
1033C2#1059418711yescharacteristic
1034C2D32×C22⋊C411yescharacteristic
1035C2#1059428011yescharacteristic
1036C2#1059432711yescharacteristic
1037C2#1059451611yescharacteristic
1038C2#1059451711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#3799C2
hypercenter#95D32
hypocenterC32#2339
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#63904C2semidirect
3. C2×C4×#626C2semidirect
4. #10592364C2semidirect
5. C3×D3×#95C2semidirect
6. C3×#4646C2semidirect
7. #10591382C2semidirect
8. #10591382C2semidirect
9. #10591380C2semidirect
10. #10591371C2semidirect
11. #10591370C2semidirect
12. #10591367C2semidirect
13. #10591294C2semidirect
14. #10591261C2semidirect
15. #10591233C2semidirect
31. C2×#3799C4semidirect
86. D3×#95D3semidirect
88. #4646D3semidirect
99. C2×C4⋊(C3⋊D3)C2×C4semidirect
118. C2×C3×C4×D3C2×C4semidirect
121. C2×C3×Dic6C2×C4semidirect
125. C2×#626C2×C4semidirect
135. C2×#624C2×C4semidirect
136. C2×#624C2×C4semidirect
268. C2×C32×C4#41semidirect
297. C2×C3×Dic3#41semidirect
303. #626C22⋊C4semidirect
429. C2×C4×D3C4×D3semidirect
432. C2×Dic6C4×D3semidirect
649. C2×C3×C4#235semidirect
650. C2×C3×C4#239semidirect
689. C2×Dic3#235semidirect
887. C32#2339semidirect
955. C2×C4#3799semidirect
1027. C3#73368semidirect
1028. C3#76613semidirect

Maximal subgroups

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

subgroupindex
C22×#37992
C2×#639042
C2×C4×#6262
#105923642
C3×D3×#952
C3×#46462
#105913822
#105913802
#105913712
#105913702
#105913672
#105912942
#105912612
#105912332
#766133
#733683