Finite Group Databasebeta

← C2×#10594510 #11900093

Subgroups — C2×#10594510 #11900093

Order 1152.

3489 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3798C211yesmaximal, characteristic
2C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×C3×#892C211yesmaximal, characteristic, complemented
4C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×#626C212yesmaximal, complemented
6C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
7C2×#63881C212yesmaximal, complemented
8C2×#63879C212yesmaximal, complemented
9C2×#63849C211yesmaximal, characteristic, complemented
10C2×#63841C211yesmaximal, characteristic, complemented
11C2×#63837C212yesmaximal, complemented
12#10594510C2116yesmaximal, direct product factor
13C2×#5523—31nomaximal
14C2×#5504—31nomaximal
15C22×C4×C3⋊D3C2212yes—
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C3×C4×D3C2212yes—
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×#627C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#625C2211yescharacteristic
24C22×D3×Dic3C2212yes—
25C2×#3798C4116yescomplemented
26C2×#3798C2218yes—
27C2×C32×C4⋊C4C2211yescharacteristic
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C2×#3750C2212yes—
30C4⋊C4×C3⋊D3C2218yescomplemented
31C2×C3×(C2×D3)⋊C4C2212yes—
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×Dic3⋊C4C2212yes—
35C2×C3×C4×Dic3C2212yes—
36C3×#892C2218yescomplemented
37C3×D3×C4⋊C4C2218yescomplemented
38C2×Dic3⋊Dic3C2212yes—
39C2×#3722C2212yes—
40C2×(C2×D3)⋊Dic3C2212yes—
41C2×Dic32C2212yes—
42C2×Dic32C2212yes—
43C4×#626C22116yescomplemented
44D3×C4⋊Dic3C2218yescomplemented
45#63881C22116yescomplemented
46#63879C22116yescomplemented
47#63849C2218yescomplemented
48#63841C2218yescomplemented
49#63837C22116yescomplemented
50C22×#235—31no—
51C22×#235—31no—
52C2×C3×#117—31no—
53C22×C3×C4⋊C4—31no—
54C2×C4×#67—32no—
55C2×C4×#67—32no—
56C2×#926—31no—
57C22×C4⋊Dic3—31no—
58#5523—316no—
59#5504—316no—
60C2×#893—32no—
61C2×#892—31no—
62C2×#892—31no—
63C2×#892—31no—
64C2×#892D311yescharacteristic, complemented
65C2×D3×C4⋊C4—31no—
66C2×D3×C4⋊C4—31no—
67C2×D3×C4⋊C4—31no—
68C2×D3×C4⋊C4—61no—
69C2×D3×C4⋊C4D311yescharacteristic, complemented
70C2×#887—32no—
71C2×#67⋊C4—32no—
72C2×#67⋊C4—32no—
73C2×C4×D12—32no—
74C2×C4×Dic6—32no—
75C23×C3⋊D3C2311yescharacteristic
76C23×C3×D3C2311yescharacteristic
77C23×C3×D3C2311yescharacteristic
78C22×C32×C4C2312yes—
79C22×C32×C4C2311yescharacteristic
80C22×C3⋊Dic3C2312yes—
81C22×C3⋊Dic3C2311yescharacteristic
82C2×C4×C3⋊D3—44no—
83C2×C4×C3⋊D3C2×C418yescomplemented
84C2×C4×C3⋊D3C2318yes—
85C2×C4×C3⋊D3C2314yes—
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2311yescharacteristic
90C2×C3×C4×D3—44no—
91C2×C3×C4×D3C2×C418yescomplemented
92C2×C3×C4×D3C2×C418yescomplemented
93C2×C3×C4×D3C2318yes—
94C2×C3×C4×D3C2314yes—
95C2×C3×C4×D3C2314yes—
96C2×#627C2×C418yescomplemented
97C2×#627C2314yes—
98C2×#626C2×C418yescomplemented
99C2×#626C2×C418yescomplemented
100C2×#626C2314yes—
101C2×#626C2314yes—
102C2×#625C2×C418yescomplemented
103C2×#625C2314yes—
104C2×D3×Dic3—44no—
105C2×D3×Dic3C2318yes—
106#3798C2×C4164yescomplemented
107C32×C4⋊C4C2314yes—
108C4⋊(C3⋊Dic3)C2314yes—
109#3750C2318yes—
110C3×(C2×D3)⋊C4C2318yes—
111C3×C4⋊Dic3C2314yes—
112C3×C4⋊Dic3C2314yes—
113C3×Dic3⋊C4C2318yes—
114C3×C4×Dic3C2318yes—
115Dic3⋊Dic3C2318yes—
116#3722C2318yes—
117(C2×D3)⋊Dic3C2318yes—
118Dic32C2318yes—
119Dic32C2318yes—
120C2×#520—91noSylow
121C23×C3×C4—31no—
122C23×C3×C4—31no—
123C23×C3×C4—32no—
124C22×#67—31no—
125C22×#67—31no—
126C22×#67—31no—
127C22×#67—31no—
128C23×Dic3—32no—
129C2×#235—316no—
130C2×#235—316no—
131C2×#235—38no—
132C2×#235—38no—
133C22×D12—31no—
134C22×D12—31no—
135C22×C4×D3—31no—
136C22×C4×D3—31no—
137C22×C4×D3—32no—
138C22×C4×D3—32no—
139C22×C4×D3—32no—
140C22×C4×D3—61no—
141C22×C4×D3—62no—
142C22×C4×D3C2×D312yes—
143C22×C4×D3C2×D311yescharacteristic
144C22×C4×D3C2×D311yescharacteristic
145C22×Dic6—31no—
146C22×Dic6—31no—
147C3×#117—38no—
148C2×C3×C4⋊C4—21no—
149C2×C3×C4⋊C4—32no—
150C2×C3×C4⋊C4—31no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4—38no—
153C2×C3×C4⋊C4C2×D311yescharacteristic
154C2×C3×C4⋊C4C2×D311yescharacteristic
155C2×C3×C22⋊C4—32no—
156C2×C3×C42—32no—
157C2×#217—32no—
158C4×#67—316no—
159C4×#67—316no—
160C2×(C2×D3)⋊C4—32no—
161C2×(C2×D3)⋊C4—32no—
162C2×(C2×D3)⋊C4—32no—
163C2×(C2×D3)⋊C4C2×D312yes—
164#926—38no—
165C2×C4⋊Dic3—31no—
166C2×C4⋊Dic3—31no—
167C2×C4⋊Dic3—32no—
168C2×C4⋊Dic3—38no—
169C2×C4⋊Dic3—61no—
170C2×C4⋊Dic3C2×D311yescharacteristic
171C2×C4⋊Dic3C2×D311yescharacteristic
172C2×Dic3⋊C4—32no—
173C2×Dic3⋊C4—32no—
174C2×Dic3⋊C4—32no—
175C2×Dic3⋊C4—62no—
176C2×Dic3⋊C4C2×D312yes—
177C2×C4×Dic3—32no—
178C2×C4×Dic3—32no—
179C2×C4×Dic3—32no—
180C2×C4×Dic3—32no—
181C2×C4×Dic3C2×D312yes—
182#893—316no—
183#892—38no—
184#892—38no—
185#892—38no—
186#892C2×D318yescomplemented
187D3×C4⋊C4—38no—
188D3×C4⋊C4—38no—
189D3×C4⋊C4—38no—
190D3×C4⋊C4—68no—
191D3×C4⋊C4C2×D318yescomplemented
192#887—316no—
193#67⋊C4—316no—
194#67⋊C4—316no—
195C4×D12—316no—
196C4×Dic6—316no—
197C23×C32C2411yescharacteristic
198C22×C3⋊D3—22no—
199C22×C3⋊D3—22no—
200C22×C3⋊D3C22×C414yes—
201C22×C3⋊D3C2412yes—
202C22×C3×D3—22no—
203C22×C3×D3—22no—
204C22×C3×D3—22no—
205C22×C3×D3—22no—
206C22×C3×D3C22×C414yes—
207C22×C3×D3C22×C414yes—
208C22×C3×D3C2412yes—
209C22×C3×D3C2412yes—
210C2×C32×C4—24no—
211C2×C32×C4C22×C414yes—
212C2×C32×C4C2414yes—
213C2×C32×C4C2412yes—
214C2×C3⋊Dic3—24no—
215C2×C3⋊Dic3C22×C414yes—
216C2×C3⋊Dic3C2414yes—
217C2×C3⋊Dic3C2412yes—
218C4×C3⋊D3—48no—
219C4×C3⋊D3C22×C4116yescomplemented
220C2×C3×Dic3—24no—
221C2×C3×Dic3—24no—
222C2×C3×Dic3C22×C414yes—
223C2×C3×Dic3C22×C414yes—
224C2×C3×Dic3C2414yes—
225C2×C3×Dic3C2414yes—
226C2×C3×Dic3C2412yes—
227C2×C3×Dic3C2412yes—
228C3×C4×D3—48no—
229C3×C4×D3C22×C4116yescomplemented
230C3×C4×D3C22×C4116yescomplemented
231#627C22×C4116yescomplemented
232#626C22×C4116yescomplemented
233#626C22×C4116yescomplemented
234#625C22×C4116yescomplemented
235D3×Dic3—48no—
236C22×#41—91no—
237#520—916no—
238C2×C4×Q8—92no—
239C2×C4×D4—92no—
240C2×C4×D4—92no—
241C2×C4×D4—92no—
242C2×#117—31no—
243C2×#117—91no—
244C2×#117—91no—
245C22×C4⋊C4—31no—
246C22×C4⋊C4—91no—
247C22×C4⋊C4—91no—
248C24×C3—31no—
249C24×C3—31no—
250C23×D3—31no—
251C23×D3—31no—
252C23×D3—61no—
253C23×D3C22×D311yescharacteristic
254C23×D3C22×D311yescharacteristic
255C22×C3×C4—21no—
256C22×C3×C4—22no—
257C22×C3×C4—31no—
258C22×C3×C4—31no—
259C22×C3×C4—38no—
260C22×C3×C4—38no—
261C22×C3×C4—34no—
262C22×C3×C4—34no—
263C22×C3×C4—32no—
264C22×C3×C4—32no—
265C22×C3×C4—38no—
266C22×C3×C4—124no—
267C22×C3×C4C22×D312yes—
268C22×C3×C4C22×D312yes—
269C22×C3×C4C22×D311yescharacteristic
270C22×C3×C4C22×D311yescharacteristic
271C2×#67—38no—
272C2×#67—38no—
273C2×#67—34no—
274C2×#67—34no—
275C2×#67—38no—
276C2×#67—38no—
277C2×#67—34no—
278C2×#67—34no—
279C22×Dic3—31no—
280C22×Dic3—31no—
281C22×Dic3—32no—
282C22×Dic3—32no—
283C22×Dic3—38no—
284C22×Dic3—61no—
285C22×Dic3—62no—
286C22×Dic3—124no—
287C22×Dic3C22×D312yes—
288C22×Dic3C22×D312yes—
289C22×Dic3C22×D311yescharacteristic
290C22×Dic3C22×D311yescharacteristic
291#235—364no—
292#235—364no—
293C2×D12—38no—
294C2×D12—38no—
295C2×D12—34no—
296C2×D12—34no—
297C2×C4×D3—38no—
298C2×C4×D3—38no—
299C2×C4×D3—34no—
300C2×C4×D3—34no—
301C2×C4×D3—38no—
302C2×C4×D3—38no—
303C2×C4×D3—38no—
304C2×C4×D3—44no—
305C2×C4×D3—64no—
306C2×C4×D3—68no—
307C2×C4×D3—68no—
308C2×C4×D3—124no—
309C2×C4×D3—124no—
310C2×C4×D3—124no—
311C2×C4×D3—128no—
312C2×C4×D3C4×D318yescomplemented
313C2×C4×D3C4×D318yescomplemented
314C2×C4×D3C22×D318yes—
315C2×C4×D3C22×D314yes—
316C2×C4×D3C22×D314yes—
317C2×Dic6—38no—
318C2×Dic6—38no—
319C2×Dic6—34no—
320C2×Dic6—34no—
321C3×C4⋊C4—24no—
322C3×C4⋊C4—38no—
323C3×C4⋊C4—34no—
324C3×C4⋊C4—34no—
325C3×C4⋊C4C22×D314yes—
326C3×C4⋊C4C22×D314yes—
327C3×C22⋊C4—38no—
328C3×C42—38no—
329#217—38no—
330(C2×D3)⋊C4—38no—
331(C2×D3)⋊C4—38no—
332(C2×D3)⋊C4—38no—
333(C2×D3)⋊C4C22×D318yes—
334C4⋊Dic3—34no—
335C4⋊Dic3—34no—
336C4⋊Dic3—38no—
337C4⋊Dic3—64no—
338C4⋊Dic3C22×D314yes—
339C4⋊Dic3C22×D314yes—
340Dic3⋊C4—38no—
341Dic3⋊C4—38no—
342Dic3⋊C4—38no—
343Dic3⋊C4—68no—
344Dic3⋊C4C22×D318yes—
345C4×Dic3—38no—
346C4×Dic3—38no—
347C4×Dic3—38no—
348C4×Dic3—38no—
349C4×Dic3C22×D318yes—
350C22×C32C23×C412yes—
351C22×C32H(5,𝔽2)12yes—
352C22×C322−1+412yes—
353C22×C32C2511yescharacteristic
354C2×C3⋊D3—28no—
355C2×C3⋊D3—22no—
356C2×C3⋊D3—22no—
357C2×C3⋊D3C23×C414yes—
358C2×C3×D3—28no—
359C2×C3×D3—28no—
360C2×C3×D3—22no—
361C2×C3×D3—22no—
362C2×C3×D3—22no—
363C2×C3×D3—22no—
364C2×C3×D3C23×C414yes—
365C2×C3×D3C23×C414yes—
366C32×C4—24no—
367C32×C4C23×C414yes—
368C3⋊Dic3—24no—
369C3⋊Dic3C23×C414yes—
370C3×Dic3—24no—
371C3×Dic3—24no—
372C3×Dic3C23×C414yes—
373C3×Dic3C23×C414yes—
374C2×#41—98no—
375C2×#41—916no—
376C22×Q8—91no—
377C22×D4—91no—
378C22×D4—91no—
379C22×D4—91no—
380C23×C4—31no—
381C23×C4—31no—
382C23×C4—32no—
383C23×C4—92no—
384C23×C4—91no—
385C23×C4—92no—
386C4×Q8—916no—
387C4×D4—916no—
388C4×D4—916no—
389C4×D4—916no—
390#117—38no—
391#117—98no—
392#117—98no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—32no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—38no—
397C2×C4⋊C4—98no—
398C2×C4⋊C4—92no—
399C2×C4⋊C4—91no—
400C2×C4⋊C4—92no—
401C2×C4⋊C4—98no—
402C2×C4⋊C4D3211yescharacteristic
403C2×C22⋊C4—32no—
404C2×C22⋊C4—92no—
405C2×C22⋊C4—92no—
406C2×C42—32no—
407C2×C42—92no—
408C2×C42—92no—
409C23×C3—21no—
410C23×C3—34no—
411C23×C3—34no—
412C23×C3—32no—
413C23×C3—32no—
414C23×C3—62no—
415C23×C3—62no—
416C23×C3—62no—
417C23×C3—62no—
418C23×C3C23×D311yescharacteristic
419C23×C3C23×D311yescharacteristic
420C22×D3—22no—
421C22×D3—22no—
422C22×D3—22no—
423C22×D3—22no—
424C22×D3—34no—
425C22×D3—34no—
426C22×D3—32no—
427C22×D3—32no—
428C22×D3—64no—
429C22×D3—62no—
430C22×D3—64no—
431C22×D3—64no—
432C22×D3—62no—
433C22×D3—62no—
434C22×D3—62no—
435C22×D3—62no—
436C22×D3C2×C4×D314yes—
437C22×D3C2×C4×D314yes—
438C22×D3C23×D312yes—
439C22×D3C23×D312yes—
440C2×C3×C4—24no—
441C2×C3×C4—24no—
442C2×C3×C4—22no—
443C2×C3×C4—24no—
444C2×C3×C4—24no—
445C2×C3×C4—34no—
446C2×C3×C4—34no—
447C2×C3×C4—32no—
448C2×C3×C4—32no—
449C2×C3×C4—316no—
450C2×C3×C4—316no—
451C2×C3×C4—34no—
452C2×C3×C4—34no—
453C2×C3×C4—44no—
454C2×C3×C4—64no—
455C2×C3×C4—64no—
456C2×C3×C4—128no—
457C2×C3×C4C2×C4×D314yes—
458C2×C3×C4C2×C4×D314yes—
459C2×C3×C4C23×D314yes—
460C2×C3×C4C23×D314yes—
461C2×C3×C4C23×D312yes—
462C2×C3×C4C23×D312yes—
463#67—316no—
464#67—316no—
465#67—316no—
466#67—316no—
467C2×Dic3—24no—
468C2×Dic3—24no—
469C2×Dic3—34no—
470C2×Dic3—34no—
471C2×Dic3—32no—
472C2×Dic3—32no—
473C2×Dic3—34no—
474C2×Dic3—34no—
475C2×Dic3—64no—
476C2×Dic3—62no—
477C2×Dic3—64no—
478C2×Dic3—64no—
479C2×Dic3—64no—
480C2×Dic3—124no—
481C2×Dic3—128no—
482C2×Dic3C2×C4×D314yes—
483C2×Dic3C2×C4×D314yes—
484C2×Dic3C23×D314yes—
485C2×Dic3C23×D314yes—
486C2×Dic3C23×D312yes—
487C2×Dic3C23×D312yes—
488D12—316no—
489D12—316no—
490C4×D3—316no—
491C4×D3—316no—
492C4×D3—48no—
493C4×D3—616no—
494C4×D3—128no—
495C4×D3—128no—
496C4×D3—128no—
497C4×D3—1216no—
498C4×D3C2×C4×D3116yescomplemented
499C4×D3C2×C4×D3116yescomplemented
500Dic6—316no—
501Dic6—316no—
502C2×C32#52014yescomplemented
503C2×C32C24×C411yescharacteristic
504C2×C32C2×H(5,𝔽2)11yescharacteristic
505C2×C32C2×2−1+411yescharacteristic
506C3⋊D3—24no—
507C3×D3—24no—
508C3×D3—24no—
509C24—31no—
510C24—31no—
511C24—91no—
512#41—964no—
513C2×Q8—94no—
514C2×Q8—98no—
515C2×D4—94no—
516C2×D4—94no—
517C2×D4—98no—
518C2×D4—98no—
519C2×D4—94no—
520C2×D4—98no—
521C22×C4—31no—
522C22×C4—31no—
523C22×C4—34no—
524C22×C4—34no—
525C22×C4—38no—
526C22×C4—38no—
527C22×C4—32no—
528C22×C4—32no—
529C22×C4—38no—
530C22×C4—98no—
531C22×C4—91no—
532C22×C4—94no—
533C22×C4—98no—
534C22×C4—92no—
535C22×C4—98no—
536C22×C4—124no—
537C22×C4—364no—
538C22×C4—364no—
539C22×C4C2×D3212yes—
540C22×C4C2×D3211yescharacteristic
541C4⋊C4—34no—
542C4⋊C4—38no—
543C4⋊C4—34no—
544C4⋊C4—98no—
545C4⋊C4—94no—
546C4⋊C4—98no—
547C4⋊C4C2×D3214yes—
548C22⋊C4—38no—
549C22⋊C4—98no—
550C22⋊C4—98no—
551C42—38no—
552C42—98no—
553C42—98no—
554C22×C3—22no—
555C22×C3—22no—
556C22×C3—22no—
557C22×C3—21no—
558C22×C3—34no—
559C22×C3—34no—
560C22×C3—62no—
561C22×C3—62no—
562C22×C3—62no—
563C22×C3—62no—
564C22×C3—68no—
565C22×C3—68no—
566C22×C3C22×C4×D312yes—
567C22×C3C22×C4×D312yes—
568C22×C3#100412yes—
569C22×C3#100712yes—
570C22×C3#100912yes—
571C22×C3#101012yes—
572C22×C3C24×D311yescharacteristic
573C22×C3C24×D311yescharacteristic
574C2×D3—22no—
575C2×D3—22no—
576C2×D3—22no—
577C2×D3—22no—
578C2×D3—28no—
579C2×D3—28no—
580C2×D3—34no—
581C2×D3—34no—
582C2×D3—64no—
583C2×D3—64no—
584C2×D3—64no—
585C2×D3—616no—
586C2×D3—62no—
587C2×D3—62no—
588C2×D3—62no—
589C2×D3—62no—
590C2×D3—68no—
591C2×D3—68no—
592C2×D3C22×C4×D314yes—
593C2×D3C22×C4×D314yes—
594C3×C4—24no—
595C3×C4—24no—
596C3×C4—24no—
597C3×C4—34no—
598C3×C4—34no—
599C3×C4—44no—
600C3×C4—64no—
601C3×C4—64no—
602C3×C4C22×C4×D314yes—
603C3×C4C22×C4×D314yes—
604Dic3—24no—
605Dic3—24no—
606Dic3—34no—
607Dic3—34no—
608Dic3—64no—
609Dic3—64no—
610Dic3—64no—
611Dic3—124no—
612Dic3C22×C4×D314yes—
613Dic3C22×C4×D314yes—
614C32C2×#52011yescharacteristic, complemented, Sylow
615C23—34no—
616C23—34no—
617C23—32no—
618C23—32no—
619C23—62no—
620C23—62no—
621C23—62no—
622C23—62no—
623C23—94no—
624C23—92no—
625C23—182no—
626C23—182no—
627C23C22×D3211yescharacteristic
628Q8—916no—
629D4—916no—
630D4—916no—
631D4—916no—
632C2×C4—24no—
633C2×C4—34no—
634C2×C4—34no—
635C2×C4—32no—
636C2×C4—32no—
637C2×C4—316no—
638C2×C4—316no—
639C2×C4—34no—
640C2×C4—34no—
641C2×C4—64no—
642C2×C4—64no—
643C2×C4—94no—
644C2×C4—92no—
645C2×C4—916no—
646C2×C4—94no—
647C2×C4—128no—
648C2×C4—184no—
649C2×C4—368no—
650C2×C4—368no—
651C2×C4C4×D3214yes—
652C2×C4C22×D3214yes—
653C2×C4C22×D3212yes—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—21no—
657C2×C3—24no—
658C2×C3—64no—
659C2×C3—64no—
660C2×C3#550414yescomplemented
661C2×C3#552314yescomplemented
662C2×C3C23×C4×D311yescharacteristic
663C2×C3C23×C4×D311yescharacteristic
664C2×C3C2×#100411yescharacteristic
665C2×C3C2×#100711yescharacteristic
666C2×C3C2×#100911yescharacteristic
667C2×C3C2×#101011yescharacteristic
668D3—24no—
669D3—24no—
670D3—68no—
671D3—64no—
672D3—64no—
673C22—34no—
674C22—34no—
675C22—62no—
676C22—62no—
677C22—62no—
678C22—62no—
679C22—68no—
680C22—68no—
681C22—94no—
682C22—182no—
683C22—182no—
684C22—188no—
685C22C2×C4×D3212yes—
686C22#6431412yes—
687C22#6431512yes—
688C22C23×D3211yescharacteristic
689C4—24no—
690C4—34no—
691C4—34no—
692C4—64no—
693C4—64no—
694C4—94no—
695C4—184no—
696C4C2×C4×D3214yes—
697C3—21no—
698C3C2×#550411yescharacteristic, complemented
699C3C2×#552311yescharacteristic, complemented
700C2—64no—
701C2—64no—
702C2—184no—
703C2#1059451014yesdirect product factor
704C2C22×C4×D3211yescharacteristic
705C2C2×#6431411yescharacteristic
706C2C2×#6431511yescharacteristic
subgroupG/H
centerC23C22×D32
commutatorC2×C32C24×C4
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC22×#3798C2
cosocleC22×C32C25
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#520
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×C3⋊D3C2semidirect
3. C2×C3×#892C2semidirect
4. C2×C3×D3×C4⋊C4C2semidirect
5. C2×C4×#626C2semidirect
6. C2×D3×C4⋊Dic3C2semidirect
7. C2×#63881C2semidirect
8. C2×#63879C2semidirect
9. C2×#63849C2semidirect
10. C2×#63841C2semidirect
11. C2×#63837C2semidirect
12. #10594510C2direct (N × H)
25. C2×#3798C4semidirect
30. C4⋊C4×C3⋊D3C22semidirect
36. C3×#892C22semidirect
37. C3×D3×C4⋊C4C22semidirect
43. C4×#626C22semidirect
44. D3×C4⋊Dic3C22semidirect
45. #63881C22semidirect
46. #63879C22semidirect
47. #63849C22semidirect
48. #63841C22semidirect
49. #63837C22semidirect
64. C2×#892D3semidirect
69. C2×D3×C4⋊C4D3semidirect
83. C2×C4×C3⋊D3C2×C4semidirect
91. C2×C3×C4×D3C2×C4semidirect
92. C2×C3×C4×D3C2×C4semidirect
96. C2×#627C2×C4semidirect
98. C2×#626C2×C4semidirect
99. C2×#626C2×C4semidirect
102. C2×#625C2×C4semidirect
106. #3798C2×C4semidirect
186. #892C2×D3semidirect
191. D3×C4⋊C4C2×D3semidirect
219. C4×C3⋊D3C22×C4semidirect
229. C3×C4×D3C22×C4semidirect
230. C3×C4×D3C22×C4semidirect
231. #627C22×C4semidirect
232. #626C22×C4semidirect
233. #626C22×C4semidirect
234. #625C22×C4semidirect
312. C2×C4×D3C4×D3semidirect
313. C2×C4×D3C4×D3semidirect
498. C4×D3C2×C4×D3semidirect
499. C4×D3C2×C4×D3semidirect
502. C2×C32#520semidirect
614. C32C2×#520semidirect
660. C2×C3#5504semidirect
661. C2×C3#5523semidirect
698. C3C2×#5504semidirect
699. C3C2×#5523semidirect
703. C2#10594510direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37982
C2×C4⋊C4×C3⋊D32
C2×C3×#8922
C2×C3×D3×C4⋊C42
C2×C4×#6262
C2×D3×C4⋊Dic32
C2×#638812
C2×#638792
C2×#638492
C2×#638412
C2×#638372
#105945102
C2×#55233
C2×#55043