Finite Group Databasebeta

← C2×#21462342 #30624687

Subgroups — C2×#21462342 #30624687

Order 15616.

3830 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×#6923C211yesmaximal, characteristic
2C22×#14519856C211yesmaximal, characteristic, complemented
3#21462342C2116yesmaximal, direct product factor
4C2×#16840713C211yesmaximal, characteristic, complemented
5C2×#16840712C211yesmaximal, characteristic, complemented
6C2×#16840712C211yesmaximal, characteristic, complemented
7C2×#16840711C211yesmaximal, characteristic, complemented
8C2×#16840711C211yesmaximal, characteristic, complemented
9C2×#16840710C211yesmaximal, characteristic
10C2×#16840709C211yesmaximal, characteristic, complemented
11C2×#16840709C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×#6923C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×#6923C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×#6923C211yesmaximal, characteristic, complemented
15C22×(C2×#6923)⋊C4C211yesmaximal, characteristic, complemented
16C2×#123×D61C211yesmaximal, characteristic
17C24×#6923C2211yescharacteristic
18C24×#6923C2211yescharacteristic
19C24×#6923C2211yescharacteristic
20C2×D4×#6923—28no—
21C2×D4×#6923C2218yes—
22C2×#14519856—28no—
23C2×#14519856C2218yescomplemented
24C22×C4⋊#6923C2211yescharacteristic
25C22×C4⋊#6923C2211yescharacteristic
26C22×C4⋊#6923C2211yescharacteristic
27C22×C4⋊#6923C2211yescharacteristic
28C22×C4⋊#6923C2211yescharacteristic
29C22×C22⋊#6923C2211yescharacteristic
30C22×C22⋊#6923C2211yescharacteristic
31C22×C22⋊#6923C2211yescharacteristic
32C22×C22⋊#6923C2211yescharacteristic
33C22×C22⋊#6923C2211yescharacteristic
34C22×C4×#6923C2211yescharacteristic
35C22×C4×#6923C2211yescharacteristic
36C22×C4×#6923C2211yescharacteristic
37C22×C4×#6923C2211yescharacteristic
38C22×C4×#6923C2211yescharacteristic
39#16840713C2218yescomplemented
40#16840712C2218yescomplemented
41#16840712C2218yescomplemented
42#16840711C2218yescomplemented
43#16840711C2218yescomplemented
44#16840710C2218yes—
45#16840709C2218yescomplemented
46#16840709C2218yescomplemented
47C4⋊C4×#6923C2218yescomplemented
48C22⋊C4×#6923C2218yescomplemented
49C22⋊C4×#6923C2218yescomplemented
50C2×(C2×#6923)⋊C4C2211yescharacteristic
51C2×(C2×#6923)⋊C4C2211yescharacteristic
52C2×(C2×#6923)⋊C4C2211yescharacteristic
53C2×(C2×#6923)⋊C4C2211yescharacteristic
54C2×(C2×#6923)⋊C4C2211yescharacteristic
55C2×(C2×#6923)⋊C4C2211yescharacteristic
56C2×(C2×#6923)⋊C4C2211yescharacteristic
57C2×(C2×#6923)⋊C4C2211yescharacteristic
58C2×(C2×#6923)⋊C4C2211yescharacteristic
59C2×(C2×#6923)⋊C4C2211yescharacteristic
60C2×(C2×#6923)⋊C4C2218yescomplemented
61C22×D4×D61C2211yescharacteristic
62C23×C4×D61C2211yescharacteristic
63C2×#14519762C411yescharacteristic, complemented
64C2×#14519762C411yescharacteristic, complemented
65C2×#14519761C411yescharacteristic, complemented
66C2×#14519760C411yescharacteristic, complemented
67C2×#14519759C411yescharacteristic, complemented
68C2×#14519759C411yescharacteristic, complemented
69C2×#14519758C411yescharacteristic, complemented
70#123×D61C418yescomplemented
71#123×D61C2218yes—
72C2×C4⋊C4×D61C2211yescharacteristic
73C2×C4⋊C4×D61C2211yescharacteristic
74C2×C22⋊C4×D61C2211yescharacteristic
75C2×C22⋊C4×D61C2211yescharacteristic
76C2×C22⋊C4×D61C2211yescharacteristic
77C2×#123×C61C411yescharacteristic, complemented
78C23×#6923—24no—
79C23×#6923—24no—
80C23×#6923—24no—
81C23×#6923—24no—
82C23×#6923—24no—
83C23×#6923—24no—
84C23×#6923—42no—
85C23×#6923—42no—
86C23×#6923—42no—
87C23×#6923C2311yescharacteristic
88C23×#6923C2311yescharacteristic
89C23×#6923C2311yescharacteristic
90C23×#6923C2311yescharacteristic
91C23×#6923C2314yes—
92C23×#6923C2314yes—
93C23×#6923C2314yes—
94C23×#6923C2311yescharacteristic
95C23×#6923C2311yescharacteristic
96C23×#6923C2311yescharacteristic
97C23×#6923C2311yescharacteristic
98D4×#6923—232no—
99#14519856—232no—
100C2×C4⋊#6923—24no—
101C2×C4⋊#6923—24no—
102C2×C4⋊#6923—24no—
103C2×C4⋊#6923—24no—
104C2×C4⋊#6923—42no—
105C2×C4⋊#6923C2314yes—
106C2×C4⋊#6923C2314yes—
107C2×C4⋊#6923C2314yes—
108C2×C4⋊#6923C2314yes—
109C2×C4⋊#6923C2314yes—
110C2×C22⋊#6923—24no—
111C2×C22⋊#6923—24no—
112C2×C22⋊#6923—24no—
113C2×C22⋊#6923—42no—
114C2×C22⋊#6923D418yes—
115C2×C22⋊#6923C2314yes—
116C2×C22⋊#6923C2314yes—
117C2×C22⋊#6923C2314yes—
118C2×C22⋊#6923C2314yes—
119C2×C22⋊#6923C2314yes—
120C2×C4×#6923—24no—
121C2×C4×#6923—24no—
122C2×C4×#6923—24no—
123C2×C4×#6923—24no—
124C2×C4×#6923—42no—
125C2×C4×#6923C2314yes—
126C2×C4×#6923C2314yes—
127C2×C4×#6923C2314yes—
128C2×C4×#6923C2314yes—
129C2×C4×#6923C2314yes—
130(C2×#6923)⋊C4C2314yes—
131(C2×#6923)⋊C4C2314yes—
132(C2×#6923)⋊C4C2314yes—
133(C2×#6923)⋊C4C2314yes—
134(C2×#6923)⋊C4C2314yes—
135(C2×#6923)⋊C4C2314yes—
136(C2×#6923)⋊C4C2314yes—
137(C2×#6923)⋊C4C2314yes—
138(C2×#6923)⋊C4C2314yes—
139(C2×#6923)⋊C4C2314yes—
140C24×D61C2311yescharacteristic
141C24×D61C2311yescharacteristic
142C22×D244C2×C411yescharacteristic
143C22×C22⋊D61C2×C411yescharacteristic
144C22×C22⋊D61C2×C411yescharacteristic
145C2×D4×D61—24no—
146C2×D4×D61—24no—
147C2×D4×D61C2×C414yes—
148C2×D4×D61C2314yes—
149C23×Dic61C2×C411yescharacteristic, complemented
150C22×C4×D61—24no—
151C22×C4×D61—24no—
152C22×C4×D61C2×C414yescomplemented
153C22×C4×D61C2×C411yescharacteristic, complemented
154C22×C4×D61C2×C411yescharacteristic, complemented
155C22×C4×D61C2311yescharacteristic
156C22×C4×D61C2311yescharacteristic
157C22×C4×D61C2311yescharacteristic
158C22×C4×D61C2311yescharacteristic
159C22×C4×D61C2311yescharacteristic
160C22×C4×D61C2314yes—
161#14519762C2×C418yescomplemented
162#14519762C2×C418yescomplemented
163#14519761C2×C418yescomplemented
164#14519760C2×C418yescomplemented
165#14519759C2×C418yescomplemented
166#14519759C2×C418yescomplemented
167#14519758C2×C418yescomplemented
168C2×C4⋊Dic61C2×C411yescharacteristic, complemented
169C2×C4⋊Dic61C2×C411yescharacteristic, complemented
170C2×#11758196C2×C411yescharacteristic, complemented
171C2×#11758196C2×C411yescharacteristic, complemented
172C2×#11758196C2×C411yescharacteristic, complemented
173C2×#11758196C2×C411yescharacteristic, complemented
174C4⋊C4×D61C2×C414yescomplemented
175C4⋊C4×D61C2×C414yescomplemented
176C4⋊C4×D61C2314yes—
177C4⋊C4×D61C2314yes—
178C2×C22⋊Dic61C2×C411yescharacteristic, complemented
179C2×C22⋊Dic61C2×C411yescharacteristic, complemented
180C2×C22⋊Dic61C2×C411yescharacteristic, complemented
181C2×#11758198C2×C411yescharacteristic, complemented
182C2×#11758198C2×C411yescharacteristic, complemented
183C2×#11758198C2×C411yescharacteristic, complemented
184C2×#11758198C2×C411yescharacteristic, complemented
185C2×#11758198C2×C411yescharacteristic, complemented
186C2×#11758198C2×C411yescharacteristic, complemented
187C22⋊C4×D61C2×C414yescomplemented
188C22⋊C4×D61C2×C414yescomplemented
189C22⋊C4×D61C2×C414yescomplemented
190C22⋊C4×D61C2314yes—
191C22⋊C4×D61C2314yes—
192C22⋊C4×D61C2314yes—
193C22×D4×C61C2×C411yescharacteristic
194C23×C4×C61C2×C411yescharacteristic, complemented
195#123×C61C2×C418yescomplemented
196C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
197C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
198C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
199C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
200C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
201C24×C61C22×C411yescharacteristic
202C24×C61C22×C411yescharacteristic
203C23×D61—22no—
204C23×D61—22no—
205C23×D61—22no—
206C23×D61—22no—
207C23×D61—22no—
208C23×D61—22no—
209C23×D61—22no—
210C23×D61—22no—
211C23×D61—22no—
212C23×D61—22no—
213C23×D61C22×C412yes—
214C23×D61C22×C411yescharacteristic
215C23×D61C22×C412yes—
216C23×D61C22×C411yescharacteristic
217C23×D61C2×D414yes—
218C23×D61#4114yes—
219C23×D61C2412yes—
220C23×D61C2412yes—
221C23×D61C2411yescharacteristic
222C22×#6923—22no—
223C22×#6923—22no—
224C22×#6923—22no—
225C22×#6923—22no—
226C22×#6923—22no—
227C22×#6923—22no—
228C22×#6923—22no—
229C22×#6923—22no—
230C22×#6923—22no—
231C22×#6923—22no—
232C22×#6923—22no—
233C22×#6923—28no—
234C22×#6923—22no—
235C22×#6923—22no—
236C22×#6923—28no—
237C22×#6923—22no—
238C22×#6923—22no—
239C22×#6923—22no—
240C22×#6923—22no—
241C22×#6923—22no—
242C22×#6923—22no—
243C22×#6923—22no—
244C22×#6923—28no—
245C22×#6923—28no—
246C22×#6923—28no—
247C22×#6923—28no—
248C22×#6923—44no—
249C22×#6923—44no—
250C22×#6923—44no—
251C22×#6923—416no—
252C22×#6923—416no—
253C22×#6923—416no—
254C22×#6923C2×D414yes—
255C22×#6923C2×D414yes—
256C22×#6923#4114yes—
257C22×#6923#4114yes—
258C22×#6923C2412yes—
259C22×#6923C2412yes—
260C22×#6923C2412yes—
261C22×#6923C2412yes—
262C22×#6923C2412yes—
263C22×#6923C2412yes—
264C22×#6923C2412yes—
265C22×#6923C2412yes—
266C2×D4×C61—24no—
267C2×D4×C61C22×C414yes—
268C22×C4×C61—24no—
269C22×C4×C61C22×C411yescharacteristic
270C22×C4×C61C22×C411yescharacteristic
271C22×C4×C61C22×C411yescharacteristic
272C22×C4×C61C22×C411yescharacteristic
273C22×C4×C61C22×C411yescharacteristic
274C22×C4×C61C22×C414yescomplemented
275C2×C22⋊D61—24no—
276C2×C22⋊D61—24no—
277C2×C22⋊D61C22×C414yes—
278C2×C22⋊D61C22×C414yes—
279C22×Dic61—24no—
280C22×Dic61C22×C411yescharacteristic
281C22×Dic61C22×C411yescharacteristic
282C22×Dic61C22×C411yescharacteristic
283C22×Dic61C22×C411yescharacteristic
284C22×Dic61C22×C411yescharacteristic
285C22×Dic61C22×C414yescomplemented
286D4×D61—216no—
287D4×D61—28no—
288D4×D61—28no—
289C2×D244—24no—
290C2×D244C22×C414yes—
291C2×C4×D61—216no—
292C2×C4×D61—24no—
293C2×C4×D61—24no—
294C2×C4×D61—22no—
295C2×C4×D61—22no—
296C2×C4×D61—28no—
297C2×C4×D61—22no—
298C2×C4×D61—22no—
299C2×C4×D61—22no—
300C2×C4×D61—28no—
301C2×C4×D61—22no—
302C2×C4×D61—22no—
303C2×C4×D61—22no—
304C2×C4×D61—22no—
305C2×C4×D61—22no—
306C2×C4×D61C22×C412yes—
307C2×C4×D61C22×C412yes—
308C2×C4×D61C22×C412yes—
309C2×C4×D61C22×C412yes—
310C2×C4×D61C22×C412yes—
311C2×C4×D61C22×C414yescomplemented
312C2×C4×D61C22×C414yescomplemented
313C2×C4×D61C2412yes—
314C2×C4×D61C2412yes—
315C2×C4×D61C2412yes—
316C2×C4×D61C2412yes—
317C2×C4×D61C2412yes—
318C22⋊#6923—28no—
319C22⋊#6923—28no—
320C22⋊#6923—28no—
321C22⋊#6923—44no—
322C22⋊#6923C2×D4116yes—
323C4⋊#6923—28no—
324C4⋊#6923—28no—
325C4⋊#6923—28no—
326C4⋊#6923—28no—
327C4⋊#6923—44no—
328C4×#6923—28no—
329C4×#6923—28no—
330C4×#6923—28no—
331C4×#6923—28no—
332C4×#6923—44no—
333C4⋊C4×C61C22×C414yescomplemented
334C4⋊C4×C61C22×C414yescomplemented
335C22⋊C4×C61C22×C414yescomplemented
336C22⋊C4×C61C22×C414yescomplemented
337C22⋊C4×C61C22×C414yescomplemented
338C22⋊Dic61C22×C414yescomplemented
339C22⋊Dic61C22×C414yescomplemented
340C22⋊Dic61C22×C414yescomplemented
341#11758198C22×C414yescomplemented
342#11758198C22×C414yescomplemented
343#11758198C22×C414yescomplemented
344#11758198C22×C414yescomplemented
345#11758198C22×C414yescomplemented
346#11758198C22×C414yescomplemented
347C4⋊Dic61C22×C414yescomplemented
348C4⋊Dic61C22×C414yescomplemented
349#11758196C22×C414yescomplemented
350#11758196C22×C414yescomplemented
351#11758196C22×C414yescomplemented
352#11758196C22×C414yescomplemented
353C23×C61—22no—
354C23×C61—22no—
355C23×C61—22no—
356C23×C61—22no—
357C23×C61—22no—
358C23×C61C4×D414yes—
359C23×C61C23×C412yes—
360C23×C61C23×C412yes—
361C23×C61C23×C411yescharacteristic
362C22×D61—22no—
363C22×D61—22no—
364C22×D61—24no—
365C22×D61—24no—
366C22×D61—28no—
367C22×D61—28no—
368C22×D61—28no—
369C22×D61—28no—
370C22×D61—22no—
371C22×D61—22no—
372C22×D61—22no—
373C22×D61—22no—
374C22×D61—22no—
375C22×D61—22no—
376C22×D61—22no—
377C22×D61—24no—
378C22×D61—24no—
379C22×D61—24no—
380C22×D61—22no—
381C22×D61—22no—
382C22×D61—22no—
383C22×D61—22no—
384C22×D61—22no—
385C22×D61—22no—
386C22×D61—44no—
387C22×D61—44no—
388C22×D61—44no—
389C22×D61—44no—
390C22×D61C4×D414yes—
391C22×D61C4×D418yes—
392C22×D61C23×C412yes—
393C22×D61C23×C412yes—
394C22×D61C23×C411yescharacteristic
395C22×D61C22×D414yes—
396C22×D61C22×D412yes—
397C22×D61C2×#4114yes—
398C22×D61C2×#4112yes—
399C22×D61C2×#4112yes—
400C22×D61C2×#4112yes—
401C22×D61H(5,𝔽2)12yes—
402C22×D612−1+412yes—
403C22×D61C2511yescharacteristic
404C2×#6923—28no—
405C2×#6923—28no—
406C2×#6923—28no—
407C2×#6923—28no—
408C2×#6923—22no—
409C2×#6923—22no—
410C2×#6923—22no—
411C2×#6923—22no—
412C2×#6923—22no—
413C2×#6923—22no—
414C2×#6923—22no—
415C2×#6923—22no—
416C2×#6923—22no—
417C2×#6923—22no—
418C2×#6923—22no—
419C2×#6923—22no—
420C2×#6923—22no—
421C2×#6923—22no—
422C2×#6923—22no—
423C2×#6923—22no—
424C2×#6923—22no—
425C2×#6923—22no—
426C2×#6923—22no—
427C2×#6923—22no—
428C2×#6923—416no—
429C2×#6923—416no—
430C2×#6923—416no—
431C2×#6923—44no—
432C2×#6923—44no—
433C2×#6923—44no—
434C2×#6923—44no—
435C2×#6923C22×D414yes—
436C2×#6923C22×D414yes—
437C2×#6923C2×#4114yes—
438C2×#6923C2×#4114yes—
439D4×C61—28no—
440C2×C4×C61—22no—
441C2×C4×C61—22no—
442C2×C4×C61—28no—
443C2×C4×C61—22no—
444C2×C4×C61—22no—
445C2×C4×C61—22no—
446C2×C4×C61C23×C412yes—
447C2×C4×C61C23×C412yes—
448C2×C4×C61C23×C412yes—
449C2×C4×C61C23×C412yes—
450C2×C4×C61C23×C412yes—
451C22⋊D61—28no—
452C22⋊D61—28no—
453C2×Dic61—22no—
454C2×Dic61—22no—
455C2×Dic61—28no—
456C2×Dic61—22no—
457C2×Dic61—22no—
458C2×Dic61—22no—
459C2×Dic61C23×C412yes—
460C2×Dic61C23×C412yes—
461C2×Dic61C23×C412yes—
462C2×Dic61C23×C412yes—
463C2×Dic61C23×C412yes—
464D244—28no—
465C4×D61—24no—
466C4×D61—24no—
467C4×D61—28no—
468C4×D61—28no—
469C4×D61—24no—
470C4×D61—24no—
471C4×D61—24no—
472C4×D61—22no—
473C4×D61—22no—
474C4×D61—22no—
475C4×D61—22no—
476C4×D61—22no—
477C4×D61—22no—
478C4×D61—22no—
479C4×D61—22no—
480C4×D61—22no—
481C4×D61—22no—
482C2×#2359—611nomaximal, Sylow
483C22×C61—28no—
484C22×C61—22no—
485C22×C61—22no—
486C22×C61—22no—
487C22×C61—22no—
488C22×C61—22no—
489C22×C61—44no—
490C22×C61C2×C4×D414yes—
491C22×C61C2×C4×D412yes—
492C22×C61C4×#4112yes—
493C22×C61#52012yes—
494C22×C61C24×C411yescharacteristic
495C2×D61—28no—
496C2×D61—22no—
497C2×D61—22no—
498C2×D61—216no—
499C2×D61—24no—
500C2×D61—24no—
501C2×D61—24no—
502C2×D61—24no—
503C2×D61—22no—
504C2×D61—22no—
505C2×D61—22no—
506C2×D61—44no—
507C2×D61—48no—
508C2×D61—42no—
509C2×D61—42no—
510C2×D61—42no—
511C2×D61—42no—
512C2×D61C2×C4×D414yes—
513C2×D61C2×C4×D412yes—
514C2×D61C4×#4112yes—
515C2×D61#52012yes—
516C2×D61#54614yes—
517C2×D61#54714yes—
518C2×D61#55114yes—
519C2×D61#55214yes—
520C2×D61C23×D411yescharacteristic
521C2×D61C22×#4111yescharacteristic
522C2×D61C22×#4111yescharacteristic
523C2×D61C22×#4111yescharacteristic
524C2×D61C2×H(5,𝔽2)11yescharacteristic
525C2×D61C2×2−1+411yescharacteristic
526#6923—24no—
527#6923—24no—
528#6923—24no—
529#6923—24no—
530#6923—42no—
531#6923—42no—
532#6923—42no—
533#6923—42no—
534C4×C61—22no—
535C4×C61—22no—
536C4×C61—22no—
537C4×C61—22no—
538C4×C61—22no—
539Dic61—22no—
540Dic61—22no—
541Dic61—22no—
542Dic61—22no—
543Dic61—22no—
544C22×#123—611no—
545C22×C4×D4—611no—
546C22×#117—611no—
547#2359—6116no—
548C2×#389—611no—
549C2×#388—611no—
550C2×#388—611no—
551C2×#387—611no—
552C2×#387—611no—
553C2×#386—611no—
554C2×#385—611no—
555C2×#385—611no—
556C2×C4×C4⋊C4—611no—
557C2×C4×C22⋊C4—611no—
558C2×C4×C22⋊C4—611no—
559C22×#95—611no—
560C2×C61—24no—
561C2×C61—42no—
562C2×C61#235914yescomplemented
563C2×C61C22×C4×D411yescharacteristic
564C2×C61C2×C4×#4111yescharacteristic
565C2×C61C2×#52011yescharacteristic
566D61—24no—
567D61—42no—
568D61#235914yescomplemented
569D61C2×#54611yescharacteristic
570D61C2×#54711yescharacteristic
571D61C2×#55111yescharacteristic
572D61C2×#55211yescharacteristic
573C23×D4—611no—
574C24×C4—611no—
575C24×C4—611no—
576C24×C4—611no—
577C24×C4—611no—
578C2×#123—611no—
579C2×#123—611no—
580C2×#123—618no—
581C2×#123—618no—
582C2×#123—611no—
583C2×#123—611no—
584C2×#123—611no—
585C2×#123—611no—
586C2×#123—611no—
587C2×#123#692311yescharacteristic, complemented
588C2×C4×D4—618no—
589C2×C4×D4—1228no—
590C2×#117—618no—
591C2×#117—1228no—
592C22×C4⋊C4—611no—
593C22×C4⋊C4—611no—
594C22×C4⋊C4—611no—
595C22×C4⋊C4—611no—
596C22×C4⋊C4—611no—
597C22×C4⋊C4—611no—
598C22×C4⋊C4—611no—
599C22×C22⋊C4—611no—
600C22×C22⋊C4—611no—
601C22×C22⋊C4—611no—
602C22×C22⋊C4—611no—
603C22×C22⋊C4—611no—
604C22×C22⋊C4—611no—
605C22×C22⋊C4—611no—
606C22×C22⋊C4—611no—
607C22×C42—611no—
608C22×C42—611no—
609C22×C42—611no—
610C22×C42—611no—
611C22×C42—611no—
612#389—618no—
613#388—618no—
614#388—618no—
615#387—618no—
616#387—618no—
617#386—618no—
618#385—618no—
619#385—618no—
620C4×C4⋊C4—618no—
621C4×C22⋊C4—618no—
622C4×C22⋊C4—618no—
623C2×#95—618no—
624C2×#95—611no—
625C2×#95—611no—
626C2×#95—611no—
627C2×#95—611no—
628C2×#95—611no—
629C2×#95—611no—
630C2×#95—611no—
631C2×#95—611no—
632C2×#95—611no—
633C2×#95—611no—
634C61C2×#235911yescharacteristic, complemented, Sylow
635C25—611no—
636C25—611no—
637C22×D4—611no—
638C22×D4—611no—
639C22×D4—614no—
640C22×D4—614no—
641C22×D4—611no—
642C22×D4—1224no—
643C22×D4—1224no—
644C22×D4C2×#692311yescharacteristic
645C23×C4—611no—
646C23×C4—611no—
647C23×C4—611no—
648C23×C4—611no—
649C23×C4—611no—
650C23×C4—611no—
651C23×C4—611no—
652C23×C4—611no—
653C23×C4—611no—
654C23×C4—611no—
655C23×C4—611no—
656C23×C4—611no—
657C23×C4—614no—
658C23×C4—614no—
659C23×C4—611no—
660C23×C4—611no—
661C23×C4—611no—
662C23×C4—611no—
663C23×C4—614no—
664C23×C4—614no—
665C23×C4—614no—
666C23×C4—1224no—
667C23×C4—1224no—
668C23×C4—1224no—
669C23×C4—1224no—
670C23×C4—1224no—
671C23×C4—1224no—
672C23×C4—1224no—
673C23×C4—1224no—
674C23×C4—2442no—
675C23×C4—2442no—
676C23×C4—2442no—
677C23×C4C2×#692311yescharacteristic, complemented
678#123—618no—
679#123—618no—
680#123—618no—
681#123—618no—
682#123—618no—
683#123—618no—
684#123—618no—
685#123C2×#692318yescomplemented
686C4×D4—12232no—
687#117—12232no—
688C2×C4⋊C4—611no—
689C2×C4⋊C4—611no—
690C2×C4⋊C4—611no—
691C2×C4⋊C4—611no—
692C2×C4⋊C4—611no—
693C2×C4⋊C4—611no—
694C2×C4⋊C4—614no—
695C2×C4⋊C4—614no—
696C2×C4⋊C4—614no—
697C2×C4⋊C4—614no—
698C2×C4⋊C4—614no—
699C2×C4⋊C4—614no—
700C2×C4⋊C4—614no—
701C2×C4⋊C4—614no—
702C2×C4⋊C4—614no—
703C2×C4⋊C4—1224no—
704C2×C4⋊C4—1224no—
705C2×C4⋊C4—1224no—
706C2×C4⋊C4—1224no—
707C2×C4⋊C4—2442no—
708C2×C4⋊C4C2×#692311yescharacteristic, complemented
709C2×C4⋊C4C2×#692311yescharacteristic, complemented
710C2×C22⋊C4—614no—
711C2×C22⋊C4—618no—
712C2×C22⋊C4—611no—
713C2×C22⋊C4—611no—
714C2×C22⋊C4—611no—
715C2×C22⋊C4—611no—
716C2×C22⋊C4—611no—
717C2×C22⋊C4—611no—
718C2×C22⋊C4—611no—
719C2×C22⋊C4—611no—
720C2×C22⋊C4—611no—
721C2×C22⋊C4—614no—
722C2×C22⋊C4—614no—
723C2×C22⋊C4—614no—
724C2×C22⋊C4—614no—
725C2×C22⋊C4—614no—
726C2×C22⋊C4—614no—
727C2×C22⋊C4—614no—
728C2×C22⋊C4—614no—
729C2×C22⋊C4—614no—
730C2×C22⋊C4—614no—
731C2×C22⋊C4—1224no—
732C2×C22⋊C4—1224no—
733C2×C22⋊C4—1224no—
734C2×C22⋊C4—2442no—
735C2×C22⋊C4C2×#692311yescharacteristic, complemented
736C2×C22⋊C4C2×#692311yescharacteristic, complemented
737C2×C22⋊C4C2×#692311yescharacteristic, complemented
738C2×C42—614no—
739C2×C42—614no—
740C2×C42—614no—
741C2×C42—614no—
742C2×C42—614no—
743C2×C42—1224no—
744C2×C42—1224no—
745C2×C42—1224no—
746C2×C42—1224no—
747C2×C42—2442no—
748#95—614no—
749#95—614no—
750#95—614no—
751#95—614no—
752#95—614no—
753#95—614no—
754#95—614no—
755#95—614no—
756#95—614no—
757#95—614no—
758C24—611no—
759C24—614no—
760C24—614no—
761C24—612no—
762C24—612no—
763C24—611no—
764C24—612no—
765C24—612no—
766C24—611no—
767C24—1222no—
768C24—1222no—
769C24—1222no—
770C24—1222no—
771C24—1222no—
772C24—1222no—
773C24—1222no—
774C24—1222no—
775C24—1222no—
776C24—1222no—
777C24C22×#692311yescharacteristic
778C24C22×#692311yescharacteristic
779C2×D4—24no—
780C2×D4—614no—
781C2×D4—614no—
782C2×D4—614no—
783C2×D4—1224no—
784C2×D4—1228no—
785C2×D4—12216no—
786C2×D4—1228no—
787C2×D4—1224no—
788C2×D4—1224no—
789C2×D4C22×#692314yes—
790C22×C4—24no—
791C22×C4—612no—
792C22×C4—612no—
793C22×C4—612no—
794C22×C4—612no—
795C22×C4—614no—
796C22×C4—614no—
797C22×C4—614no—
798C22×C4—614no—
799C22×C4—614no—
800C22×C4—611no—
801C22×C4—611no—
802C22×C4—611no—
803C22×C4—611no—
804C22×C4—611no—
805C22×C4—612no—
806C22×C4—612no—
807C22×C4—612no—
808C22×C4—612no—
809C22×C4—612no—
810C22×C4—612no—
811C22×C4—612no—
812C22×C4—612no—
813C22×C4—612no—
814C22×C4—612no—
815C22×C4—614no—
816C22×C4—614no—
817C22×C4—612no—
818C22×C4—612no—
819C22×C4—612no—
820C22×C4—612no—
821C22×C4—1222no—
822C22×C4—1222no—
823C22×C4—1222no—
824C22×C4—1222no—
825C22×C4—1222no—
826C22×C4—1222no—
827C22×C4—1228no—
828C22×C4—1222no—
829C22×C4—1222no—
830C22×C4—1224no—
831C22×C4—1224no—
832C22×C4—12216no—
833C22×C4—1228no—
834C22×C4—1222no—
835C22×C4—1222no—
836C22×C4—1228no—
837C22×C4—1228no—
838C22×C4—1228no—
839C22×C4—1228no—
840C22×C4—1222no—
841C22×C4—1222no—
842C22×C4—1222no—
843C22×C4—1222no—
844C22×C4—1222no—
845C22×C4—1222no—
846C22×C4—1222no—
847C22×C4—1222no—
848C22×C4—1224no—
849C22×C4—1222no—
850C22×C4—1222no—
851C22×C4—1222no—
852C22×C4—1222no—
853C22×C4—1222no—
854C22×C4—1222no—
855C22×C4—1222no—
856C22×C4—1222no—
857C22×C4—1228no—
858C22×C4—1228no—
859C22×C4—1222no—
860C22×C4—1222no—
861C22×C4—1222no—
862C22×C4—1222no—
863C22×C4—2444no—
864C22×C4—2444no—
865C22×C4—2444no—
866C22×C4—24416no—
867C22×C4—24416no—
868C22×C4—24416no—
869C22×C4C22×#692311yescharacteristic
870C22×C4C22×#692311yescharacteristic
871C22×C4C22×#692311yescharacteristic
872C22×C4C22×#692311yescharacteristic
873C22×C4C22×#692311yescharacteristic
874C22×C4C22×#692314yescomplemented
875C4⋊C4—614no—
876C4⋊C4—614no—
877C4⋊C4—614no—
878C4⋊C4—614no—
879C4⋊C4—614no—
880C4⋊C4—614no—
881C4⋊C4—1228no—
882C4⋊C4—1228no—
883C4⋊C4—1228no—
884C4⋊C4—1228no—
885C4⋊C4—2444no—
886C4⋊C4C22×#692314yescomplemented
887C4⋊C4C22×#692314yescomplemented
888C22⋊C4—6116no—
889C22⋊C4—614no—
890C22⋊C4—614no—
891C22⋊C4—614no—
892C22⋊C4—614no—
893C22⋊C4—614no—
894C22⋊C4—614no—
895C22⋊C4—614no—
896C22⋊C4—614no—
897C22⋊C4—614no—
898C22⋊C4—1228no—
899C22⋊C4—1228no—
900C22⋊C4—1228no—
901C22⋊C4—2444no—
902C22⋊C4C22×#692314yescomplemented
903C22⋊C4C22×#692314yescomplemented
904C22⋊C4C22×#692314yescomplemented
905C42—1228no—
906C42—1228no—
907C42—1228no—
908C42—1228no—
909C42—2444no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—612no—
916C23—612no—
917C23—612no—
918C23—612no—
919C23—612no—
920C23—612no—
921C23—611no—
922C23—611no—
923C23—618no—
924C23—614no—
925C23—614no—
926C23—614no—
927C23—612no—
928C23—612no—
929C23—1222no—
930C23—1222no—
931C23—1222no—
932C23—1228no—
933C23—1228no—
934C23—1224no—
935C23—1222no—
936C23—1224no—
937C23—1228no—
938C23—1228no—
939C23—1222no—
940C23—1222no—
941C23—1222no—
942C23—1222no—
943C23—1222no—
944C23—1224no—
945C23—1224no—
946C23—1222no—
947C23—1224no—
948C23—1222no—
949C23—1222no—
950C23—1222no—
951C23—1222no—
952C23—1222no—
953C23—2444no—
954C23—2444no—
955C23—2444no—
956C23—2444no—
957C23D4×#692314yes—
958C23C23×#692312yes—
959C23C23×#692312yes—
960C23C23×#692311yescharacteristic
961D4—28no—
962D4—1228no—
963D4—1228no—
964D4—1228no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—28no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—614no—
972C2×C4—614no—
973C2×C4—614no—
974C2×C4—614no—
975C2×C4—612no—
976C2×C4—612no—
977C2×C4—612no—
978C2×C4—612no—
979C2×C4—612no—
980C2×C4—1222no—
981C2×C4—1222no—
982C2×C4—1222no—
983C2×C4—1222no—
984C2×C4—1222no—
985C2×C4—1222no—
986C2×C4—1224no—
987C2×C4—1222no—
988C2×C4—1224no—
989C2×C4—1222no—
990C2×C4—1222no—
991C2×C4—1224no—
992C2×C4—1224no—
993C2×C4—1228no—
994C2×C4—1228no—
995C2×C4—1222no—
996C2×C4—1224no—
997C2×C4—1222no—
998C2×C4—1222no—
999C2×C4—1222no—
1000C2×C4—1222no—
1001C2×C4—1222no—
1002C2×C4—1228no—
1003C2×C4—1222no—
1004C2×C4—1222no—
1005C2×C4—1228no—
1006C2×C4—1228no—
1007C2×C4—1222no—
1008C2×C4—1228no—
1009C2×C4—1228no—
1010C2×C4—1222no—
1011C2×C4—1222no—
1012C2×C4—1222no—
1013C2×C4—1222no—
1014C2×C4—1222no—
1015C2×C4—1222no—
1016C2×C4—1222no—
1017C2×C4—1222no—
1018C2×C4—1222no—
1019C2×C4—1222no—
1020C2×C4—1222no—
1021C2×C4—1222no—
1022C2×C4—1222no—
1023C2×C4—1222no—
1024C2×C4—1222no—
1025C2×C4—1222no—
1026C2×C4—1222no—
1027C2×C4—24416no—
1028C2×C4—24416no—
1029C2×C4—24416no—
1030C2×C4—2444no—
1031C2×C4—2444no—
1032C2×C4—2444no—
1033C2×C4—2444no—
1034C2×C4C23×#692312yes—
1035C2×C4C23×#692312yes—
1036C2×C4C23×#692312yes—
1037C2×C4C23×#692312yes—
1038C2×C4C23×#692312yes—
1039C22—22no—
1040C22—22no—
1041C22—28no—
1042C22—22no—
1043C22—22no—
1044C22—22no—
1045C22—44no—
1046C22—611no—
1047C22—611no—
1048C22—612no—
1049C22—611no—
1050C22—611no—
1051C22—612no—
1052C22—611no—
1053C22—611no—
1054C22—612no—
1055C22—614no—
1056C22—614no—
1057C22—614no—
1058C22—614no—
1059C22—614no—
1060C22—1224no—
1061C22—1224no—
1062C22—1224no—
1063C22—12216no—
1064C22—1224no—
1065C22—1222no—
1066C22—1222no—
1067C22—1228no—
1068C22—1222no—
1069C22—1222no—
1070C22—1222no—
1071C22—2442no—
1072C22—2442no—
1073C22—2442no—
1074C22—2448no—
1075C22—2442no—
1076C22—2444no—
1077C22C2×D4×#692314yes—
1078C22C2×D4×#692312yes—
1079C22#41×#692312yes—
1080C22#1684083112yes—
1081C22C24×#692311yescharacteristic
1082C4—22no—
1083C4—22no—
1084C4—22no—
1085C4—22no—
1086C4—22no—
1087C4—1224no—
1088C4—1224no—
1089C4—1224no—
1090C4—1224no—
1091C4—1222no—
1092C4—1222no—
1093C4—1222no—
1094C4—1222no—
1095C4—1222no—
1096C4—2442no—
1097C4—2442no—
1098C4—2442no—
1099C4—2442no—
1100C2—24no—
1101C2—42no—
1102C2—611no—
1103C2—611no—
1104C2—611no—
1105C2—614no—
1106C2—611no—
1107C2—1224no—
1108C2—2442no—
1109C2#2146234214yesdirect product factor
1110C2C22×D4×#692311yescharacteristic
1111C2C2×#41×#692311yescharacteristic
1112C2C2×#1684083111yescharacteristic
subgroupG/H
centerC23C23×#6923
commutatorC22×C61C24×C4
FrattiniC22C24×#6923
FittingC2×#123×C61C4
socleC23×C61C23×C4
prime radicalC22×D4×D61C22
cosocleC22×D61C25
hypercenterC2×#123#6923
hypocenterC61C2×#2359
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. C22×#14519856C2semidirect
3. #21462342C2direct (N × H)
4. C2×#16840713C2semidirect
5. C2×#16840712C2semidirect
6. C2×#16840712C2semidirect
7. C2×#16840711C2semidirect
8. C2×#16840711C2semidirect
10. C2×#16840709C2semidirect
11. C2×#16840709C2semidirect
12. C2×C4⋊C4×#6923C2semidirect
13. C2×C22⋊C4×#6923C2semidirect
14. C2×C22⋊C4×#6923C2semidirect
15. C22×(C2×#6923)⋊C4C2semidirect
23. C2×#14519856C22semidirect
39. #16840713C22semidirect
40. #16840712C22semidirect
41. #16840712C22semidirect
42. #16840711C22semidirect
43. #16840711C22semidirect
45. #16840709C22semidirect
46. #16840709C22semidirect
47. C4⋊C4×#6923C22semidirect
48. C22⋊C4×#6923C22semidirect
49. C22⋊C4×#6923C22semidirect
60. C2×(C2×#6923)⋊C4C22semidirect
63. C2×#14519762C4semidirect
64. C2×#14519762C4semidirect
65. C2×#14519761C4semidirect
66. C2×#14519760C4semidirect
67. C2×#14519759C4semidirect
68. C2×#14519759C4semidirect
69. C2×#14519758C4semidirect
70. #123×D61C4semidirect
77. C2×#123×C61C4semidirect
149. C23×Dic61C2×C4semidirect
152. C22×C4×D61C2×C4semidirect
153. C22×C4×D61C2×C4semidirect
154. C22×C4×D61C2×C4semidirect
161. #14519762C2×C4semidirect
162. #14519762C2×C4semidirect
163. #14519761C2×C4semidirect
164. #14519760C2×C4semidirect
165. #14519759C2×C4semidirect
166. #14519759C2×C4semidirect
167. #14519758C2×C4semidirect
168. C2×C4⋊Dic61C2×C4semidirect
169. C2×C4⋊Dic61C2×C4semidirect
170. C2×#11758196C2×C4semidirect
171. C2×#11758196C2×C4semidirect
172. C2×#11758196C2×C4semidirect
173. C2×#11758196C2×C4semidirect
174. C4⋊C4×D61C2×C4semidirect
175. C4⋊C4×D61C2×C4semidirect
178. C2×C22⋊Dic61C2×C4semidirect
179. C2×C22⋊Dic61C2×C4semidirect
180. C2×C22⋊Dic61C2×C4semidirect
181. C2×#11758198C2×C4semidirect
182. C2×#11758198C2×C4semidirect
183. C2×#11758198C2×C4semidirect
184. C2×#11758198C2×C4semidirect
185. C2×#11758198C2×C4semidirect
186. C2×#11758198C2×C4semidirect
187. C22⋊C4×D61C2×C4semidirect
188. C22⋊C4×D61C2×C4semidirect
189. C22⋊C4×D61C2×C4semidirect
194. C23×C4×C61C2×C4semidirect
195. #123×C61C2×C4semidirect
196. C2×C4⋊C4×C61C2×C4semidirect
197. C2×C4⋊C4×C61C2×C4semidirect
198. C2×C22⋊C4×C61C2×C4semidirect
199. C2×C22⋊C4×C61C2×C4semidirect
200. C2×C22⋊C4×C61C2×C4semidirect
274. C22×C4×C61C22×C4semidirect
285. C22×Dic61C22×C4semidirect
311. C2×C4×D61C22×C4semidirect
312. C2×C4×D61C22×C4semidirect
333. C4⋊C4×C61C22×C4semidirect
334. C4⋊C4×C61C22×C4semidirect
335. C22⋊C4×C61C22×C4semidirect
336. C22⋊C4×C61C22×C4semidirect
337. C22⋊C4×C61C22×C4semidirect
338. C22⋊Dic61C22×C4semidirect
339. C22⋊Dic61C22×C4semidirect
340. C22⋊Dic61C22×C4semidirect
341. #11758198C22×C4semidirect
342. #11758198C22×C4semidirect
343. #11758198C22×C4semidirect
344. #11758198C22×C4semidirect
345. #11758198C22×C4semidirect
346. #11758198C22×C4semidirect
347. C4⋊Dic61C22×C4semidirect
348. C4⋊Dic61C22×C4semidirect
349. #11758196C22×C4semidirect
350. #11758196C22×C4semidirect
351. #11758196C22×C4semidirect
352. #11758196C22×C4semidirect
562. C2×C61#2359semidirect
568. D61#2359semidirect
587. C2×#123#6923semidirect
634. C61C2×#2359semidirect
677. C23×C4C2×#6923semidirect
685. #123C2×#6923semidirect
708. C2×C4⋊C4C2×#6923semidirect
709. C2×C4⋊C4C2×#6923semidirect
735. C2×C22⋊C4C2×#6923semidirect
736. C2×C22⋊C4C2×#6923semidirect
737. C2×C22⋊C4C2×#6923semidirect
874. C22×C4C22×#6923semidirect
886. C4⋊C4C22×#6923semidirect
887. C4⋊C4C22×#6923semidirect
902. C22⋊C4C22×#6923semidirect
903. C22⋊C4C22×#6923semidirect
904. C22⋊C4C22×#6923semidirect
1109. C2#21462342direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×#69232
C22×#145198562
#214623422
C2×#168407132
C2×#168407122
C2×#168407112
C2×#168407102
C2×#168407092
C2×C4⋊C4×#69232
C2×C22⋊C4×#69232
C22×(C2×#6923)⋊C42
C2×#123×D612
C2×#235961