Finite Group Databasebeta

← C2×C4×#14519763 #29838482

Subgroups — C2×C4×#14519763 #29838482

Order 15616.

3790 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519763C211yesmaximal, characteristic
2C22×C4×Dic122C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D61C211yesmaximal, characteristic
4C4×#14519763C2116yesmaximal, direct product factor
5C2×#16839666C211yesmaximal, characteristic, complemented
6C2×#16839662C211yesmaximal, characteristic
7C2×#16839655C211yesmaximal, characteristic, complemented
8C2×#16839654C211yesmaximal, characteristic, complemented
9C2×#16839651C211yesmaximal, characteristic, complemented
10C2×#16839650C211yesmaximal, characteristic, complemented
11C2×#16839626C211yesmaximal, characteristic, complemented
12C2×C4×#11758198C211yesmaximal, characteristic, complemented
13C2×C4×#11758198C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
15C2×C42×Dic61C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
17C23×Dic122C2211yescharacteristic
18C23×C22⋊D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519763C4116yesdirect product factor
21C2×#14519763C2218yes—
22C2×C4×Dic122—28no—
23C2×C4×Dic122C2218yescomplemented
24C2×C4×C22⋊D61—28no—
25C2×C4×C22⋊D61C2218yes—
26C22×C4⋊Dic61C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×C22⋊Dic61C2211yescharacteristic
31C22×C22⋊Dic61C2211yescharacteristic
32C22×C22⋊Dic61C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×C4×Dic61C2211yescharacteristic
39C22×C4×Dic61C2211yescharacteristic
40C22×C4×Dic61C2211yescharacteristic
41C22×C4×Dic61C2211yescharacteristic
42C22×C4×Dic61C2211yescharacteristic
43C22×C4×Dic61C2211yescharacteristic
44C22×C4×Dic61C2211yescharacteristic
45#16839666C2218yescomplemented
46#16839662C2218yes—
47#16839655C2218yescomplemented
48#16839654C2218yescomplemented
49#16839651C2218yescomplemented
50#16839650C2218yescomplemented
51#16839626C2218yescomplemented
52C4×#11758198C2218yescomplemented
53C4×#11758198C2218yescomplemented
54C4×C22⋊Dic61C2218yescomplemented
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C42×Dic61C2218yescomplemented
62C24×C4×C61C2211yescharacteristic
63C22×C22⋊C4×C61C2211yescharacteristic
64C22×C22⋊C4×C61C2211yescharacteristic
65C22×C42×C61C2211yescharacteristic
66C22×C42×C61C2211yescharacteristic
67C4×C22⋊C4×C61C2218yescomplemented
68C2×#95×C61C2211yescharacteristic
69C2×#95×C61C2211yescharacteristic
70C24×D61C2311yescharacteristic
71C22×Dic122—24no—
72C22×Dic122—24no—
73C22×Dic122C2×C418yescomplemented
74C22×Dic122C2314yes—
75C22×C22⋊D61—24no—
76C22×C22⋊D61—24no—
77C22×C22⋊D61C2×C418yes—
78C22×C22⋊D61C2314yes—
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C22×C4×D61—24no—
87C22×C4×D61—24no—
88C22×C4×D61—24no—
89C22×C4×D61C2314yes—
90#14519763C2×C4164yesdirect product factor
91C4×Dic122—232no—
92C4×C22⋊D61—232no—
93C2×C4⋊Dic61—24no—
94C2×C4⋊Dic61C2314yes—
95C2×#11758196—24no—
96C2×#11758196—24no—
97C2×#11758196—24no—
98C2×#11758196C2314yes—
99C2×#11758196C2314yes—
100C2×#11758196C2314yes—
101C2×C22⋊Dic61—24no—
102C2×C22⋊Dic61—24no—
103C2×C22⋊Dic61C2×C418yescomplemented
104C2×C22⋊Dic61C2314yes—
105C2×C22⋊Dic61C2314yes—
106C2×C22⋊Dic61C2314yes—
107C2×#11758198—24no—
108C2×#11758198—24no—
109C2×#11758198—24no—
110C2×#11758198C2×C418yescomplemented
111C2×#11758198C2×C418yescomplemented
112C2×#11758198C2314yes—
113C2×#11758198C2314yes—
114C2×#11758198C2314yes—
115C2×#11758198C2314yes—
116C2×#11758198C2314yes—
117C2×C4×Dic61—24no—
118C2×C4×Dic61—24no—
119C2×C4×Dic61—24no—
120C2×C4×Dic61—24no—
121C2×C4×Dic61—24no—
122C2×C4×Dic61C2×C418yescomplemented
123C2×C4×Dic61D418yes—
124C2×C4×Dic61C2314yes—
125C2×C4×Dic61C2314yes—
126C2×C4×Dic61C2314yes—
127C2×C4×Dic61C2314yes—
128C2×C4×Dic61C2314yes—
129C2×C4×Dic61C2314yes—
130C2×C4×Dic61C2314yes—
131#14519684C2314yes—
132#14519684C2314yes—
133#14519684C2314yes—
134#14519684C2314yes—
135#14519684C2314yes—
136#14519684C2314yes—
137C25×C61C2311yescharacteristic
138C23×C4×C61—24no—
139C23×C4×C61—24no—
140C23×C4×C61—24no—
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2314yes—
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C2×C22⋊C4×C61—24no—
149C2×C22⋊C4×C61C2×C418yescomplemented
150C2×C22⋊C4×C61C2314yes—
151C2×C22⋊C4×C61C2314yes—
152C2×C42×C61—24no—
153C2×C42×C61—24no—
154C2×C42×C61C2314yes—
155C2×C42×C61C2314yes—
156#95×C61C2314yes—
157#95×C61C2314yes—
158C24×C61—22no—
159C24×C61—22no—
160C24×C61—22no—
161C24×C61—22no—
162C24×C61—22no—
163C24×C61—22no—
164C24×C61C22×C414yes—
165C24×C61C2412yes—
166C24×C61C2411yescharacteristic
167C23×D61—22no—
168C23×D61—22no—
169C23×D61—22no—
170C23×D61—22no—
171C23×D61—22no—
172C23×D61—22no—
173C23×D61C22×C414yes—
174C23×D61C2412yes—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61—22no—
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—28no—
188C22×C4×C61—28no—
189C22×C4×C61—28no—
190C22×C4×C61—416no—
191C22×C4×C61C22×C414yes—
192C22×C4×C61C22×C414yes—
193C22×C4×C61C2×D414yes—
194C22×C4×C61#4114yes—
195C22×C4×C61#4114yes—
196C22×C4×C61#4114yes—
197C22×C4×C61C2412yes—
198C22×C4×C61C2412yes—
199C22×C4×C61C2412yes—
200C22×C4×C61C2412yes—
201C22×C4×C61C2412yes—
202C22×C4×C61C2412yes—
203C2×C22⋊D61—232no—
204C2×C22⋊D61—28no—
205C2×C22⋊D61—28no—
206C2×C22⋊D61C22×C4116yes—
207C22×Dic61—22no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61—22no—
220C22×Dic61—22no—
221C22×Dic61C22×C414yes—
222C22×Dic61C22×C414yes—
223C22×Dic61C22×C414yes—
224C22×Dic61C2×D414yes—
225C22×Dic61C2×D414yes—
226C22×Dic61#4114yes—
227C22×Dic61#4114yes—
228C22×Dic61C2412yes—
229C22×Dic61C2412yes—
230C22×Dic61C2412yes—
231C22×Dic61C2412yes—
232C22×Dic61C2412yes—
233C22×Dic61C2412yes—
234C22×Dic61C2412yes—
235C2×C4×D61—28no—
236C2×C4×D61—28no—
237C2×C4×D61—28no—
238C2×C4×D61—416no—
239C2×Dic122—232no—
240C2×Dic122—28no—
241C2×Dic122—28no—
242C2×Dic122C22×C4116yescomplemented
243C22⋊C4×C61—28no—
244C22⋊C4×C61C22×C4116yescomplemented
245C42×C61—28no—
246C42×C61—28no—
247C22⋊Dic61—28no—
248C22⋊Dic61—28no—
249C22⋊Dic61C22×C4116yescomplemented
250#11758198—28no—
251#11758198—28no—
252#11758198—28no—
253#11758198C22×C4116yescomplemented
254#11758198C22×C4116yescomplemented
255C4⋊Dic61—28no—
256#11758196—28no—
257#11758196—28no—
258#11758196—28no—
259C4×Dic61—28no—
260C4×Dic61—28no—
261C4×Dic61—28no—
262C4×Dic61—28no—
263C4×Dic61—28no—
264C4×Dic61C22×C4116yescomplemented
265C4×Dic61C2×D4116yes—
266C23×C61—28no—
267C23×C61—28no—
268C23×C61—28no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—44no—
276C23×C61—44no—
277C23×C61—44no—
278C23×C61—44no—
279C23×C61C23×C414yes—
280C23×C61C23×C412yes—
281C23×C61C22×D412yes—
282C23×C61C2×#4112yes—
283C23×C61C2×#4112yes—
284C23×C61C2×#4112yes—
285C23×C61C2×#4112yes—
286C23×C61C2×#4112yes—
287C23×C61C2511yescharacteristic
288C22×D61—28no—
289C22×D61—28no—
290C22×D61—28no—
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—44no—
298C22×D61—44no—
299C22×D61—44no—
300C22×D61—44no—
301C22×D61C23×C414yes—
302C2×C4×C61—28no—
303C2×C4×C61—28no—
304C2×C4×C61—28no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—44no—
318C2×C4×C61—44no—
319C2×C4×C61—416no—
320C2×C4×C61#124116yescomplemented
321C2×C4×C61C23×C414yes—
322C2×C4×C61C23×C414yes—
323C2×C4×C61C22×D414yes—
324C2×C4×C61C2×#4114yes—
325C2×C4×C61C2×#4114yes—
326C2×C4×C61C2×#4114yes—
327C22⋊D61—232no—
328C2×Dic61—28no—
329C2×Dic61—28no—
330C2×Dic61—28no—
331C2×Dic61—28no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—44no—
347C2×Dic61—44no—
348C2×Dic61C4×D4116yes—
349C2×Dic61C23×C414yes—
350C2×Dic61C23×C414yes—
351C2×Dic61C23×C414yes—
352C2×Dic61C22×D414yes—
353C2×Dic61C22×D414yes—
354C2×Dic61C2×#4114yes—
355C2×Dic61C2×#4114yes—
356C4×D61—416no—
357Dic122—232no—
358C2×C4×#124—611nomaximal, Sylow
359C22×C61—24no—
360C22×C61—24no—
361C22×C61—24no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61—416no—
367C22×C61C2×C4×D414yes—
368C22×C61C4×#4114yes—
369C22×C61C4×#4114yes—
370C22×C61C2×#12414yes—
371C22×C61#52914yes—
372C22×C61#52914yes—
373C22×C61#53214yes—
374C22×C61C24×C411yescharacteristic
375C22×C61C23×D411yescharacteristic
376C22×C61C22×#4111yescharacteristic
377C22×C61C22×#4111yescharacteristic
378C22×C61C22×#4111yescharacteristic
379C22×C61C22×#4111yescharacteristic
380C22×C61C22×#4111yescharacteristic
381C2×D61—24no—
382C2×D61—24no—
383C2×D61—24no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—416no—
389C4×C61—24no—
390C4×C61—24no—
391C4×C61—24no—
392C4×C61—42no—
393C4×C61—42no—
394C4×C61C2×#12418yescomplemented
395Dic61—24no—
396Dic61—24no—
397Dic61—24no—
398Dic61—24no—
399Dic61—42no—
400Dic61—42no—
401Dic61C2×C4×D418yes—
402C22×#124—611no—
403C22×C4×Q8—611no—
404C22×C4×D4—611no—
405C4×#124—6116no—
406C2×#391—611no—
407C2×#390—611no—
408C2×#388—611no—
409C2×#388—611no—
410C2×#388—611no—
411C2×#388—611no—
412C2×#382—611no—
413C2×C4×C22⋊C4—611no—
414C2×C4×C22⋊C4—611no—
415C2×C4×C22⋊C4—611no—
416C2×C4×C22⋊C4D6111yescharacteristic, complemented
417C2×C43—611no—
418C2×C61—44no—
419C2×C61C4×#12418yescomplemented
420C2×C61C22×C4×D411yescharacteristic
421C2×C61C2×C4×#4111yescharacteristic
422C2×C61C2×C4×#4111yescharacteristic
423C2×C61C22×#12411yescharacteristic
424C2×C61C2×#52911yescharacteristic
425C2×C61C2×#52911yescharacteristic
426C2×C61C2×#53211yescharacteristic
427D61—44no—
428C23×Q8—611no—
429C23×D4—611no—
430C24×C4—611no—
431C24×C4C2×D6111yescharacteristic
432C2×#124—6116no—
433C2×#124—618no—
434C2×C4×Q8—618no—
435C2×C4×Q8—1228no—
436C2×C4×D4—618no—
437C2×C4×D4—1228no—
438C22×C4⋊C4—611no—
439C22×C4⋊C4—611no—
440C22×C4⋊C4—611no—
441C22×C4⋊C4—611no—
442C22×C22⋊C4—611no—
443C22×C22⋊C4—611no—
444C22×C22⋊C4—611no—
445C22×C22⋊C4—611no—
446C22×C22⋊C4—611no—
447C22×C22⋊C4—611no—
448C22×C22⋊C4—611no—
449C22×C22⋊C4—611no—
450C22×C22⋊C4C2×D6111yescharacteristic
451C22×C22⋊C4C2×D6111yescharacteristic
452C22×C42—611no—
453C22×C42—611no—
454C22×C42—611no—
455C22×C42—611no—
456C22×C42—611no—
457C22×C42—611no—
458C22×C42—611no—
459C22×C42C2×D6111yescharacteristic
460C22×C42C2×D6111yescharacteristic
461#391—618no—
462#390—618no—
463#388—618no—
464#388—618no—
465#388—618no—
466#388—618no—
467#382—618no—
468C4×C22⋊C4—618no—
469C4×C22⋊C4—618no—
470C4×C22⋊C4—618no—
471C4×C22⋊C4C2×D6118yescomplemented
472C2×#95—611no—
473C2×#95—611no—
474C2×#95—611no—
475C2×#95—611no—
476C2×#95—611no—
477C2×#95—611no—
478C2×#95C2×D6111yescharacteristic
479C2×#95C2×D6111yescharacteristic
480C43—618no—
481C61C2×C4×#12411yescharacteristic, complemented, Sylow
482C25—611no—
483C25C22×D6111yescharacteristic
484C22×Q8—618no—
485C22×Q8—614no—
486C22×Q8—1224no—
487C22×Q8—1224no—
488C22×D4—618no—
489C22×D4—614no—
490C22×D4—1224no—
491C22×D4—1224no—
492C23×C4—24no—
493C23×C4—24no—
494C23×C4—24no—
495C23×C4—611no—
496C23×C4—611no—
497C23×C4—611no—
498C23×C4—611no—
499C23×C4—611no—
500C23×C4—611no—
501C23×C4—611no—
502C23×C4—614no—
503C23×C4—1224no—
504C23×C4—1224no—
505C23×C4—1224no—
506C23×C4C22×D6111yescharacteristic
507C23×C4C22×D6111yescharacteristic
508C23×C4C22×D6114yes—
509C23×C4C22×D6111yescharacteristic
510C23×C4C22×D6111yescharacteristic
511C23×C4C22×D6111yescharacteristic
512C23×C4C22×D6111yescharacteristic
513#124—6164no—
514C4×Q8—12232no—
515C4×D4—12232no—
516C2×C4⋊C4—614no—
517C2×C4⋊C4—614no—
518C2×C4⋊C4—614no—
519C2×C4⋊C4—614no—
520C2×C4⋊C4—1224no—
521C2×C4⋊C4—1224no—
522C2×C4⋊C4—1224no—
523C2×C4⋊C4—1224no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—618no—
526C2×C22⋊C4—614no—
527C2×C22⋊C4—618no—
528C2×C22⋊C4—618no—
529C2×C22⋊C4—614no—
530C2×C22⋊C4—614no—
531C2×C22⋊C4—614no—
532C2×C22⋊C4—614no—
533C2×C22⋊C4—614no—
534C2×C22⋊C4—614no—
535C2×C22⋊C4—614no—
536C2×C22⋊C4—1224no—
537C2×C22⋊C4—1224no—
538C2×C22⋊C4—1224no—
539C2×C22⋊C4—1224no—
540C2×C22⋊C4—1224no—
541C2×C22⋊C4C4×D6118yescomplemented
542C2×C22⋊C4C22×D6114yes—
543C2×C22⋊C4C22×D6114yes—
544C2×C42—24no—
545C2×C42—24no—
546C2×C42—618no—
547C2×C42—618no—
548C2×C42—614no—
549C2×C42—614no—
550C2×C42—614no—
551C2×C42—614no—
552C2×C42—614no—
553C2×C42—614no—
554C2×C42—614no—
555C2×C42—1224no—
556C2×C42—1224no—
557C2×C42—1224no—
558C2×C42—1224no—
559C2×C42—1224no—
560C2×C42C22×D6114yes—
561C2×C42C22×D6114yes—
562#95—614no—
563#95—614no—
564#95—614no—
565#95—614no—
566#95—614no—
567#95—614no—
568#95C22×D6114yes—
569#95C22×D6114yes—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—614no—
577C24—612no—
578C24—1222no—
579C24—1222no—
580C24—1222no—
581C24—1222no—
582C24—1222no—
583C24—1222no—
584C24C2×C4×D6114yes—
585C24C23×D6112yes—
586C24C23×D6111yescharacteristic
587C2×Q8—6116no—
588C2×Q8—1228no—
589C2×Q8—12232no—
590C2×Q8—1228no—
591C2×D4—6116no—
592C2×D4—1228no—
593C2×D4—12232no—
594C2×D4—1228no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—28no—
608C22×C4—28no—
609C22×C4—28no—
610C22×C4—416no—
611C22×C4—614no—
612C22×C4—614no—
613C22×C4—614no—
614C22×C4—612no—
615C22×C4—614no—
616C22×C4—614no—
617C22×C4—614no—
618C22×C4—614no—
619C22×C4—612no—
620C22×C4—612no—
621C22×C4—612no—
622C22×C4—612no—
623C22×C4—612no—
624C22×C4—612no—
625C22×C4—1222no—
626C22×C4—1222no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—1222no—
630C22×C4—1222no—
631C22×C4—1222no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1222no—
635C22×C4—1222no—
636C22×C4—1222no—
637C22×C4—1222no—
638C22×C4—1222no—
639C22×C4—1228no—
640C22×C4—1228no—
641C22×C4—1228no—
642C22×C4—24416no—
643C22×C4C2×C4×D6114yes—
644C22×C4C2×C4×D6114yes—
645C22×C4#1175822214yes—
646C22×C4#1175822214yes—
647C22×C4D4×D6114yes—
648C22×C4#1175822414yes—
649C22×C4C23×D6112yes—
650C22×C4C23×D6112yes—
651C22×C4C23×D6112yes—
652C22×C4C23×D6112yes—
653C22×C4C23×D6112yes—
654C22×C4C23×D6112yes—
655C4⋊C4—1228no—
656C4⋊C4—1228no—
657C4⋊C4—1228no—
658C4⋊C4—1228no—
659C22⋊C4—28no—
660C22⋊C4—6116no—
661C22⋊C4—6116no—
662C22⋊C4—6116no—
663C22⋊C4—1228no—
664C22⋊C4—1228no—
665C22⋊C4—1228no—
666C22⋊C4—1228no—
667C22⋊C4—1228no—
668C22⋊C4C2×C4×D61116yescomplemented
669C42—28no—
670C42—28no—
671C42—6116no—
672C42—6116no—
673C42—1228no—
674C42—1228no—
675C42—1228no—
676C42—1228no—
677C42—1228no—
678C23—28no—
679C23—28no—
680C23—28no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—614no—
692C23—1228no—
693C23—1228no—
694C23—1228no—
695C23—1222no—
696C23—1222no—
697C23—1222no—
698C23—1222no—
699C23—1222no—
700C23—1222no—
701C23—2444no—
702C23—2444no—
703C23—2444no—
704C23—2444no—
705C23C22×C4×D6114yes—
706C23C22×C4×D6112yes—
707C23C2×D4×D6112yes—
708C23#41×D6112yes—
709C23#41×D6112yes—
710C23C2×#1175822412yes—
711C23C2×#1175822212yes—
712C23C2×#1175822212yes—
713C23C24×D6111yescharacteristic
714Q8—12232no—
715D4—12232no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—416no—
734C2×C4—6116no—
735C2×C4—614no—
736C2×C4—614no—
737C2×C4—614no—
738C2×C4—614no—
739C2×C4—614no—
740C2×C4—614no—
741C2×C4—614no—
742C2×C4—1228no—
743C2×C4—1228no—
744C2×C4—1228no—
745C2×C4—1228no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—2444no—
761C2×C4—2444no—
762C2×C4—24416no—
763C2×C4#14519763116yesdirect product factor
764C2×C4C22×C4×D6114yes—
765C2×C4C22×C4×D6114yes—
766C2×C4C2×D4×D6114yes—
767C2×C4C2×#1175822414yes—
768C2×C4C2×#1175822214yes—
769C2×C4C2×#1175822214yes—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—416no—
778C22—1224no—
779C22—1224no—
780C22—1224no—
781C22—2442no—
782C22—2442no—
783C22—2442no—
784C22—2442no—
785C22—24416no—
786C22C4×D4×D6114yes—
787C22C4×#1175822414yes—
788C22C4×#1175822214yes—
789C22C2×#1451976314yes—
790C22#1684029014yes—
791C22#1684029214yes—
792C22#1684030914yes—
793C22C23×C4×D6111yescharacteristic
794C22C22×D4×D6111yescharacteristic
795C22C2×#41×D6111yescharacteristic
796C22C2×#41×D6111yescharacteristic
797C22C22×#1175822411yescharacteristic
798C22C22×#1175822211yescharacteristic
799C22C22×#1175822211yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—42no—
804C4—42no—
805C4—618no—
806C4—1224no—
807C4—1224no—
808C4—1224no—
809C4—1224no—
810C4—2442no—
811C4—2442no—
812C4C2×#1451976318yesdirect product factor
813C2—44no—
814C2—2444no—
815C2C4×#1451976318yesdirect product factor
816C2C2×C4×D4×D6111yescharacteristic
817C2C2×C4×#1175822411yescharacteristic
818C2C2×C4×#1175822211yescharacteristic
819C2C22×#1451976311yescharacteristic
820C2C2×#1684029011yescharacteristic
821C2C2×#1684029211yescharacteristic
822C2C2×#1684030911yescharacteristic
subgroupG/H
centerC23×C4C22×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C4×C22⋊C4×C61C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
cosocleC23×C61C25
hypercenterC2×C4×C22⋊C4D61
hypocenterC61C2×C4×#124
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic122C2semidirect
4. C4×#14519763C2direct (N × H)
5. C2×#16839666C2semidirect
7. C2×#16839655C2semidirect
8. C2×#16839654C2semidirect
9. C2×#16839651C2semidirect
10. C2×#16839650C2semidirect
11. C2×#16839626C2semidirect
12. C2×C4×#11758198C2semidirect
13. C2×C4×#11758198C2semidirect
14. C2×C4×C22⋊Dic61C2semidirect
15. C2×C42×Dic61C2semidirect
16. C2×C4×C22⋊C4×C61C2semidirect
20. C2×#14519763C4direct (N × H)
23. C2×C4×Dic122C22semidirect
45. #16839666C22semidirect
47. #16839655C22semidirect
48. #16839654C22semidirect
49. #16839651C22semidirect
50. #16839650C22semidirect
51. #16839626C22semidirect
52. C4×#11758198C22semidirect
53. C4×#11758198C22semidirect
54. C4×C22⋊Dic61C22semidirect
61. C42×Dic61C22semidirect
67. C4×C22⋊C4×C61C22semidirect
73. C22×Dic122C2×C4semidirect
90. #14519763C2×C4direct (N × H)
103. C2×C22⋊Dic61C2×C4semidirect
110. C2×#11758198C2×C4semidirect
111. C2×#11758198C2×C4semidirect
122. C2×C4×Dic61C2×C4semidirect
149. C2×C22⋊C4×C61C2×C4semidirect
242. C2×Dic122C22×C4semidirect
244. C22⋊C4×C61C22×C4semidirect
249. C22⋊Dic61C22×C4semidirect
253. #11758198C22×C4semidirect
254. #11758198C22×C4semidirect
264. C4×Dic61C22×C4semidirect
320. C2×C4×C61#124semidirect
394. C4×C61C2×#124semidirect
416. C2×C4×C22⋊C4D61semidirect
419. C2×C61C4×#124semidirect
471. C4×C22⋊C4C2×D61semidirect
481. C61C2×C4×#124semidirect
541. C2×C22⋊C4C4×D61semidirect
668. C22⋊C4C2×C4×D61semidirect
763. C2×C4#14519763direct (N × H)
812. C4C2×#14519763direct (N × H)
815. C2C4×#14519763direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197632
C22×C4×Dic1222
C22×C4×C22⋊D612
C4×#145197632
C2×#168396662
C2×#168396622
C2×#168396552
C2×#168396542
C2×#168396512
C2×#168396502
C2×#168396262
C2×C4×#117581982
C2×C4×C22⋊Dic612
C2×C42×Dic612
C2×C4×C22⋊C4×C612
C2×C4×#12461