Finite Group Databasebeta

← C2×#21457390 #30555059

Subgroups — C2×#21457390 #30555059

Order 15616.

2742 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519808C211yesmaximal, characteristic, complemented
2C23×#11758202C211yesmaximal, characteristic, complemented
3C2×#16840421C211yesmaximal, characteristic
4#21457390C2116yesmaximal, direct product factor
5C2×#16840154C211yesmaximal, characteristic, complemented
6C2×#16840018C211yesmaximal, characteristic, complemented
7C2×#16839993C211yesmaximal, characteristic, complemented
8C2×#16839984C211yesmaximal, characteristic, complemented
9C2×#16839969C211yesmaximal, characteristic, complemented
10C2×#16839922C211yesmaximal, characteristic, complemented
11C2×#16839918C211yesmaximal, characteristic, complemented
12C2×#16839917C211yesmaximal, characteristic, complemented
13C2×#16839901C211yesmaximal, characteristic, complemented
14C2×#16839867C211yesmaximal, characteristic, complemented
15C2×#16839834C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C61C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C23×Dic122C2211yescharacteristic
19C2×#14519808—28no—
20C2×#14519808C2218yescomplemented
21C22×#11758202—28no—
22C22×#11758202C2211yescharacteristic
23C22×#11758202C2211yescharacteristic
24C22×#11758202C2211yescharacteristic
25C22×#11758202C2211yescharacteristic
26C22×#11758202C2211yescharacteristic
27C22×#11758202C2211yescharacteristic
28C22×#11758202C2218yescomplemented
29C22×#11758201C2211yescharacteristic
30C22×#11758201C2211yescharacteristic
31C22×#11758201C2211yescharacteristic
32C22×#11758194C2211yescharacteristic
33C23×#92418C2211yescharacteristic
34#16840421—24no—
35#16840421C2218yes—
36C2×#14519765C2211yescharacteristic
37C2×#14519763—21no—
38C2×#14519756C2211yescharacteristic
39C2×#14519755—21no—
40C2×#14519751C2211yescharacteristic
41C2×#14519749—21no—
42C2×C4×Dic122C2211yescharacteristic
43C2×#14519737—21no—
44#16840154C2218yescomplemented
45#16840018C2218yescomplemented
46#16839993C2218yescomplemented
47#16839984C2218yescomplemented
48#16839969C2218yescomplemented
49#16839922C2218yescomplemented
50#16839918C2218yescomplemented
51#16839917C2218yescomplemented
52#16839901C2218yescomplemented
53#16839867C2218yescomplemented
54#16839834C2218yescomplemented
55C2×#14519708C2211yescharacteristic
56C2×C4⋊#92418C2211yescharacteristic
57C2×#14519701C2211yescharacteristic
58C2×#14519701C2211yescharacteristic
59C2×#14519701C2211yescharacteristic
60C2×#14519700C2211yescharacteristic
61C2×#14519700C2211yescharacteristic
62C2×#14519697C2211yescharacteristic
63C2×C22⋊#92418C2211yescharacteristic
64C2×C22⋊#92418C2211yescharacteristic
65C2×#14519688C2211yescharacteristic
66C23×Q8×C61C2211yescharacteristic
67C23×Q8×C61C2211yescharacteristic
68D4×Q8×C61—24no—
69D4×Q8×C61C2218yescomplemented
70C2×C4⋊Q8×C61—21no—
71C2×C4⋊Q8×C61C2211yescharacteristic
72C2×C22⋊Q8×C61—21no—
73C2×C22⋊Q8×C61—21no—
74C2×C22⋊Q8×C61C2211yescharacteristic
75C2×C22⋊Q8×C61C2211yescharacteristic
76C2×C4×Q8×C61C2211yescharacteristic
77C2×C4×D4×C61—21no—
78C2×C4×D4×C61C2211yescharacteristic
79C2×#11758222—22no—
80C2×#11758222—24no—
81C2×#11758222—42no—
82C2×#11758222C2314yes—
83C22×Dic122—24no—
84C22×Dic122—21no—
85C22×Dic122—22no—
86C22×Dic122—42no—
87C22×Dic122C2311yescharacteristic
88C22×Dic122C2314yes—
89C22×Dic122C2311yescharacteristic
90C22×D244C2311yescharacteristic
91C22×C22⋊D61—21no—
92C22×C22⋊D61—21no—
93C23×Dic61—21no—
94C22×C4×D61—21no—
95#14519808—232no—
96C2×#11758202—24no—
97C2×#11758202—24no—
98C2×#11758202—24no—
99C2×#11758202—232no—
100C2×#11758202—24no—
101C2×#11758202—42no—
102C2×#11758202D418yescomplemented
103C2×#11758202C2314yes—
104C2×#11758202C2314yes—
105C2×#11758202C2314yes—
106C2×#11758202C2314yes—
107C2×#11758202C2314yes—
108C2×#11758202C2314yes—
109C2×#11758201—24no—
110C2×#11758201—24no—
111C2×#11758201—42no—
112C2×#11758201C2314yes—
113C2×#11758201C2314yes—
114C2×#11758201C2314yes—
115C2×#11758194—24no—
116C2×#11758194C2314yes—
117C22×#92418—24no—
118C22×#92418C2311yescharacteristic
119C22×#92418C2311yescharacteristic
120C22×#92418C2311yescharacteristic
121C22×#92418C2314yes—
122C22×#92418C2311yescharacteristic
123#14519765—22no—
124#14519765C2314yes—
125#14519763—28no—
126#14519756—22no—
127#14519756C2314yes—
128#14519755—28no—
129#14519751—22no—
130#14519751C2314yes—
131#14519749—28no—
132C4×Dic122—22no—
133C4×Dic122C2314yes—
134#14519737—28no—
135C2×C4⋊Dic61C2311yescharacteristic
136C2×#11758196—21no—
137C2×#11758196—21no—
138C2×C22⋊Dic61—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×C4×Dic61—21no—
143#14519708C2314yes—
144C4⋊#92418C2314yes—
145#14519701C2314yes—
146#14519701C2314yes—
147#14519701C2314yes—
148#14519700C2314yes—
149#14519700C2314yes—
150#14519697C2314yes—
151C22⋊#92418C2314yes—
152C22⋊#92418C2314yes—
153#14519688C2314yes—
154C22×Q8×C61—21no—
155C22×Q8×C61—21no—
156C22×Q8×C61—22no—
157C22×Q8×C61—22no—
158C22×Q8×C61—24no—
159C22×Q8×C61—24no—
160C22×Q8×C61—42no—
161C22×Q8×C61—42no—
162C22×Q8×C61C2311yescharacteristic
163C22×Q8×C61C2311yescharacteristic
164C22×Q8×C61C2314yes—
165C22×Q8×C61C2314yes—
166C22×Q8×C61C2311yescharacteristic
167C22×D4×C61D411yescharacteristic
168C23×C4×C61—21no—
169C23×C4×C61—21no—
170C23×C4×C61C2311yescharacteristic
171C23×C4×C61C2311yescharacteristic
172C4⋊Q8×C61—28no—
173C4⋊Q8×C61—22no—
174C4⋊Q8×C61C2314yes—
175C22⋊Q8×C61—22no—
176C22⋊Q8×C61—22no—
177C22⋊Q8×C61—28no—
178C22⋊Q8×C61—28no—
179C22⋊Q8×C61C2314yes—
180C22⋊Q8×C61C2314yes—
181C4×Q8×C61—22no—
182C4×Q8×C61C2314yes—
183C4×D4×C61—28no—
184C4×D4×C61D414yes—
185C4×D4×C61C2314yes—
186C2×C4⋊C4×C61—21no—
187C2×C4⋊C4×C61—21no—
188C2×C4⋊C4×C61—21no—
189C2×C4⋊C4×C61—21no—
190C2×C4⋊C4×C61—21no—
191C2×C4⋊C4×C61D411yescharacteristic
192C2×C4⋊C4×C61C2311yescharacteristic
193C2×C22⋊C4×C61—21no—
194C2×C22⋊C4×C61—21no—
195C2×C22⋊C4×C61D411yescharacteristic
196C2×C22⋊C4×C61D411yescharacteristic
197C2×C42×C61—21no—
198C2×C42×C61C2311yescharacteristic
199C24×C61C2×D411yescharacteristic
200C24×C61C2×D411yescharacteristic
201C23×D61—21no—
202C2×Q8×C61—21no—
203C2×Q8×C61—24no—
204C2×Q8×C61—24no—
205C2×Q8×C61—21no—
206C2×Q8×C61—21no—
207C2×Q8×C61—22no—
208C2×Q8×C61—28no—
209C2×Q8×C61—28no—
210C2×Q8×C61—22no—
211C2×Q8×C61—22no—
212C2×Q8×C61—22no—
213C2×Q8×C61—22no—
214C2×Q8×C61—44no—
215C2×Q8×C61—44no—
216C2×Q8×C61—44no—
217C2×Q8×C61—44no—
218C2×Q8×C61—48no—
219C2×Q8×C61—48no—
220C2×Q8×C61C2×D414yes—
221C2×Q8×C61C2412yes—
222C2×Q8×C61C2412yes—
223C2×Q8×C61C2412yes—
224C2×D4×C61—24no—
225C2×D4×C61C2×D414yes—
226C22×C4×C61—21no—
227C22×C4×C61—22no—
228C22×C4×C61—22no—
229C22×C4×C61—22no—
230C22×C4×C61—22no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—24no—
235C22×C4×C61—24no—
236C22×C4×C61—44no—
237C22×C4×C61—44no—
238C22×C4×C61C2×D411yescharacteristic
239C22×C4×C61C2×D411yescharacteristic
240C22×C4×C61C2×D412yes—
241C22×C4×C61C2×D412yes—
242C22×C4×C61C2×D411yescharacteristic
243C22×C4×C61C2×D411yescharacteristic
244C22×C4×C61C2412yes—
245C22×C4×C61C2412yes—
246C22×C4×C61C2411yescharacteristic
247C2×C22⋊D61—24no—
248C2×C22⋊D61—24no—
249C2×C22⋊D61—44no—
250C2×C22⋊D61—44no—
251C22×Dic61—21no—
252C22×Dic61—21no—
253C22×Dic61—24no—
254C22×Dic61—21no—
255C22×Dic61—44no—
256#11758222—28no—
257#11758222—44no—
258#11758222—48no—
259C2×D244—22no—
260C2×D244—22no—
261C2×D244—21no—
262C2×D244C2412yes—
263C2×C4×D61—24no—
264C2×C4×D61—44no—
265C2×Dic122—21no—
266C2×Dic122—22no—
267C2×Dic122—22no—
268C2×Dic122—22no—
269C2×Dic122—28no—
270C2×Dic122—24no—
271C2×Dic122—21no—
272C2×Dic122—44no—
273C2×Dic122—48no—
274C2×Dic122—44no—
275C2×Dic122C2×D414yes—
276C2×Dic122C2412yes—
277C2×Dic122C2412yes—
278C4⋊C4×C61—24no—
279C4⋊C4×C61—24no—
280C4⋊C4×C61—24no—
281C4⋊C4×C61—24no—
282C4⋊C4×C61—24no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61C2×D414yes—
285C4⋊C4×C61C2412yes—
286C22⋊C4×C61—24no—
287C22⋊C4×C61—24no—
288C22⋊C4×C61C2×D414yes—
289C22⋊C4×C61C2×D414yes—
290C42×C61—24no—
291C42×C61C2×D412yes—
292C42×C61C2412yes—
293C22⋊Dic61—24no—
294#11758202—28no—
295#11758202—28no—
296#11758202—28no—
297#11758202—28no—
298#11758202—44no—
299#11758202C2×D4116yescomplemented
300#11758201—28no—
301#11758201—28no—
302#11758201—44no—
303#11758198—24no—
304#11758198—24no—
305#11758198—24no—
306C4⋊Dic61—21no—
307C4⋊Dic61C2412yes—
308#11758196—24no—
309#11758196—24no—
310C4×Dic61—24no—
311#11758194—28no—
312C2×#92418—22no—
313C2×#92418—22no—
314C2×#92418—22no—
315C2×#92418—28no—
316C2×#92418C2×D414yes—
317C2×#92418C2412yes—
318C2×#92418C2412yes—
319C2×#92418C2412yes—
320C2×#92418C2412yes—
321C23×C61—22no—
322C23×C61—22no—
323C23×C61—22no—
324C23×C61—22no—
325C23×C61—22no—
326C23×C61#13714yescomplemented
327C23×C61C22×D412yes—
328C23×C61C22×D412yes—
329C23×C61C22×D411yescharacteristic
330C22×D61—22no—
331C22×D61—42no—
332C22×D61—42no—
333C22×D61—42no—
334Q8×C61—24no—
335Q8×C61—22no—
336Q8×C61—22no—
337Q8×C61—22no—
338Q8×C61—22no—
339Q8×C61—22no—
340Q8×C61—48no—
341Q8×C61—48no—
342Q8×C61—42no—
343Q8×C61—42no—
344Q8×C61C22×D414yes—
345D4×C61—28no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—24no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—24no—
353C2×C4×C61—24no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—48no—
362C2×C4×C61—48no—
363C2×C4×C61—42no—
364C2×C4×C61—42no—
365C2×C4×C61—42no—
366C2×C4×C61C22×D412yes—
367C2×C4×C61C22×D412yes—
368C2×C4×C61C22×D412yes—
369C2×C4×C61C22×D412yes—
370C2×C4×C61C22×D411yescharacteristic
371C2×C4×C61C22×D412yes—
372C2×C4×C61H(5,𝔽2)12yes—
373C2×C4×C61C2511yescharacteristic
374C22⋊D61—48no—
375C22⋊D61—48no—
376C2×Dic61—24no—
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—22no—
380C2×Dic61—48no—
381C2×Dic61—42no—
382C2×Dic61—42no—
383D244—22no—
384D244—22no—
385D244—42no—
386C4×D61—48no—
387Dic122—24no—
388Dic122—22no—
389Dic122—22no—
390Dic122—22no—
391Dic122—48no—
392Dic122—42no—
393Dic122C22×D414yes—
394#92418—22no—
395#92418—22no—
396#92418—22no—
397#92418C22×D414yes—
398C2×#3270—611nomaximal, Sylow
399C22×C61—22no—
400C22×C61—28no—
401C22×C61—22no—
402C22×C61—22no—
403C22×C61—22no—
404C22×C61—22no—
405C22×C61—44no—
406C22×C61D4212yes—
407C22×C61C2×#13712yes—
408C22×C61C2×#13714yescomplemented
409C22×C61#57812yes—
410C22×C61C23×D411yescharacteristic
411C2×D61—42no—
412C2×D61—42no—
413C2×D61—42no—
414C2×D61—84no—
415C4×C61—22no—
416C4×C61—22no—
417C4×C61—24no—
418C4×C61—22no—
419C4×C61—22no—
420C4×C61—42no—
421C4×C61—42no—
422C4×C61—42no—
423C4×C61D4212yes—
424C4×C61C23×D411yescharacteristic
425C4×C61C2×H(5,𝔽2)11yescharacteristic
426Dic61—24no—
427Dic61—42no—
428Dic61—42no—
429C22×#137—611no—
430C23×Q16—611no—
431C2×D4×Q8D6111yescharacteristic, complemented
432C2×#548—611no—
433#3270—6116no—
434C2×#497—611no—
435C2×#470—611no—
436C2×#465—611no—
437C2×#464—611no—
438C2×#462—611no—
439C2×#452—611no—
440C2×#451—611no—
441C2×#451—611no—
442C2×#448—611no—
443C2×#441—611no—
444C2×#435—611no—
445C2×C61—24no—
446C2×C61—42no—
447C2×C61#327014yescomplemented
448C2×C61C2×D4211yescharacteristic
449C2×C61C22×#13711yescharacteristic
450C2×C61C2×#57811yescharacteristic
451D61—82no—
452C22×#41—611no—
453C23×Q8—611no—
454C23×Q8C2×D6111yescharacteristic
455C23×Q8C2×D6111yescharacteristic
456C2×#137—618no—
457C2×#137—1228no—
458C22×Q16—611no—
459C22×Q16—611no—
460C22×Q16—611no—
461C22×Q16—611no—
462C22×Q16—611no—
463C22×Q16—618no—
464C22×Q16—611no—
465C22×Q16—1228no—
466C22×SD16—611no—
467C22×SD16—611no—
468C22×SD16—611no—
469C22×M16—611no—
470C23×C8—611no—
471D4×Q8—24no—
472D4×Q8C2×D6118yescomplemented
473#548—618no—
474#548—1224no—
475C2×C4⋊Q8—21no—
476C2×C4⋊Q8C2×D6111yescharacteristic
477C2×#124—611no—
478C2×#124—1221no—
479C2×C22⋊Q8—21no—
480C2×C22⋊Q8—21no—
481C2×C22⋊Q8—611no—
482C2×C22⋊Q8—1221no—
483C2×C22⋊Q8C2×D6111yescharacteristic
484C2×C22⋊Q8C2×D6111yescharacteristic
485C2×#121—611no—
486C2×#121—1221no—
487C2×C4×Q8—611no—
488C2×C4×Q8C2×D6111yescharacteristic
489C2×C4×D4—21no—
490C2×C4×D4—1221no—
491C2×C4×D4C2×D6111yescharacteristic
492#497—618no—
493#470—618no—
494#465—618no—
495#464—618no—
496#462—618no—
497#452—618no—
498#451—618no—
499#451—618no—
500#448—618no—
501#441—618no—
502#435—618no—
503C2×#106—611no—
504C2×C4⋊C8—611no—
505C2×#103—611no—
506C2×#103—611no—
507C2×#103—611no—
508C2×#103—611no—
509C2×#103—611no—
510C2×#102—611no—
511C2×C22⋊C8—611no—
512C2×C22⋊C8—611no—
513C2×#97—611no—
514C61C2×#327011yescharacteristic, complemented, Sylow
515C2×#41—614no—
516C2×#41—1224no—
517C2×#41—1222no—
518C2×#41—2442no—
519C22×Q8—21no—
520C22×Q8—21no—
521C22×Q8—22no—
522C22×Q8—22no—
523C22×Q8—24no—
524C22×Q8—24no—
525C22×Q8—42no—
526C22×Q8—42no—
527C22×Q8—611no—
528C22×Q8—611no—
529C22×Q8—614no—
530C22×Q8—1224no—
531C22×Q8—1221no—
532C22×Q8—1222no—
533C22×Q8—2442no—
534C22×Q8C22×D6111yescharacteristic
535C22×Q8C22×D6111yescharacteristic
536C22×Q8C22×D6114yes—
537C22×Q8C22×D6114yes—
538C22×Q8C22×D6111yescharacteristic
539C22×D4—611no—
540C22×D4—1221no—
541C22×D4—1221no—
542C22×D4C22⋊D6111yescharacteristic
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—1221no—
546C23×C4—1221no—
547C23×C4C22×D6111yescharacteristic
548C23×C4C22×D6111yescharacteristic
549#137—12232no—
550C2×Q16—618no—
551C2×Q16—614no—
552C2×Q16—614no—
553C2×Q16—614no—
554C2×Q16—614no—
555C2×Q16—614no—
556C2×Q16—614no—
557C2×Q16—1224no—
558C2×Q16—12232no—
559C2×Q16—1224no—
560C2×Q16—1224no—
561C2×Q16—1224no—
562C2×Q16—2442no—
563C2×SD16—614no—
564C2×SD16—614no—
565C2×SD16—614no—
566C2×SD16—1224no—
567C2×SD16—1224no—
568C2×SD16—2442no—
569C2×M16—614no—
570C2×M16—1224no—
571C22×C8—611no—
572C22×C8—611no—
573C22×C8—614no—
574C22×C8—611no—
575C22×C8—611no—
576C22×C8—1224no—
577C4⋊Q8—28no—
578C4⋊Q8—22no—
579C4⋊Q8C22×D6114yes—
580#124—614no—
581#124—1228no—
582#124—1222no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585C22⋊Q8—28no—
586C22⋊Q8—28no—
587C22⋊Q8—614no—
588C22⋊Q8—1222no—
589C22⋊Q8—1228no—
590C22⋊Q8C22×D6114yes—
591C22⋊Q8C22×D6114yes—
592#121—614no—
593#121—1228no—
594#121—1222no—
595C4×Q8—22no—
596C4×Q8—614no—
597C4×Q8—1222no—
598C4×Q8C22×D6114yes—
599C4×D4—28no—
600C4×D4—1228no—
601C4×D4C22⋊D6114yes—
602C4×D4C22×D6114yes—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—611no—
609C2×C4⋊C4—1221no—
610C2×C4⋊C4—1221no—
611C2×C4⋊C4C22⋊D6111yescharacteristic
612C2×C4⋊C4C22×D6111yescharacteristic
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—1221no—
616C2×C22⋊C4—1221no—
617C2×C22⋊C4—1221no—
618C2×C22⋊C4—1221no—
619C2×C22⋊C4C22⋊D6111yescharacteristic
620C2×C22⋊C4C22⋊D6111yescharacteristic
621C2×C42—21no—
622C2×C42—1221no—
623C2×C42C22×D6111yescharacteristic
624#106—614no—
625C4⋊C8—614no—
626#103—614no—
627#103—614no—
628#103—614no—
629#103—614no—
630#103—614no—
631#102—614no—
632C22⋊C8—614no—
633C22⋊C8—614no—
634#97—614no—
635C24—1221no—
636C24C2×C22⋊D6111yescharacteristic
637C24C2×C22⋊D6111yescharacteristic
638#41—1228no—
639#41—2444no—
640#41—2448no—
641C2×Q8—21no—
642C2×Q8—24no—
643C2×Q8—24no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—22no—
647C2×Q8—28no—
648C2×Q8—28no—
649C2×Q8—22no—
650C2×Q8—22no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—44no—
654C2×Q8—44no—
655C2×Q8—44no—
656C2×Q8—44no—
657C2×Q8—48no—
658C2×Q8—48no—
659C2×Q8—614no—
660C2×Q8—612no—
661C2×Q8—612no—
662C2×Q8—1228no—
663C2×Q8—1221no—
664C2×Q8—1224no—
665C2×Q8—1221no—
666C2×Q8—1222no—
667C2×Q8—1222no—
668C2×Q8—1222no—
669C2×Q8—2444no—
670C2×Q8—2444no—
671C2×Q8—2448no—
672C2×Q8D4×D6114yes—
673C2×Q8C23×D6112yes—
674C2×Q8C23×D6112yes—
675C2×Q8C23×D6112yes—
676C2×D4—24no—
677C2×D4—612no—
678C2×D4—1224no—
679C2×D4—1224no—
680C2×D4—1222no—
681C2×D4—1221no—
682C2×D4—1222no—
683C2×D4—2444no—
684C2×D4—2444no—
685C2×D4C2×C22⋊D6114yes—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—24no—
692C22×C4—24no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—1221no—
699C22×C4—1224no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1224no—
703C22×C4—2444no—
704C22×C4—2444no—
705C22×C4C2×C22⋊D6112yes—
706C22×C4C2×C22⋊D6112yes—
707C22×C4C2×C22⋊D6111yescharacteristic
708C22×C4C2×C22⋊D6111yescharacteristic
709C22×C4C2×C22⋊D6111yescharacteristic
710C22×C4C2×C22⋊D6111yescharacteristic
711C22×C4C23×D6112yes—
712C22×C4C23×D6112yes—
713C22×C4C23×D6111yescharacteristic
714Q16—6116no—
715Q16—1228no—
716Q16—1228no—
717Q16—1228no—
718Q16—1228no—
719Q16—2444no—
720SD16—1228no—
721SD16—1228no—
722SD16—2444no—
723M16—1228no—
724C2×C8—614no—
725C2×C8—612no—
726C2×C8—612no—
727C2×C8—612no—
728C2×C8—612no—
729C2×C8—1228no—
730C2×C8—1222no—
731C2×C8—1222no—
732C2×C8—1222no—
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—24no—
737C4⋊C4—24no—
738C4⋊C4—21no—
739C4⋊C4—612no—
740C4⋊C4—1221no—
741C4⋊C4—1224no—
742C4⋊C4—1224no—
743C4⋊C4C2×C22⋊D6114yes—
744C4⋊C4C23×D6112yes—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—1224no—
748C22⋊C4—1224no—
749C22⋊C4—1224no—
750C22⋊C4—1224no—
751C22⋊C4C2×C22⋊D6114yes—
752C22⋊C4C2×C22⋊D6114yes—
753C42—24no—
754C42—1224no—
755C42C2×C22⋊D6112yes—
756C42C23×D6112yes—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—1222no—
763C23—2442no—
764C23—2442no—
765C23—2442no—
766C23#1451980814yescomplemented
767C23C22×C22⋊D6112yes—
768C23C22×C22⋊D6112yes—
769C23C22×C22⋊D6111yescharacteristic
770Q8—22no—
771Q8—24no—
772Q8—22no—
773Q8—22no—
774Q8—22no—
775Q8—22no—
776Q8—48no—
777Q8—48no—
778Q8—42no—
779Q8—42no—
780Q8—614no—
781Q8—1222no—
782Q8—1224no—
783Q8—1222no—
784Q8—1222no—
785Q8—2448no—
786Q8—2442no—
787Q8C2×D4×D6114yes—
788D4—28no—
789D4—1222no—
790D4—1222no—
791D4—2448no—
792D4—2448no—
793D4—2442no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—48no—
810C2×C4—48no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—1222no—
815C2×C4—1224no—
816C2×C4—1222no—
817C2×C4—1222no—
818C2×C4—2448no—
819C2×C4—2448no—
820C2×C4—2442no—
821C2×C4—2442no—
822C2×C4C2×D4×D6112yes—
823C2×C4C22×C22⋊D6112yes—
824C2×C4C22×C22⋊D6112yes—
825C2×C4C22×C22⋊D6112yes—
826C2×C4C22×C22⋊D6112yes—
827C2×C4C22×C22⋊D6111yescharacteristic
828C2×C4#1451982212yes—
829C2×C4C24×D6111yescharacteristic
830C8—614no—
831C8—1222no—
832C8—1222no—
833C8—1222no—
834C22—22no—
835C22—22no—
836C22—28no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—44no—
841C22—4884no—
842C22—2442no—
843C22—2442no—
844C22—2442no—
845C22D4×C22⋊D6112yes—
846C22C2×#1451980812yes—
847C22C2×#1451980814yescomplemented
848C22#1684057712yes—
849C22C23×C22⋊D6111yescharacteristic
850C4—22no—
851C4—22no—
852C4—24no—
853C4—22no—
854C4—22no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—1224no—
859C4—2442no—
860C4—2442no—
861C4D4×C22⋊D6112yes—
862C4C22×D4×D6111yescharacteristic
863C4C2×#1451982211yescharacteristic
864C2—24no—
865C2—42no—
866C2—4882no—
867C2#2145739014yesdirect product factor
868C2C2×D4×C22⋊D6111yescharacteristic
869C2C22×#1451980811yescharacteristic
870C2C2×#1684057711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×D4×Q8×C61C2
socleC23×C61C22×D4
prime radicalC2×#16840421C2
hypercenterC2×D4×Q8D61
hypocenterC61C2×#3270
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14519808C2semidirect
2. C23×#11758202C2semidirect
4. #21457390C2direct (N × H)
5. C2×#16840154C2semidirect
6. C2×#16840018C2semidirect
7. C2×#16839993C2semidirect
8. C2×#16839984C2semidirect
9. C2×#16839969C2semidirect
10. C2×#16839922C2semidirect
11. C2×#16839918C2semidirect
12. C2×#16839917C2semidirect
13. C2×#16839901C2semidirect
14. C2×#16839867C2semidirect
15. C2×#16839834C2semidirect
16. C2×D4×Q8×C61C2semidirect
20. C2×#14519808C22semidirect
28. C22×#11758202C22semidirect
44. #16840154C22semidirect
45. #16840018C22semidirect
46. #16839993C22semidirect
47. #16839984C22semidirect
48. #16839969C22semidirect
49. #16839922C22semidirect
50. #16839918C22semidirect
51. #16839917C22semidirect
52. #16839901C22semidirect
53. #16839867C22semidirect
54. #16839834C22semidirect
69. D4×Q8×C61C22semidirect
102. C2×#11758202D4semidirect
299. #11758202C2×D4semidirect
326. C23×C61#137semidirect
408. C22×C61C2×#137semidirect
431. C2×D4×Q8D61semidirect
447. C2×C61#3270semidirect
472. D4×Q8C2×D61semidirect
514. C61C2×#3270semidirect
766. C23#14519808semidirect
847. C22C2×#14519808semidirect
867. C2#21457390direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198082
C23×#117582022
C2×#168404212
#214573902
C2×#168401542
C2×#168400182
C2×#168399932
C2×#168399842
C2×#168399692
C2×#168399222
C2×#168399182
C2×#168399172
C2×#168399012
C2×#168398672
C2×#168398342
C2×D4×Q8×C612
C2×#327061