Finite Group Databasebeta

← C2×#21458276 #30558562

Subgroups — C2×#21458276 #30558562

Order 15616.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840469C211yesmaximal, characteristic
2C2×#16840452C211yesmaximal, characteristic
3#21458276C2116yesmaximal, direct product factor
4C2×#16840171C211yesmaximal, characteristic, complemented
5C2×#16840098C211yesmaximal, characteristic, complemented
6C2×#16840104C211yesmaximal, characteristic, complemented
7C2×#16840093C211yesmaximal, characteristic, complemented
8C2×#16840093C211yesmaximal, characteristic, complemented
9C2×#16840070C211yesmaximal, characteristic, complemented
10C2×#16840048C211yesmaximal, characteristic, complemented
11C2×#16840020C211yesmaximal, characteristic, complemented
12C2×#16840003C211yesmaximal, characteristic, complemented
13C2×#16839870C211yesmaximal, characteristic, complemented
14C2×#16839804C211yesmaximal, characteristic, complemented
15C22×#14519709C211yesmaximal, characteristic, complemented
16C2×C61×#435C211yesmaximal, characteristic
17C22×Dic244C2211yescharacteristic
18#16840469—24no—
19#16840469C2218yes—
20#16840452—24no—
21#16840452C2218yes—
22C2×#14519777C2211yescharacteristic
23C2×#14519770—21no—
24C2×#14519769C2211yescharacteristic
25C2×#14519768—21no—
26C2×#14519767—21no—
27C2×#14519758—21no—
28C2×#14519756C2211yescharacteristic
29C2×#14519756C2211yescharacteristic
30C2×#14519756C2211yescharacteristic
31C2×#14519756C2211yescharacteristic
32C2×#14519754—21no—
33C2×#14519754—21no—
34C2×C4×Dic122C2211yescharacteristic
35C2×C4×Dic122C2211yescharacteristic
36C2×D4×Dic61—21no—
37C2×#14519736C2211yescharacteristic
38C2×#14519733—21no—
39C22×C4⋊Dic61C2211yescharacteristic
40C22×C4⋊Dic61C2211yescharacteristic
41C22×C4⋊Dic61C2211yescharacteristic
42#16840171C2218yescomplemented
43#16840104C2218yescomplemented
44#16840098C2218yescomplemented
45#16840093C2218yescomplemented
46#16840093C2218yescomplemented
47#16840070C2218yescomplemented
48#16840048C2218yescomplemented
49#16840020C2218yescomplemented
50#16840003C2218yescomplemented
51#16839870C2218yescomplemented
52#16839804C2218yescomplemented
53C2×#14519711C2211yescharacteristic
54C2×#14519711C2211yescharacteristic
55C2×#14519711C2211yescharacteristic
56C2×#14519709C2211yescharacteristic
57C2×#14519709C2211yescharacteristic
58C2×#14519709C2211yescharacteristic
59C2×#14519709C2211yescharacteristic
60C2×#14519709C2211yescharacteristic
61C2×#14519709C2211yescharacteristic
62C2×#14519709C2218yescomplemented
63C2×#14519702C2211yescharacteristic
64C2×#14519702C2211yescharacteristic
65C2×#14519702C2211yescharacteristic
66C2×#14519702C2211yescharacteristic
67C2×#14519702C2211yescharacteristic
68C2×#14519702C2211yescharacteristic
69C22×M16×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic
71C2×C4×D4×C61C2211yescharacteristic
72C61×#435C2218yes—
73C2×C4⋊C8×C61C2211yescharacteristic
74C2×C22⋊C8×C61C2211yescharacteristic
75C2×C22⋊C8×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122C2311yescharacteristic
79C22×Dic122C2311yescharacteristic
80C23×Dic61—21no—
81C23×Dic61—21no—
82C23×Dic61—21no—
83C2×Dic244—24no—
84C2×Dic244C2314yes—
85#14519777—22no—
86#14519777C2314yes—
87#14519770—28no—
88#14519769—22no—
89#14519769C2314yes—
90#14519768—28no—
91#14519767—28no—
92#14519758—28no—
93#14519756—22no—
94#14519756—22no—
95#14519756—22no—
96#14519756—22no—
97#14519756C2314yes—
98#14519756C2314yes—
99#14519756C2314yes—
100#14519756C2314yes—
101#14519754—28no—
102#14519754—28no—
103C4×Dic122—22no—
104C4×Dic122—22no—
105C4×Dic122C2314yes—
106C4×Dic122C2314yes—
107D4×Dic61—28no—
108#14519736—22no—
109#14519736C2314yes—
110#14519733—28no—
111C2×C4⋊Dic61—22no—
112C2×C4⋊Dic61—22no—
113C2×C4⋊Dic61—22no—
114C2×C4⋊Dic61—21no—
115C2×C4⋊Dic61—21no—
116C2×C4⋊Dic61—21no—
117C2×C4⋊Dic61—21no—
118C2×C4⋊Dic61C2314yes—
119C2×C4⋊Dic61C2311yescharacteristic
120C2×C4⋊Dic61C2314yes—
121C2×C4⋊Dic61C2314yes—
122C2×C4⋊Dic61C2311yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×C4⋊Dic61C2311yescharacteristic
126C2×C4⋊Dic61C2311yescharacteristic
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61—21no—
137C2×C22⋊Dic61—21no—
138C2×C22⋊Dic61—21no—
139C2×C22⋊Dic61—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61—21no—
142C2×C4×Dic61—21no—
143#14519711C2314yes—
144#14519711C2314yes—
145#14519711C2314yes—
146#14519709C2314yes—
147#14519709C2314yes—
148#14519709C2314yes—
149#14519709C2314yes—
150#14519709C2314yes—
151#14519709C2314yes—
152#14519702C2314yes—
153#14519702C2314yes—
154#14519702C2314yes—
155#14519702C2314yes—
156#14519702C2314yes—
157#14519702C2314yes—
158C22×D4×C61D411yescharacteristic
159C23×C4×C61C2311yescharacteristic
160C23×C4×C61C2311yescharacteristic
161C2×M16×C61—24no—
162C2×M16×C61C2314yes—
163C22×C8×C61—24no—
164C22×C8×C61C2314yes—
165C22×C8×C61C2311yescharacteristic
166C22×C8×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2311yescharacteristic
169C4×D4×C61D414yes—
170C4×D4×C61C2314yes—
171C2×C4⋊C4×C61D411yescharacteristic
172C2×C22⋊C4×C61D411yescharacteristic
173C2×C22⋊C4×C61D411yescharacteristic
174C2×C42×C61C2311yescharacteristic
175C4⋊C8×C61C2314yes—
176C22⋊C8×C61C2314yes—
177C22⋊C8×C61C2314yes—
178#97×C61C2314yes—
179C24×C61C2×D411yescharacteristic
180C24×C61C2×D411yescharacteristic
181C2×D4×C61—24no—
182C2×D4×C61C2×D414yes—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D412yes—
192C22×C4×C61C2×D412yes—
193C22×C4×C61C2412yes—
194C22×C4×C61C2412yes—
195C22×C4×C61C2411yescharacteristic
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—24no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—24no—
206C22×Dic61—24no—
207C22×Dic61—44no—
208C22×Dic61—82no—
209C22×Dic61—82no—
210C2×Dic122—22no—
211C2×Dic122—22no—
212C2×Dic122—22no—
213C2×Dic122—22no—
214C2×Dic122—21no—
215C2×Dic122—21no—
216C2×Dic122—24no—
217C2×Dic122—82no—
218C2×Dic122C2412yes—
219C2×Dic122C2412yes—
220M16×C61—28no—
221C2×C8×C61—22no—
222C2×C8×C61—22no—
223C2×C8×C61—22no—
224C2×C8×C61—28no—
225C2×C8×C61#4114yes—
226C2×C8×C61C2412yes—
227C2×C8×C61C2412yes—
228C2×C8×C61C2412yes—
229C2×C8×C61C2412yes—
230C4⋊C4×C61C2×D414yes—
231C22⋊C4×C61C2×D414yes—
232C22⋊C4×C61C2×D414yes—
233C42×C61C2×D412yes—
234C42×C61C2412yes—
235C22⋊Dic61—24no—
236C22⋊Dic61—24no—
237C22⋊Dic61—24no—
238C22⋊Dic61—24no—
239C22⋊Dic61—24no—
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242C4⋊Dic61—24no—
243C4⋊Dic61—24no—
244C4⋊Dic61—21no—
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61—24no—
248C4⋊Dic61—24no—
249C4⋊Dic61—21no—
250C4⋊Dic61C2412yes—
251C4⋊Dic61C2412yes—
252C4⋊Dic61C2412yes—
253C4⋊Dic61C2412yes—
254C4⋊Dic61C2412yes—
255C4⋊Dic61C2412yes—
256#11758196—24no—
257#11758196—24no—
258#11758196—24no—
259#11758196—24no—
260#11758196—24no—
261#11758196—24no—
262#11758196—24no—
263#11758196—24no—
264C4×Dic61—24no—
265C4×Dic61—24no—
266C4×Dic61—24no—
267Dic244—28no—
268C23×C61—22no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61#13714yes—
274C23×C61C22×D412yes—
275C23×C61C22×D412yes—
276C23×C61C22×D411yescharacteristic
277D4×C61—28no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—24no—
283C2×C4×C61—24no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61C22×D412yes—
289C2×C4×C61C22×D412yes—
290C2×C4×C61C22×D412yes—
291C2×C4×C61C22×D412yes—
292C2×C4×C61C22×D411yescharacteristic
293C2×C4×C61C2×#4112yes—
294C2×C4×C612−1+412yes—
295C2×C4×C61C2511yescharacteristic
296C2×Dic61—22no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—42no—
305C2×Dic61—42no—
306C2×Dic61—48no—
307C2×Dic61—42no—
308C2×Dic61—42no—
309C2×Dic61—42no—
310C2×Dic61—42no—
311C2×Dic61—42no—
312C2×Dic61—42no—
313C2×Dic61—84no—
314C2×Dic61—84no—
315Dic122—22no—
316Dic122—22no—
317Dic122—22no—
318Dic122—22no—
319Dic122—42no—
320Dic122—42no—
321Dic122—84no—
322C8×C61—22no—
323C8×C61—22no—
324C8×C61—22no—
325C8×C61C2×#4114yes—
326C2×#3344—611nomaximal, Sylow
327C22×C61—28no—
328C22×C61—22no—
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—22no—
333C22×C61—44no—
334C22×C61#54712yes—
335C22×C61C2×#13714yes—
336C22×C61C2×#13712yes—
337C22×C61#57712yes—
338C22×C61C23×D411yescharacteristic
339C4×C61—22no—
340C4×C61—22no—
341C4×C61—22no—
342C4×C61—22no—
343C4×C61#54712yes—
344C4×C61C22×#4111yescharacteristic
345C4×C61C2×2−1+411yescharacteristic
346Dic61—42no—
347Dic61—42no—
348Dic61—42no—
349Dic61—42no—
350Dic61—42no—
351Dic61—42no—
352Dic61—42no—
353Dic61—42no—
354C2×#554—611no—
355C2×#552—611no—
356#3344—6116no—
357C2×#501—611no—
358C2×#484—611no—
359C2×#485—611no—
360C2×#483—611no—
361C2×#483—611no—
362C2×#479—611no—
363C2×#475—611no—
364C2×#470—611no—
365C2×#467—611no—
366C2×#441—611no—
367C2×#435D6111yescharacteristic
368C2×#428—611no—
369C22×#106—611no—
370C2×C61—24no—
371C2×C61—42no—
372C2×C61#334414yescomplemented
373C2×C61C2×#54711yescharacteristic
374C2×C61C22×#13711yescharacteristic
375C2×C61C2×#57711yescharacteristic
376C22×Q16—611no—
377C22×M16C2×D6111yescharacteristic
378C23×C8C2×D6111yescharacteristic
379#554—618no—
380#554—1224no—
381#552—618no—
382#552—1224no—
383C2×C4⋊Q8—611no—
384C2×#126—1221no—
385C2×#125—611no—
386C2×#125—1221no—
387C2×#125—1221no—
388C2×#123—1221no—
389C2×C22⋊Q8—611no—
390C2×C22⋊Q8—611no—
391C2×C22⋊Q8—611no—
392C2×C22⋊Q8—611no—
393C2×C22⋊Q8—1221no—
394C2×C22⋊Q8—1221no—
395C2×C4×Q8—611no—
396C2×C4×Q8—611no—
397C2×C4×D4—1221no—
398C2×C4×D4C2×D6111yescharacteristic
399C2×#117—611no—
400C2×#117—1221no—
401C22×C4⋊C4—611no—
402C22×C4⋊C4—611no—
403C22×C4⋊C4—611no—
404#501—618no—
405#485—618no—
406#484—618no—
407#483—618no—
408#483—618no—
409#479—618no—
410#475—618no—
411#470—618no—
412#467—618no—
413#441—618no—
414#435C2×D6118yes—
415#428—618no—
416C2×#107—611no—
417C2×#107—611no—
418C2×#107—611no—
419C2×#106—611no—
420C2×#106—611no—
421C2×#106—611no—
422C2×#106—611no—
423C2×#106—618no—
424C2×#106—611no—
425C2×#106—611no—
426C2×C4⋊C8C2×D6111yescharacteristic
427C2×#103—611no—
428C2×#103—611no—
429C2×#103—611no—
430C2×#103—611no—
431C2×#103—611no—
432C2×#103—611no—
433C2×C22⋊C8C2×D6111yescharacteristic
434C2×C22⋊C8C2×D6111yescharacteristic
435C2×#97C2×D6111yescharacteristic
436C61C2×#334411yescharacteristic, complemented, Sylow
437C22×Q8—611no—
438C22×Q8—611no—
439C22×Q8—1221no—
440C22×D4D24411yescharacteristic
441C23×C4—1221no—
442C23×C4—1221no—
443C23×C4—1221no—
444C23×C4C22×D6111yescharacteristic
445C23×C4C22×D6111yescharacteristic
446C2×Q16—614no—
447C2×Q16—1224no—
448C2×M16—24no—
449C2×M16C22×D6114yes—
450C22×C8—24no—
451C22×C8C22×D6111yescharacteristic
452C22×C8C22×D6114yes—
453C22×C8C22×D6111yescharacteristic
454C22×C8C22×D6111yescharacteristic
455C22×C8C22×D6111yescharacteristic
456C4⋊Q8—614no—
457C4⋊Q8—1222no—
458#126—1228no—
459#125—614no—
460#125—1228no—
461#125—1228no—
462#125—1222no—
463#123—1228no—
464C22⋊Q8—614no—
465C22⋊Q8—614no—
466C22⋊Q8—614no—
467C22⋊Q8—614no—
468C22⋊Q8—1222no—
469C22⋊Q8—1222no—
470C22⋊Q8—1222no—
471C22⋊Q8—1222no—
472C22⋊Q8—1228no—
473C22⋊Q8—1228no—
474C4×Q8—614no—
475C4×Q8—614no—
476C4×Q8—1222no—
477C4×Q8—1222no—
478C4×D4—1228no—
479C4×D4D24414yes—
480C4×D4C22×D6114yes—
481#117—614no—
482#117—1222no—
483#117—1228no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4—611no—
489C2×C4⋊C4—614no—
490C2×C4⋊C4—614no—
491C2×C4⋊C4—614no—
492C2×C4⋊C4—611no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—1221no—
495C2×C4⋊C4—1221no—
496C2×C4⋊C4—1222no—
497C2×C4⋊C4—1222no—
498C2×C4⋊C4—1222no—
499C2×C4⋊C4—1221no—
500C2×C4⋊C4—1221no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—1221no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4D24411yescharacteristic
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C22⋊C4D24411yescharacteristic
515C2×C22⋊C4D24411yescharacteristic
516C2×C42—1221no—
517C2×C42—1221no—
518C2×C42—1221no—
519C2×C42C22×D6111yescharacteristic
520#107—614no—
521#107—614no—
522#107—614no—
523#106—614no—
524#106—614no—
525#106—614no—
526#106—614no—
527#106—614no—
528#106—614no—
529C4⋊C8C22×D6114yes—
530#103—614no—
531#103—614no—
532#103—614no—
533#103—614no—
534#103—614no—
535#103—614no—
536C22⋊C8C22×D6114yes—
537C22⋊C8C22×D6114yes—
538#97C22×D6114yes—
539C24C2×D24411yescharacteristic
540C24C2×D24411yescharacteristic
541C2×Q8—612no—
542C2×Q8—612no—
543C2×Q8—1224no—
544C2×Q8—1221no—
545C2×Q8—1221no—
546C2×Q8—1222no—
547C2×Q8—1222no—
548C2×Q8—1222no—
549C2×Q8—1222no—
550C2×Q8—4882no—
551C2×D4—24no—
552C2×D4C2×D24414yes—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—1224no—
558C22×C4—1224no—
559C22×C4—1224no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—4882no—
569C22×C4—4882no—
570C22×C4—2444no—
571C22×C4C2×D24412yes—
572C22×C4C2×D24412yes—
573C22×C4C2×D24411yescharacteristic
574C22×C4C2×D24411yescharacteristic
575C22×C4C2×D24411yescharacteristic
576C22×C4C2×D24411yescharacteristic
577C22×C4C23×D6112yes—
578C22×C4C23×D6112yes—
579C22×C4C23×D6111yescharacteristic
580Q16—1228no—
581M16—28no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—28no—
586C2×C8#1175822414yes—
587C2×C8C23×D6112yes—
588C2×C8C23×D6112yes—
589C2×C8C23×D6112yes—
590C2×C8C23×D6112yes—
591C4⋊C4—612no—
592C4⋊C4—612no—
593C4⋊C4—612no—
594C4⋊C4—612no—
595C4⋊C4—612no—
596C4⋊C4—612no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—1224no—
600C4⋊C4—1224no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1224no—
605C4⋊C4—1221no—
606C4⋊C4—1224no—
607C4⋊C4—1224no—
608C4⋊C4—1224no—
609C4⋊C4—1224no—
610C4⋊C4—1224no—
611C4⋊C4—1224no—
612C4⋊C4—1224no—
613C4⋊C4—1224no—
614C4⋊C4—1224no—
615C4⋊C4C2×D24414yes—
616C22⋊C4—1224no—
617C22⋊C4—1224no—
618C22⋊C4—1224no—
619C22⋊C4—1224no—
620C22⋊C4—1224no—
621C22⋊C4C2×D24414yes—
622C22⋊C4C2×D24414yes—
623C42—1224no—
624C42—1224no—
625C42—1224no—
626C42C2×D24412yes—
627C42C23×D6112yes—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23#1451981014yes—
634C23C22×D24412yes—
635C23C22×D24412yes—
636C23C22×D24411yescharacteristic
637Q8—1222no—
638Q8—1222no—
639Q8—1222no—
640Q8—1222no—
641Q8—4884no—
642Q8—2442no—
643Q8—2442no—
644D4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—1222no—
656C2×C4—1222no—
657C2×C4—1222no—
658C2×C4—1222no—
659C2×C4—1222no—
660C2×C4—1222no—
661C2×C4—1222no—
662C2×C4—1222no—
663C2×C4—4884no—
664C2×C4—4884no—
665C2×C4—2448no—
666C2×C4—2442no—
667C2×C4—2442no—
668C2×C4—2442no—
669C2×C4—2442no—
670C2×C4—2442no—
671C2×C4—2442no—
672C2×C4—2442no—
673C2×C4—2442no—
674C2×C4C22×D24412yes—
675C2×C4C22×D24412yes—
676C2×C4C22×D24412yes—
677C2×C4C22×D24412yes—
678C2×C4C22×D24411yescharacteristic
679C2×C4C2×#1175822412yes—
680C2×C4#1451982412yes—
681C2×C4C24×D6111yescharacteristic
682C8—22no—
683C8—22no—
684C8—22no—
685C8C2×#1175822414yes—
686C22—22no—
687C22—28no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—44no—
693C22#1684041612yes—
694C22C2×#1451981014yes—
695C22C2×#1451981012yes—
696C22#1684057412yes—
697C22C23×D24411yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—2442no—
703C4—2442no—
704C4—2442no—
705C4—2442no—
706C4—2442no—
707C4—2442no—
708C4—2442no—
709C4—2442no—
710C4#1684041612yes—
711C4C22×#1175822411yescharacteristic
712C4C2×#1451982411yescharacteristic
713C2—24no—
714C2—42no—
715C2#2145827614yesdirect product factor
716C2C2×#1684041611yescharacteristic
717C2C22×#1451981011yescharacteristic
718C2C2×#1684057411yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#435C2
socleC23×C61C22×D4
prime radicalC22×D4×C61D4
hypercenterC2×#435D61
hypocenterC61C2×#3344
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #21458276C2direct (N × H)
4. C2×#16840171C2semidirect
5. C2×#16840098C2semidirect
6. C2×#16840104C2semidirect
7. C2×#16840093C2semidirect
8. C2×#16840093C2semidirect
9. C2×#16840070C2semidirect
10. C2×#16840048C2semidirect
11. C2×#16840020C2semidirect
12. C2×#16840003C2semidirect
13. C2×#16839870C2semidirect
14. C2×#16839804C2semidirect
15. C22×#14519709C2semidirect
42. #16840171C22semidirect
43. #16840104C22semidirect
44. #16840098C22semidirect
45. #16840093C22semidirect
46. #16840093C22semidirect
47. #16840070C22semidirect
48. #16840048C22semidirect
49. #16840020C22semidirect
50. #16840003C22semidirect
51. #16839870C22semidirect
52. #16839804C22semidirect
62. C2×#14519709C22semidirect
372. C2×C61#3344semidirect
436. C61C2×#3344semidirect
715. C2#21458276direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404692
C2×#168404522
#214582762
C2×#168401712
C2×#168400982
C2×#168401042
C2×#168400932
C2×#168400702
C2×#168400482
C2×#168400202
C2×#168400032
C2×#168398702
C2×#168398042
C22×#145197092
C2×C61×#4352
C2×#334461