Finite Group Databasebeta

← C2×#21458309 #30558597

Subgroups — C2×#21458309 #30558597

Order 15616.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840472C211yesmaximal, characteristic, complemented
2C2×#16840462C211yesmaximal, characteristic
3#21458309C2116yesmaximal, direct product factor
4C2×#16840171C211yesmaximal, characteristic, complemented
5C2×#16840096C211yesmaximal, characteristic, complemented
6C2×#16840079C211yesmaximal, characteristic, complemented
7C2×#16840101C211yesmaximal, characteristic, complemented
8C2×#16840074C211yesmaximal, characteristic, complemented
9C2×#16840069C211yesmaximal, characteristic, complemented
10C2×#16840042C211yesmaximal, characteristic, complemented
11C2×#16840005C211yesmaximal, characteristic, complemented
12C2×#16839988C211yesmaximal, characteristic, complemented
13C2×#16839835C211yesmaximal, characteristic, complemented
14C2×#16839803C211yesmaximal, characteristic, complemented
15C2×#107×D61C211yesmaximal, characteristic, complemented
16C2×C61×#440C211yesmaximal, characteristic, complemented
17C22×#11758189C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840472—24no—
20#16840472C2218yescomplemented
21#16840462—24no—
22#16840462C2218yes—
23C2×#14519777C2211yescharacteristic
24C2×#14519770—21no—
25C2×#14519769—21no—
26C2×#14519769C2211yescharacteristic
27C2×#14519760—21no—
28C2×#14519755—21no—
29C2×#14519755—21no—
30C2×#14519753C2211yescharacteristic
31C2×#14519753C2211yescharacteristic
32C2×#14519750—21no—
33C2×#14519748C2211yescharacteristic
34C2×#14519748C2211yescharacteristic
35C2×C4×D244—21no—
36C2×C4×D244C2211yescharacteristic
37C2×C4×C22⋊D61—21no—
38C2×#14519735C2211yescharacteristic
39C2×C4⋊C4×D61C2211yescharacteristic
40C2×C4⋊C4×D61C2211yescharacteristic
41C2×C4⋊C4×D61C2211yescharacteristic
42#16840171C2218yescomplemented
43#16840101C2218yescomplemented
44#16840096C2218yescomplemented
45#16840079C2218yescomplemented
46#16840074C2218yescomplemented
47#16840069C2218yescomplemented
48#16840042C2218yescomplemented
49#16840005C2218yescomplemented
50#16839988C2218yescomplemented
51#16839835C2218yescomplemented
52#16839803C2218yescomplemented
53C2×#14519711C2211yescharacteristic
54C2×#14519711C2211yescharacteristic
55C2×#14519710C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519710C2211yescharacteristic
58#107×D61C2218yescomplemented
59C2×#14519709C2211yescharacteristic
60C2×#14519709C2211yescharacteristic
61C2×#14519708C2211yescharacteristic
62C2×C4⋊#92418C2211yescharacteristic
63C2×#14519701C2211yescharacteristic
64C2×#14519701C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×#14519698C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519689C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C2×C4×Q8×C61C2211yescharacteristic
71C2×C4×D4×C61C2211yescharacteristic
72C61×#440C2218yescomplemented
73C2×#107×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×D244D411yescharacteristic
79C22×C22⋊D61—21no—
80C22×C22⋊D61—21no—
81C22×C4×D61—21no—
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61C2311yescharacteristic
85C22×C4×D61C2311yescharacteristic
86C2×#11758189—24no—
87C2×#11758189C2314yes—
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90C2×C8×D61—24no—
91C2×C8×D61C2314yes—
92#14519777—22no—
93#14519777C2314yes—
94#14519770—28no—
95#14519769—22no—
96#14519769—28no—
97#14519769C2314yes—
98#14519760—28no—
99#14519755—28no—
100#14519755—28no—
101#14519753—22no—
102#14519753—22no—
103#14519753C2314yes—
104#14519753C2314yes—
105#14519750—28no—
106#14519748—22no—
107#14519748—22no—
108#14519748C2314yes—
109#14519748C2314yes—
110C4×D244—28no—
111C4×D244D414yes—
112C4×D244C2314yes—
113C4×C22⋊D61—28no—
114#14519735—22no—
115#14519735C2314yes—
116C2×C4⋊Dic61—21no—
117C2×C4⋊Dic61D411yescharacteristic
118C2×C4⋊Dic61C2311yescharacteristic
119C2×C4⋊Dic61C2311yescharacteristic
120C2×C4⋊Dic61C2311yescharacteristic
121C2×C4⋊Dic61C2311yescharacteristic
122C2×#11758196—21no—
123C2×#11758196—21no—
124C2×#11758196—21no—
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C4⋊C4×D61—22no—
130C4⋊C4×D61—22no—
131C4⋊C4×D61—22no—
132C4⋊C4×D61C2314yes—
133C4⋊C4×D61C2314yes—
134C4⋊C4×D61C2314yes—
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198D411yescharacteristic
141C2×#11758198D411yescharacteristic
142C2×C4×Dic61—21no—
143#14519711C2314yes—
144#14519711C2314yes—
145#14519710C2314yes—
146#14519710C2314yes—
147#14519710C2314yes—
148#14519709C2314yes—
149#14519709C2314yes—
150#14519708C2314yes—
151C4⋊#92418C2314yes—
152#14519701C2314yes—
153#14519701C2314yes—
154#14519698C2314yes—
155#14519698C2314yes—
156#14519689C2314yes—
157#14519689C2314yes—
158C22×Q8×C61C2311yescharacteristic
159C22×D4×C61C2311yescharacteristic
160C23×C4×C61—21no—
161C2×SD16×C61—24no—
162C2×SD16×C61C2314yes—
163C22×C8×C61C2311yescharacteristic
164C22×C8×C61C2311yescharacteristic
165C4×Q8×C61—22no—
166C4×Q8×C61C2314yes—
167C4×D4×C61—22no—
168C4×D4×C61C2314yes—
169C2×C4⋊C4×C61—21no—
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C22⋊C4×C61—21no—
173C2×C42×C61—21no—
174C2×C42×C61C2311yescharacteristic
175#107×C61C2314yes—
176#103×C61C2314yes—
177#102×C61C2314yes—
178#97×C61C2314yes—
179C24×C61—21no—
180C23×D61C2×D411yescharacteristic
181C23×D61C2×D411yescharacteristic
182C2×Q8×C61—21no—
183C2×Q8×C61—22no—
184C2×Q8×C61—22no—
185C2×Q8×C61C2412yes—
186C2×D4×C61—21no—
187C2×D4×C61—22no—
188C2×D4×C61—22no—
189C2×D4×C61C2412yes—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—24no—
194C22×C4×C61—82no—
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2411yescharacteristic
198C2×C22⋊D61—24no—
199C2×C22⋊D61—24no—
200C2×C22⋊D61—44no—
201C2×C22⋊D61—82no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208C2×D244—24no—
209C2×D244C2×D414yes—
210C2×C4×D61—22no—
211C2×C4×D61—22no—
212C2×C4×D61—22no—
213C2×C4×D61—22no—
214C2×C4×D61—24no—
215C2×C4×D61—24no—
216C2×C4×D61—24no—
217C2×C4×D61—82no—
218C2×C4×D61—82no—
219C2×C4×D61—82no—
220C2×C4×D61C2×D412yes—
221C2×C4×D61C2×D412yes—
222C2×C4×D61C2412yes—
223C2×C4×D61C2412yes—
224C2×Dic122—24no—
225C2×Dic122—82no—
226SD16×C61—28no—
227C2×C8×C61—22no—
228C2×C8×C61#4114yes—
229C2×C8×C61C2412yes—
230C2×C8×C61C2412yes—
231C4⋊C4×C61—24no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61C2412yes—
235C4⋊C4×C61C2412yes—
236C22⋊C4×C61—24no—
237C42×C61—24no—
238C42×C61C2×D412yes—
239C42×C61C2412yes—
240C22⋊Dic61—24no—
241C22⋊Dic61—24no—
242#11758198—24no—
243#11758198—24no—
244#11758198—24no—
245#11758198C2×D414yes—
246#11758198C2×D414yes—
247C4⋊Dic61—21no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—24no—
251C4⋊Dic61—21no—
252C4⋊Dic61C2×D414yes—
253C4⋊Dic61C2412yes—
254C4⋊Dic61C2412yes—
255C4⋊Dic61C2412yes—
256C4⋊Dic61C2412yes—
257#11758196—24no—
258#11758196—24no—
259#11758196—24no—
260#11758196—24no—
261#11758196—24no—
262#11758196—24no—
263#11758196—24no—
264C4×Dic61—24no—
265C2×#92418—22no—
266C2×#92418—22no—
267C2×#92418C2412yes—
268C2×#92418C2412yes—
269#11758189—28no—
270C8×D61—28no—
271C23×C61—22no—
272C23×C61—42no—
273C23×C61—42no—
274C23×C61—42no—
275C23×C61C22×D411yescharacteristic
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—22no—
279C22×D61—22no—
280C22×D61—22no—
281C22×D61#13714yes—
282C22×D61C22×D412yes—
283C22×D61C22×D412yes—
284Q8×C61—22no—
285Q8×C61—22no—
286Q8×C61—42no—
287D4×C61—22no—
288D4×C61—22no—
289D4×C61—42no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—42no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61—84no—
299C2×C4×C61C22×D412yes—
300C2×C4×C61C22×D412yes—
301C2×C4×C61C22×D411yescharacteristic
302C2×C4×C61C2×#4112yes—
303C2×C4×C612−1+412yes—
304C2×C4×C61C2511yescharacteristic
305C22⋊D61—48no—
306C22⋊D61—84no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61C22×D412yes—
318C2×Dic61C22×D412yes—
319D244—28no—
320C4×D61—24no—
321C4×D61—24no—
322C4×D61—22no—
323C4×D61—22no—
324C4×D61—22no—
325C4×D61—22no—
326C4×D61—84no—
327C4×D61—84no—
328C4×D61—84no—
329Dic122—84no—
330C8×C61—22no—
331C8×C61C2×#4114yes—
332#92418—22no—
333#92418—22no—
334C2×#3346—611nomaximal, Sylow
335C22×C61—42no—
336C22×C61—42no—
337C22×C61—42no—
338C22×C61—84no—
339C22×C61#54712yes—
340C22×C61C2×#13712yes—
341C22×C61#57612yes—
342C22×C61C23×D411yescharacteristic
343C2×D61—28no—
344C2×D61—22no—
345C2×D61—22no—
346C2×D61—22no—
347C2×D61—22no—
348C2×D61—22no—
349C2×D61—44no—
350C2×D61C2×#13714yes—
351C4×C61—22no—
352C4×C61—22no—
353C4×C61—42no—
354C4×C61—42no—
355C4×C61—42no—
356C4×C61#54712yes—
357C4×C61C22×#4111yescharacteristic
358C4×C61C2×2−1+411yescharacteristic
359Dic61—22no—
360Dic61—22no—
361Dic61—42no—
362Dic61—42no—
363Dic61—42no—
364Dic61—42no—
365C2×#554—611no—
366C2×#553—611no—
367#3346—6116no—
368C2×#501—611no—
369C2×#484—611no—
370C2×#481—611no—
371C2×#485—611no—
372C2×#480—611no—
373C2×#479—611no—
374C2×#474—611no—
375C2×#468—611no—
376C2×#465—611no—
377C2×#440D6111yescharacteristic, complemented
378C2×#435—611no—
379C2×#428—611no—
380C22×#107—611no—
381C2×C61—82no—
382C2×C61#334614yescomplemented
383C2×C61C2×#54711yescharacteristic
384C2×C61C22×#13711yescharacteristic
385C2×C61C2×#57611yescharacteristic
386D61—24no—
387D61—42no—
388C22×SD16C2×D6111yescharacteristic
389C22×M16—611no—
390C23×C8—611no—
391#554—618no—
392#554—1224no—
393#553—618no—
394#553—1224no—
395C2×C4⋊Q8—611no—
396C2×#126—1221no—
397C2×#125—611no—
398C2×#125—1221no—
399C2×#123—1221no—
400C2×C22⋊Q8—611no—
401C2×C22⋊Q8—611no—
402C2×C22⋊Q8—1221no—
403C2×C22⋊Q8—1221no—
404C2×#121—611no—
405C2×#121—611no—
406C2×#121—1221no—
407C2×C4×Q8C2×D6111yescharacteristic
408C2×C4×D4—611no—
409C2×C4×D4—1221no—
410C2×C4×D4—1221no—
411C2×C4×D4C2×D6111yescharacteristic
412C2×#117—611no—
413C22×C4⋊C4—611no—
414C22×C4⋊C4—611no—
415C22×C4⋊C4—611no—
416#501—618no—
417#485—618no—
418#484—618no—
419#481—618no—
420#480—618no—
421#479—618no—
422#474—618no—
423#468—618no—
424#465—618no—
425#440C2×D6118yescomplemented
426#435—618no—
427#428—618no—
428C2×#107—611no—
429C2×#107—611no—
430C2×#107—611no—
431C2×#107—611no—
432C2×#107—611no—
433C2×#107—618no—
434C2×#107C2×D6111yescharacteristic
435C2×#106—611no—
436C2×#106—611no—
437C2×#106—611no—
438C2×C4⋊C8—611no—
439C2×#103—611no—
440C2×#103—611no—
441C2×#103C2×D6111yescharacteristic
442C2×#102—611no—
443C2×#102—611no—
444C2×#102C2×D6111yescharacteristic
445C2×C22⋊C8—611no—
446C2×C22⋊C8—611no—
447C2×#97C2×D6111yescharacteristic
448C61C2×#334611yescharacteristic, complemented, Sylow
449C22×Q8—1221no—
450C22×Q8C22×D6111yescharacteristic
451C22×D4—611no—
452C22×D4—1221no—
453C22×D4—1221no—
454C22×D4C22×D6111yescharacteristic
455C23×C4—21no—
456C23×C4—611no—
457C23×C4—611no—
458C23×C4—1221no—
459C23×C4—1221no—
460C23×C4—1221no—
461C2×SD16—24no—
462C2×SD16C22×D6114yes—
463C2×M16—614no—
464C2×M16—1224no—
465C22×C8—611no—
466C22×C8—611no—
467C22×C8—614no—
468C22×C8—1224no—
469C22×C8C22×D6111yescharacteristic
470C22×C8C22×D6111yescharacteristic
471C4⋊Q8—614no—
472C4⋊Q8—1222no—
473#126—1228no—
474#125—614no—
475#125—1228no—
476#125—1222no—
477#123—1228no—
478C22⋊Q8—614no—
479C22⋊Q8—614no—
480C22⋊Q8—1228no—
481C22⋊Q8—1228no—
482C22⋊Q8—1222no—
483C22⋊Q8—1222no—
484#121—614no—
485#121—614no—
486#121—1228no—
487#121—1222no—
488#121—1222no—
489C4×Q8—22no—
490C4×Q8C22×D6114yes—
491C4×D4—22no—
492C4×D4—614no—
493C4×D4—614no—
494C4×D4—1228no—
495C4×D4—1228no—
496C4×D4C22×D6114yes—
497#117—614no—
498#117—1222no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—614no—
506C2×C4⋊C4—614no—
507C2×C4⋊C4—614no—
508C2×C4⋊C4—1222no—
509C2×C4⋊C4—1222no—
510C2×C4⋊C4—1222no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4C22×D6111yescharacteristic
520C2×C4⋊C4C22×D6111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—611no—
523C2×C22⋊C4—611no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C42—21no—
530C2×C42—1221no—
531C2×C42C22×D6111yescharacteristic
532#107—614no—
533#107—614no—
534#107—614no—
535#107—614no—
536#107—614no—
537#107C22×D6114yes—
538#106—614no—
539#106—614no—
540#106—614no—
541C4⋊C8—614no—
542#103—614no—
543#103—614no—
544#103C22×D6114yes—
545#102—614no—
546#102—614no—
547#102C22×D6114yes—
548C22⋊C8—614no—
549C22⋊C8—614no—
550#97C22×D6114yes—
551C24—21no—
552C24—611no—
553C24—611no—
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—1224no—
558C2×Q8—4882no—
559C2×Q8C23×D6112yes—
560C2×D4—21no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—614no—
564C2×D4—1224no—
565C2×D4—1224no—
566C2×D4—1224no—
567C2×D4—4882no—
568C2×D4—2444no—
569C2×D4C23×D6112yes—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—24no—
574C22×C4—82no—
575C22×C4—611no—
576C22×C4—611no—
577C22×C4—612no—
578C22×C4—612no—
579C22×C4—612no—
580C22×C4—612no—
581C22×C4—1224no—
582C22×C4—1224no—
583C22×C4—1224no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—4882no—
593C22×C4—4882no—
594C22×C4—4882no—
595C22×C4D4×D6111yescharacteristic
596C22×C4D4×D6111yescharacteristic
597C22×C4C23×D6111yescharacteristic
598SD16—28no—
599M16—1228no—
600C2×C8—22no—
601C2×C8—612no—
602C2×C8—612no—
603C2×C8—1222no—
604C2×C8—1222no—
605C2×C8—1228no—
606C2×C8#1175822214yes—
607C2×C8C23×D6112yes—
608C2×C8C23×D6112yes—
609C4⋊C4—24no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—614no—
613C4⋊C4—612no—
614C4⋊C4—612no—
615C4⋊C4—612no—
616C4⋊C4—612no—
617C4⋊C4—1224no—
618C4⋊C4—1224no—
619C4⋊C4—1224no—
620C4⋊C4—1224no—
621C4⋊C4—1224no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—1221no—
625C4⋊C4—1221no—
626C4⋊C4—1224no—
627C4⋊C4—1224no—
628C4⋊C4—1224no—
629C4⋊C4C23×D6112yes—
630C4⋊C4C23×D6112yes—
631C22⋊C4—24no—
632C22⋊C4—614no—
633C22⋊C4—614no—
634C22⋊C4—1224no—
635C22⋊C4—1224no—
636C22⋊C4—1224no—
637C22⋊C4—1224no—
638C22⋊C4—1224no—
639C42—24no—
640C42—1224no—
641C42D4×D6112yes—
642C42C23×D6112yes—
643C23—22no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—614no—
648C23—612no—
649C23—612no—
650C23—1222no—
651C23—1222no—
652C23—1222no—
653C23—1222no—
654C23—1222no—
655C23C2×D4×D6111yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—4884no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—1228no—
664D4—4884no—
665D4—2448no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—84no—
675C2×C4—612no—
676C2×C4—612no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1224no—
684C2×C4—1224no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—4884no—
690C2×C4—4884no—
691C2×C4—4884no—
692C2×C4—2442no—
693C2×C4—2442no—
694C2×C4—2442no—
695C2×C4—2442no—
696C2×C4C2×D4×D6112yes—
697C2×C4C2×D4×D6112yes—
698C2×C4C2×D4×D6111yescharacteristic
699C2×C4C2×#1175822212yes—
700C2×C4#1451982412yes—
701C2×C4C24×D6111yescharacteristic
702C8—22no—
703C8—1222no—
704C8—1222no—
705C8C2×#1175822214yes—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—84no—
710C22—614no—
711C22—1222no—
712C22—1222no—
713C22—1228no—
714C22—1222no—
715C22—1222no—
716C22—1222no—
717C22—2444no—
718C22#1684041712yes—
719C22#137×D6112yes—
720C22#1684056612yes—
721C22C22×D4×D6111yescharacteristic
722C4—22no—
723C4—22no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—1222no—
728C4—1222no—
729C4—2442no—
730C4—2442no—
731C4—2442no—
732C4—2442no—
733C4#1684041712yes—
734C4C22×#1175822211yescharacteristic
735C4C2×#1451982411yescharacteristic
736C2—82no—
737C2—1224no—
738C2—2442no—
739C2#2145830914yesdirect product factor
740C2C2×#1684041711yescharacteristic
741C2C2×#137×D6111yescharacteristic
742C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#440C2
socleC23×C61C22×D4
prime radicalC2×#16840462C2
hypercenterC2×#440D61
hypocenterC61C2×#3346
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#16840472C2semidirect
3. #21458309C2direct (N × H)
4. C2×#16840171C2semidirect
5. C2×#16840096C2semidirect
6. C2×#16840079C2semidirect
7. C2×#16840101C2semidirect
8. C2×#16840074C2semidirect
9. C2×#16840069C2semidirect
10. C2×#16840042C2semidirect
11. C2×#16840005C2semidirect
12. C2×#16839988C2semidirect
13. C2×#16839835C2semidirect
14. C2×#16839803C2semidirect
15. C2×#107×D61C2semidirect
16. C2×C61×#440C2semidirect
20. #16840472C22semidirect
42. #16840171C22semidirect
43. #16840101C22semidirect
44. #16840096C22semidirect
45. #16840079C22semidirect
46. #16840074C22semidirect
47. #16840069C22semidirect
48. #16840042C22semidirect
49. #16840005C22semidirect
50. #16839988C22semidirect
51. #16839835C22semidirect
52. #16839803C22semidirect
58. #107×D61C22semidirect
72. C61×#440C22semidirect
377. C2×#440D61semidirect
382. C2×C61#3346semidirect
425. #440C2×D61semidirect
448. C61C2×#3346semidirect
739. C2#21458309direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404722
C2×#168404622
#214583092
C2×#168401712
C2×#168400962
C2×#168400792
C2×#168401012
C2×#168400742
C2×#168400692
C2×#168400422
C2×#168400052
C2×#168399882
C2×#168398352
C2×#168398032
C2×#107×D612
C2×C61×#4402
C2×#334661