Finite Group Databasebeta

← C2×#21458399 #30558713

Subgroups — C2×#21458399 #30558713

Order 15616.

2082 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840480C211yesmaximal, characteristic, complemented
2C2×#16840413C211yesmaximal, characteristic
3#21458399C2116yesmaximal, direct product factor
4C2×#16840166C211yesmaximal, characteristic, complemented
5C2×#16840099C211yesmaximal, characteristic, complemented
6C2×#16840097C211yesmaximal, characteristic, complemented
7C2×#16840088C211yesmaximal, characteristic, complemented
8C2×#16840086C211yesmaximal, characteristic, complemented
9C2×#16840046C211yesmaximal, characteristic, complemented
10C2×#16840041C211yesmaximal, characteristic, complemented
11C2×#16840009C211yesmaximal, characteristic, complemented
12C2×#16840008C211yesmaximal, characteristic, complemented
13C2×#16839849C211yesmaximal, characteristic, complemented
14C2×#16839838C211yesmaximal, characteristic, complemented
15C2×#16839801C211yesmaximal, characteristic, complemented
16C2×C61×#428C211yesmaximal, characteristic, complemented
17C22×#11758222—21no—
18C22×#11758190C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20#16840480—24no—
21#16840480C2218yescomplemented
22#16840413—24no—
23#16840413C2218yes—
24C2×#14519776C2211yescharacteristic
25C2×#14519776C2211yescharacteristic
26C2×#14519771—21no—
27C2×#14519770—21no—
28C2×#14519763—21no—
29C2×#14519762—21no—
30C2×#14519760—21no—
31C2×#14519757C2211yescharacteristic
32C2×#14519756C2211yescharacteristic
33C2×#14519755—21no—
34C2×#14519752C2211yescharacteristic
35C2×#14519751C2211yescharacteristic
36C2×C4×Dic122—21no—
37C2×#14519742C2211yescharacteristic
38C2×#14519739C2211yescharacteristic
39C2×C4×C22⋊D61C2211yescharacteristic
40C2×#14519735C2211yescharacteristic
41C2×C4⋊C4×D61C2211yescharacteristic
42#16840166C2218yescomplemented
43#16840099C2218yescomplemented
44#16840097C2218yescomplemented
45#16840088C2218yescomplemented
46#16840086C2218yescomplemented
47#16840046C2218yescomplemented
48#16840041C2218yescomplemented
49#16840009C2218yescomplemented
50#16840008C2218yescomplemented
51#16839849C2218yescomplemented
52#16839838C2218yescomplemented
53#16839801C2218yescomplemented
54C2×#14519711C2211yescharacteristic
55C2×#14519710C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519710C2211yescharacteristic
58C2×#14519708C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519700C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×M16×C61C2211yescharacteristic
70C2×#117×C61C2211yescharacteristic
71C22×C4⋊C4×C61C2211yescharacteristic
72C61×#428C2218yescomplemented
73C2×#107×C61C2211yescharacteristic
74C2×#107×C61C2211yescharacteristic
75C2×#106×C61C2211yescharacteristic
76C2×#106×C61C2211yescharacteristic
77C2×#11758222—28no—
78C2×#11758222—48no—
79C22×Dic122—21no—
80C22×Dic122—21no—
81C22×Dic122C2311yescharacteristic
82C22×D244—21no—
83C22×D244C2311yescharacteristic
84C22×C22⋊D61—21no—
85C22×C22⋊D61D411yescharacteristic
86C22×C4×D61—21no—
87C22×C4×D61—21no—
88C22×C4×D61C2311yescharacteristic
89C2×#11758190—24no—
90C2×#11758190C2314yes—
91C2×#11758189—24no—
92C2×#11758189C2314yes—
93C22×#92418C2311yescharacteristic
94C22×#92418C2311yescharacteristic
95#14519776—22no—
96#14519776—22no—
97#14519776C2314yes—
98#14519776C2314yes—
99#14519771—28no—
100#14519770—28no—
101#14519763—28no—
102#14519762—28no—
103#14519760—28no—
104#14519757—22no—
105#14519757C2314yes—
106#14519756—22no—
107#14519756C2314yes—
108#14519755—28no—
109#14519752—22no—
110#14519752C2314yes—
111#14519751—22no—
112#14519751C2314yes—
113C4×Dic122—28no—
114#14519742—22no—
115#14519742C2314yes—
116#14519739—22no—
117#14519739C2314yes—
118C4×C22⋊D61D414yes—
119C4×C22⋊D61C2314yes—
120#14519735—22no—
121#14519735C2314yes—
122C2×C4⋊Dic61—21no—
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196D411yescharacteristic
131C4⋊C4×D61—22no—
132C4⋊C4×D61C2314yes—
133C2×C22⋊Dic61—21no—
134C2×C22⋊Dic61D411yescharacteristic
135C2×#11758198—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198D411yescharacteristic
141C2×C4×Dic61—21no—
142C2×C4×Dic61—21no—
143C2×C4×Dic61C2311yescharacteristic
144#14519711C2314yes—
145#14519710C2314yes—
146#14519710C2314yes—
147#14519710C2314yes—
148#14519708C2314yes—
149#14519706C2314yes—
150#14519702C2314yes—
151#14519700C2314yes—
152#14519700C2314yes—
153#14519699C2314yes—
154#14519697C2314yes—
155#14519697C2314yes—
156C22⋊#92418C2314yes—
157#14519689C2314yes—
158C8×Dic61C2314yes—
159C23×C4×C61—21no—
160C23×C4×C61C2311yescharacteristic
161C2×M16×C61—24no—
162C2×M16×C61C2314yes—
163C22×C8×C61C2311yescharacteristic
164C22×C8×C61C2311yescharacteristic
165#117×C61—22no—
166#117×C61C2314yes—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61—22no—
169C2×C4⋊C4×C61C2311yescharacteristic
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2314yes—
174C2×C22⋊C4×C61—21no—
175C2×C42×C61—21no—
176#107×C61C2314yes—
177#107×C61C2314yes—
178#106×C61C2314yes—
179#106×C61C2314yes—
180C24×C61C2×D411yescharacteristic
181C23×D61—21no—
182C23×D61C2×D411yescharacteristic
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—24no—
189C22×C4×C61—21no—
190C22×C4×C61—44no—
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D412yes—
193C22×C4×C61C2412yes—
194C22×C4×C61C2411yescharacteristic
195C2×C22⋊D61—24no—
196C2×C22⋊D61—24no—
197C2×C22⋊D61—44no—
198C2×C22⋊D61C2×D414yes—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61C2×D411yescharacteristic
203C22×Dic61C2×D411yescharacteristic
204C22×Dic61C2×D411yescharacteristic
205#11758222—432no—
206C2×D244—22no—
207C2×D244—22no—
208C2×D244—24no—
209C2×D244—21no—
210C2×D244—44no—
211C2×D244C2412yes—
212C2×C4×D61—22no—
213C2×C4×D61—22no—
214C2×C4×D61—24no—
215C2×C4×D61—24no—
216C2×C4×D61—44no—
217C2×C4×D61—44no—
218C2×C4×D61C2×D412yes—
219C2×C4×D61C2412yes—
220C2×Dic122—22no—
221C2×Dic122—22no—
222C2×Dic122—21no—
223C2×Dic122—24no—
224C2×Dic122—24no—
225C2×Dic122—44no—
226C2×Dic122—44no—
227C2×Dic122C2412yes—
228M16×C61—28no—
229C2×C8×C61—22no—
230C2×C8×C61#4114yescomplemented
231C2×C8×C61C2412yes—
232C2×C8×C61C2412yes—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—24no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61C2412yes—
239C4⋊C4×C61C2412yes—
240C4⋊C4×C61C2412yes—
241C4⋊C4×C61C2412yes—
242C22⋊C4×C61—24no—
243C42×C61—24no—
244C22⋊Dic61—24no—
245C22⋊Dic61C2×D414yes—
246#11758198—24no—
247#11758198—24no—
248#11758198—24no—
249#11758198—24no—
250#11758198—24no—
251#11758198C2×D414yes—
252C4⋊Dic61—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61—24no—
255C4⋊Dic61C2412yes—
256C4⋊Dic61C2412yes—
257#11758196—24no—
258#11758196—24no—
259#11758196—24no—
260#11758196—24no—
261#11758196—24no—
262#11758196C2×D414yes—
263C4×Dic61—24no—
264C4×Dic61—24no—
265C4×Dic61C2×D412yes—
266C4×Dic61C2412yes—
267C2×#92418—22no—
268C2×#92418—22no—
269C2×#92418C2412yes—
270C2×#92418C2412yes—
271#11758190—28no—
272#11758189—28no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61C22×D412yes—
277C23×C61C22×D411yescharacteristic
278C22×D61—22no—
279C22×D61—22no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—42no—
283C22×D61—42no—
284C22×D61—42no—
285C22×D61C22×D412yes—
286C2×C4×C61—22no—
287C2×C4×C61—24no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—48no—
295C2×C4×C61—42no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61—42no—
299C2×C4×C61C22×D412yes—
300C2×C4×C61C22×D411yescharacteristic
301C2×C4×C61C2×#4112yes—
302C2×C4×C612−1+412yes—
303C2×C4×C61C2511yescharacteristic
304C22⋊D61—28no—
305C22⋊D61—48no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—42no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61AGL(1,ℤ/8)14yes—
315C2×Dic61C22×D412yes—
316C2×Dic61C22×D412yes—
317C2×Dic61C22×D412yes—
318D244—22no—
319D244—22no—
320D244—48no—
321D244—42no—
322C4×D61—24no—
323C4×D61—22no—
324C4×D61—22no—
325C4×D61—48no—
326C4×D61—48no—
327Dic122—22no—
328Dic122—22no—
329Dic122—42no—
330Dic122—48no—
331Dic122—48no—
332C8×C61—22no—
333C8×C61C2×#4114yescomplemented
334#92418—22no—
335#92418—22no—
336C2×#3353—611nomaximal, Sylow
337C22×C61—22no—
338C22×C61—22no—
339C22×C61—22no—
340C22×C61—44no—
341C22×C61#54712yes—
342C22×C61C2×AGL(1,ℤ/8)12yes—
343C22×C61#57812yes—
344C22×C61C23×D411yescharacteristic
345C2×D61—22no—
346C2×D61—22no—
347C2×D61—22no—
348C2×D61—44no—
349C2×D61—42no—
350C2×D61—42no—
351C2×D61—42no—
352C2×D61—84no—
353C4×C61—22no—
354C4×C61—42no—
355C4×C61—42no—
356C4×C61—42no—
357C4×C61—42no—
358C4×C61#54712yes—
359C4×C61C22×#4111yescharacteristic
360C4×C61C2×2−1+411yescharacteristic
361Dic61—22no—
362Dic61—22no—
363Dic61—42no—
364Dic61—42no—
365Dic61—42no—
366Dic61C2×AGL(1,ℤ/8)14yes—
367C2×#556—611no—
368C2×#547—611no—
369#3353—6116no—
370C2×#500—611no—
371C2×#484—611no—
372C2×#484—611no—
373C2×#482—611no—
374C2×#482—611no—
375C2×#475—611no—
376C2×#474—611no—
377C2×#468—611no—
378C2×#468—611no—
379C2×C4×SD16—611no—
380C2×#436—611no—
381C2×#428—611no—
382C2×#428D6111yescharacteristic, complemented
383C2×C61—42no—
384C2×C61#335314yescomplemented
385C2×C61C2×#54711yescharacteristic
386C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
387C2×C61C2×#57811yescharacteristic
388D61—42no—
389D61—82no—
390C22×#41—1221no—
391C22×SD16—611no—
392C22×M16—611no—
393C22×M16C2×D6111yescharacteristic
394#556—618no—
395#556—1224no—
396#547—618no—
397#547—1224no—
398C2×C4⋊Q8—611no—
399C2×C4⋊Q8—611no—
400C2×#126—1221no—
401C2×#126—1221no—
402C2×#124—1221no—
403C2×#123—1221no—
404C2×#123—1221no—
405C2×C22⋊Q8—611no—
406C2×C22⋊Q8—611no—
407C2×C22⋊Q8—1221no—
408C2×#121—611no—
409C2×#121—611no—
410C2×C4×Q8—611no—
411C2×C4×Q8—1221no—
412C2×C4×D4—611no—
413C2×C4×D4—611no—
414C2×#117—611no—
415C2×#117C2×D6111yescharacteristic
416C22×C4⋊C4—611no—
417C22×C4⋊C4C2×D6111yescharacteristic
418#500—618no—
419#484—618no—
420#484—618no—
421#482—618no—
422#482—618no—
423#475—618no—
424#474—618no—
425#468—618no—
426#468—618no—
427C4×SD16—618no—
428#436—618no—
429#428—618no—
430#428C2×D6118yescomplemented
431C2×#107—611no—
432C2×#107—611no—
433C2×#107—611no—
434C2×#107—611no—
435C2×#107C2×D6111yescharacteristic
436C2×#107C2×D6111yescharacteristic
437C2×#106—611no—
438C2×#106C2×D6111yescharacteristic
439C2×#106C2×D6111yescharacteristic
440C2×C4⋊C8—611no—
441C2×#103—611no—
442C2×#103—611no—
443C2×#103—611no—
444C2×#102—611no—
445C2×#102—611no—
446C2×#102—611no—
447C2×C22⋊C8—611no—
448C2×C22⋊C8—611no—
449C2×C4×C8—611no—
450C61C2×#335311yescharacteristic, complemented, Sylow
451C2×#41—1228no—
452C2×#41—2448no—
453C22×Q8—611no—
454C22×Q8—1221no—
455C22×Q8—1221no—
456C22×D4—611no—
457C22×D4—611no—
458C22×D4—1221no—
459C22×D4—1221no—
460C23×C4—21no—
461C23×C4—611no—
462C23×C4—1221no—
463C23×C4—1221no—
464C23×C4C22×D6111yescharacteristic
465C2×SD16—614no—
466C2×SD16—1224no—
467C2×M16—24no—
468C2×M16—614no—
469C2×M16—1224no—
470C2×M16C22×D6114yes—
471C22×C8—611no—
472C22×C8—611no—
473C22×C8C22×D6111yescharacteristic
474C22×C8C22×D6111yescharacteristic
475C4⋊Q8—614no—
476C4⋊Q8—614no—
477C4⋊Q8—1222no—
478C4⋊Q8—1222no—
479#126—1228no—
480#126—1228no—
481#124—1228no—
482#123—1228no—
483#123—1228no—
484C22⋊Q8—614no—
485C22⋊Q8—614no—
486C22⋊Q8—1228no—
487C22⋊Q8—1222no—
488C22⋊Q8—1222no—
489#121—614no—
490#121—614no—
491#121—1222no—
492#121—1222no—
493C4×Q8—614no—
494C4×Q8—1228no—
495C4×Q8—1222no—
496C4×D4—614no—
497C4×D4—614no—
498C4×D4—614no—
499C4×D4—1222no—
500#117—22no—
501#117—614no—
502#117—1222no—
503#117C22×D6114yes—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—614no—
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⋊C4C22×D6111yescharacteristic
518C2×C4⋊C4C22×D6111yescharacteristic
519C2×C4⋊C4C22×D6114yes—
520C2×C4⋊C4C22×D6111yescharacteristic
521C2×C4⋊C4C22×D6111yescharacteristic
522C2×C22⋊C4—21no—
523C2×C22⋊C4—611no—
524C2×C22⋊C4—611no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C42—21no—
532C2×C42—611no—
533C2×C42—1221no—
534C2×C42—1221no—
535#107—614no—
536#107—614no—
537#107—614no—
538#107—614no—
539#107C22×D6114yes—
540#107C22×D6114yes—
541#106—614no—
542#106C22×D6114yes—
543#106C22×D6114yes—
544C4⋊C8—614no—
545#103—614no—
546#103—614no—
547#103—614no—
548#102—614no—
549#102—614no—
550#102—614no—
551C22⋊C8—614no—
552C22⋊C8—614no—
553C4×C8—614no—
554C24—611no—
555C24—1221no—
556C24D4×D6111yescharacteristic
557#41—24432no—
558C2×Q8—612no—
559C2×Q8—1224no—
560C2×Q8—1224no—
561C2×Q8—1221no—
562C2×Q8—1222no—
563C2×Q8—1222no—
564C2×Q8—2444no—
565C2×Q8—2444no—
566C2×D4—614no—
567C2×D4—612no—
568C2×D4—1224no—
569C2×D4—1224no—
570C2×D4—1224no—
571C2×D4—1221no—
572C2×D4—1222no—
573C2×D4—1222no—
574C2×D4—2444no—
575C2×D4—2444no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—44no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—612no—
588C22×C4—612no—
589C22×C4—1224no—
590C22×C4—1224no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—2444no—
597C22×C4—2444no—
598C22×C4D4×D6112yes—
599C22×C4D4×D6111yescharacteristic
600C22×C4C23×D6112yes—
601C22×C4C23×D6111yescharacteristic
602SD16—1228no—
603M16—28no—
604M16—1228no—
605C2×C8—22no—
606C2×C8—612no—
607C2×C8—612no—
608C2×C8—1222no—
609C2×C8—1222no—
610C2×C8#1175822214yescomplemented
611C2×C8C23×D6112yes—
612C2×C8C23×D6112yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—614no—
619C4⋊C4—612no—
620C4⋊C4—612no—
621C4⋊C4—1224no—
622C4⋊C4—1224no—
623C4⋊C4—1224no—
624C4⋊C4—1224no—
625C4⋊C4—1224no—
626C4⋊C4—1221no—
627C4⋊C4—1221no—
628C4⋊C4—1224no—
629C4⋊C4C23×D6112yes—
630C4⋊C4C23×D6112yes—
631C4⋊C4C23×D6112yes—
632C4⋊C4C23×D6112yes—
633C22⋊C4—24no—
634C22⋊C4—614no—
635C22⋊C4—614no—
636C22⋊C4—1224no—
637C22⋊C4—1224no—
638C22⋊C4—1224no—
639C22⋊C4—1224no—
640C22⋊C4—1224no—
641C22⋊C4—1224no—
642C42—24no—
643C42—612no—
644C42—612no—
645C42—1224no—
646C42—1224no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—612no—
651C23—1222no—
652C23—1222no—
653C23—1222no—
654C23—1222no—
655C23—2442no—
656C23—2442no—
657C23—2442no—
658C23C2×D4×D6112yes—
659C23C2×D4×D6111yescharacteristic
660Q8—1222no—
661Q8—1222no—
662Q8—2448no—
663Q8—2448no—
664Q8—2442no—
665D4—1228no—
666D4—1222no—
667D4—1222no—
668D4—2448no—
669D4—2448no—
670D4—2442no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—48no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—614no—
685C2×C4—612no—
686C2×C4—612no—
687C2×C4—612no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—1224no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—2448no—
697C2×C4—2448no—
698C2×C4—2442no—
699C2×C4—2442no—
700C2×C4—2442no—
701C2×C4C2×D4×D6112yes—
702C2×C4C2×D4×D6111yescharacteristic
703C2×C4C2×#1175822212yes—
704C2×C4#1451982512yes—
705C2×C4C24×D6111yescharacteristic
706C8—22no—
707C8—1222no—
708C8—1222no—
709C8C2×#1175822214yescomplemented
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—1222no—
715C22—1222no—
716C22—1222no—
717C22—4884no—
718C22—2442no—
719C22—2442no—
720C22—2442no—
721C22—2444no—
722C22#1684041312yes—
723C22AGL(1,ℤ/8)×D6112yes—
724C22#1684057812yes—
725C22C22×D4×D6111yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—614no—
732C4—1222no—
733C4—1222no—
734C4—2442no—
735C4—2442no—
736C4—2442no—
737C4#1684041312yes—
738C4C22×#1175822211yescharacteristic
739C4C2×#1451982511yescharacteristic
740C2—42no—
741C2—4882no—
742C2—2442no—
743C2#2145839914yesdirect product factor
744C2C2×#1684041311yescharacteristic
745C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
746C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#428C2
socleC23×C61C22×D4
prime radicalC2×#16840413C2
hypercenterC2×#428D61
hypocenterC61C2×#3353
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#16840480C2semidirect
3. #21458399C2direct (N × H)
4. C2×#16840166C2semidirect
5. C2×#16840099C2semidirect
6. C2×#16840097C2semidirect
7. C2×#16840088C2semidirect
8. C2×#16840086C2semidirect
9. C2×#16840046C2semidirect
10. C2×#16840041C2semidirect
11. C2×#16840009C2semidirect
12. C2×#16840008C2semidirect
13. C2×#16839849C2semidirect
14. C2×#16839838C2semidirect
15. C2×#16839801C2semidirect
16. C2×C61×#428C2semidirect
21. #16840480C22semidirect
42. #16840166C22semidirect
43. #16840099C22semidirect
44. #16840097C22semidirect
45. #16840088C22semidirect
46. #16840086C22semidirect
47. #16840046C22semidirect
48. #16840041C22semidirect
49. #16840009C22semidirect
50. #16840008C22semidirect
51. #16839849C22semidirect
52. #16839838C22semidirect
53. #16839801C22semidirect
72. C61×#428C22semidirect
230. C2×C8×C61#41semidirect
333. C8×C61C2×#41semidirect
382. C2×#428D61semidirect
384. C2×C61#3353semidirect
430. #428C2×D61semidirect
450. C61C2×#3353semidirect
610. C2×C8#11758222semidirect
709. C8C2×#11758222semidirect
743. C2#21458399direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404802
C2×#168404132
#214583992
C2×#168401662
C2×#168400992
C2×#168400972
C2×#168400882
C2×#168400862
C2×#168400462
C2×#168400412
C2×#168400092
C2×#168400082
C2×#168398492
C2×#168398382
C2×#168398012
C2×C61×#4282
C2×#335361