Finite Group Databasebeta

← C2×#21458261 #30558546

Subgroups — C2×#21458261 #30558546

Order 15616.

2094 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×#16840452C211yesmaximal, characteristic, complemented
2C2×#16840416C211yesmaximal, characteristic
3#21458261C2116yesmaximal, direct product factor
4C2×#16840171C211yesmaximal, characteristic, complemented
5C2×#16840098C211yesmaximal, characteristic, complemented
6C2×#16840087C211yesmaximal, characteristic, complemented
7C2×#16840093C211yesmaximal, characteristic, complemented
8C2×#16840076C211yesmaximal, characteristic, complemented
9C2×#16840058C211yesmaximal, characteristic, complemented
10C2×#16840063C211yesmaximal, characteristic, complemented
11C2×#16840008C211yesmaximal, characteristic, complemented
12C2×#16839991C211yesmaximal, characteristic, complemented
13C2×#16839864C211yesmaximal, characteristic, complemented
14C2×#16839804C211yesmaximal, characteristic, complemented
15C22×#14519711C211yesmaximal, characteristic, complemented
16C2×C61×#435C211yesmaximal, characteristic, complemented
17C22×#11758224—21no—
18C22×#11758190C2211yescharacteristic
19#16840452—24no—
20#16840452C2218yescomplemented
21#16840416—24no—
22#16840416C2218yes—
23C2×#14519777C2211yescharacteristic
24C2×#14519770—21no—
25C2×#14519769C2211yescharacteristic
26C2×#14519767—21no—
27C2×#14519761—21no—
28C2×#14519761—21no—
29C2×#14519758—21no—
30C2×#14519757—21no—
31C2×#14519756C2211yescharacteristic
32C2×#14519756C2211yescharacteristic
33C2×#14519751C2211yescharacteristic
34C2×#14519751C2211yescharacteristic
35C2×C4×Dic122C2211yescharacteristic
36C2×C4×D244C2211yescharacteristic
37C2×#14519736C2211yescharacteristic
38C2×#14519733—21no—
39C22×C4⋊Dic61C2211yescharacteristic
40C22×C4⋊Dic61C2211yescharacteristic
41C22×C4⋊Dic61C2211yescharacteristic
42#16840171C2218yescomplemented
43#16840098C2218yescomplemented
44#16840093C2218yescomplemented
45#16840087C2218yescomplemented
46#16840076C2218yescomplemented
47#16840063C2218yescomplemented
48#16840058C2218yescomplemented
49#16840008C2218yescomplemented
50#16839991C2218yescomplemented
51#16839864C2218yescomplemented
52#16839804C2218yescomplemented
53C2×#14519711C2211yescharacteristic
54C2×#14519711C2211yescharacteristic
55C2×#14519711C2211yescharacteristic
56C2×#14519711C2211yescharacteristic
57C2×#14519711C2211yescharacteristic
58C2×#14519711C2211yescharacteristic
59C2×#14519711C2218yescomplemented
60C2×#14519709C2211yescharacteristic
61C2×#14519709C2211yescharacteristic
62C2×#14519709C2211yescharacteristic
63C2×#14519702C2211yescharacteristic
64C2×#14519702C2211yescharacteristic
65C2×#14519702C2211yescharacteristic
66C2×#14519699C2211yescharacteristic
67C2×#14519699C2211yescharacteristic
68C2×#14519699C2211yescharacteristic
69C22×M16×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic
71C2×C4×D4×C61C2211yescharacteristic
72C61×#435C2218yescomplemented
73C2×C4⋊C8×C61C2211yescharacteristic
74C2×C22⋊C8×C61C2211yescharacteristic
75C2×C22⋊C8×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C2×#11758224—28no—
78C2×#11758224—48no—
79C22×Dic122—21no—
80C22×Dic122C2311yescharacteristic
81C22×D244C2311yescharacteristic
82C22×C22⋊D61—21no—
83C22×C22⋊D61—21no—
84C23×Dic61—21no—
85C23×Dic61—21no—
86C23×Dic61—21no—
87C22×C4×D61—21no—
88C2×#11758190—24no—
89C2×#11758190C2314yes—
90#14519777—22no—
91#14519777C2314yes—
92#14519770—28no—
93#14519769—22no—
94#14519769C2314yes—
95#14519767—28no—
96#14519761—28no—
97#14519761—28no—
98#14519758—28no—
99#14519757—28no—
100#14519756—22no—
101#14519756—22no—
102#14519756C2314yes—
103#14519756C2314yes—
104#14519751—22no—
105#14519751—22no—
106#14519751C2314yes—
107#14519751C2314yes—
108C4×Dic122—22no—
109C4×Dic122C2314yes—
110C4×D244—22no—
111C4×D244C2314yes—
112#14519736—22no—
113#14519736C2314yes—
114#14519733—28no—
115C2×C4⋊Dic61—22no—
116C2×C4⋊Dic61—21no—
117C2×C4⋊Dic61—21no—
118C2×C4⋊Dic61—21no—
119C2×C4⋊Dic61—22no—
120C2×C4⋊Dic61—22no—
121C2×C4⋊Dic61—21no—
122C2×C4⋊Dic61C2314yes—
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×C4⋊Dic61C2311yescharacteristic
126C2×C4⋊Dic61C2311yescharacteristic
127C2×C4⋊Dic61C2311yescharacteristic
128C2×C4⋊Dic61C2314yes—
129C2×C4⋊Dic61C2314yes—
130C2×C4⋊Dic61C2311yescharacteristic
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×C22⋊Dic61—21no—
137C2×C22⋊Dic61—21no—
138C2×C22⋊Dic61—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×C4×Dic61—21no—
143C2×C4×Dic61—21no—
144#14519711C2314yes—
145#14519711C2314yes—
146#14519711C2314yes—
147#14519711C2314yes—
148#14519711C2314yes—
149#14519711C2314yes—
150#14519709C2314yes—
151#14519709C2314yes—
152#14519709C2314yes—
153#14519702C2314yes—
154#14519702C2314yes—
155#14519702C2314yes—
156#14519699C2314yes—
157#14519699C2314yes—
158#14519699C2314yes—
159C22×D4×C61D411yescharacteristic
160C23×C4×C61C2311yescharacteristic
161C23×C4×C61C2311yescharacteristic
162C2×M16×C61—24no—
163C2×M16×C61C2314yes—
164C22×C8×C61—24no—
165C22×C8×C61C2314yes—
166C22×C8×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2311yescharacteristic
169C22×C8×C61C2311yescharacteristic
170C4×D4×C61D414yes—
171C4×D4×C61C2314yes—
172C2×C4⋊C4×C61D411yescharacteristic
173C2×C22⋊C4×C61D411yescharacteristic
174C2×C22⋊C4×C61D411yescharacteristic
175C2×C42×C61C2311yescharacteristic
176C4⋊C8×C61C2314yes—
177C22⋊C8×C61C2314yes—
178C22⋊C8×C61C2314yes—
179#97×C61C2314yes—
180C24×C61C2×D411yescharacteristic
181C24×C61C2×D411yescharacteristic
182C23×D61—21no—
183C2×D4×C61—24no—
184C2×D4×C61C2×D414yes—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61—22no—
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D412yes—
194C22×C4×C61C2×D412yes—
195C22×C4×C61C2412yes—
196C22×C4×C61C2412yes—
197C22×C4×C61C2411yescharacteristic
198C2×C22⋊D61—24no—
199C2×C22⋊D61—24no—
200C2×C22⋊D61—44no—
201C2×C22⋊D61—44no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—24no—
206C22×Dic61—24no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—24no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—44no—
213C22×Dic61—44no—
214C22×Dic61—44no—
215#11758224—432no—
216C2×D244—22no—
217C2×D244—22no—
218C2×D244—21no—
219C2×D244C2412yes—
220C2×C4×D61—24no—
221C2×C4×D61—44no—
222C2×Dic122—22no—
223C2×Dic122—22no—
224C2×Dic122—24no—
225C2×Dic122—21no—
226C2×Dic122—44no—
227C2×Dic122C2412yes—
228M16×C61—28no—
229C2×C8×C61—22no—
230C2×C8×C61—22no—
231C2×C8×C61—22no—
232C2×C8×C61—28no—
233C2×C8×C61#4114yescomplemented
234C2×C8×C61C2412yes—
235C2×C8×C61C2412yes—
236C2×C8×C61C2412yes—
237C2×C8×C61C2412yes—
238C4⋊C4×C61C2×D414yes—
239C22⋊C4×C61C2×D414yes—
240C22⋊C4×C61C2×D414yes—
241C42×C61C2×D412yes—
242C42×C61C2412yes—
243C22⋊Dic61—24no—
244C22⋊Dic61—24no—
245C22⋊Dic61—24no—
246#11758198—24no—
247#11758198—24no—
248#11758198—24no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61—24no—
255C4⋊Dic61—24no—
256C4⋊Dic61—24no—
257C4⋊Dic61—24no—
258C4⋊Dic61—21no—
259C4⋊Dic61C2412yes—
260C4⋊Dic61C2412yes—
261C4⋊Dic61C2412yes—
262C4⋊Dic61C2412yes—
263C4⋊Dic61C2412yes—
264C4⋊Dic61C2412yes—
265#11758196—24no—
266#11758196—24no—
267#11758196—24no—
268#11758196—24no—
269#11758196—24no—
270C4×Dic61—24no—
271C4×Dic61—24no—
272#11758190—28no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61—22no—
278C23×C61AGL(1,ℤ/8)14yes—
279C23×C61C22×D412yes—
280C23×C61C22×D412yes—
281C23×C61C22×D411yescharacteristic
282C22×D61—22no—
283C22×D61—42no—
284C22×D61—42no—
285C22×D61—42no—
286D4×C61—28no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—24no—
292C2×C4×C61—24no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61C22×D412yes—
298C2×C4×C61C22×D412yes—
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—48no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—48no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—48no—
320C2×Dic61—48no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324D244—22no—
325D244—22no—
326D244—42no—
327C4×D61—48no—
328Dic122—22no—
329Dic122—22no—
330Dic122—48no—
331Dic122—42no—
332C8×C61—22no—
333C8×C61—22no—
334C8×C61—22no—
335C8×C61C2×#4114yescomplemented
336C2×#3343—611nomaximal, Sylow
337C22×C61—28no—
338C22×C61—22no—
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—44no—
344C22×C61#54712yes—
345C22×C61C2×AGL(1,ℤ/8)14yes—
346C22×C61C2×AGL(1,ℤ/8)12yes—
347C22×C61#57812yes—
348C22×C61C23×D411yescharacteristic
349C2×D61—42no—
350C2×D61—42no—
351C2×D61—42no—
352C2×D61—84no—
353C4×C61—22no—
354C4×C61—22no—
355C4×C61—22no—
356C4×C61—22no—
357C4×C61#54712yes—
358C4×C61C22×#4111yescharacteristic
359C4×C61C2×2−1+411yescharacteristic
360Dic61—42no—
361Dic61—42no—
362Dic61—42no—
363Dic61—42no—
364Dic61—42no—
365Dic61—42no—
366Dic61—42no—
367C2×#552—611no—
368C2×#547—611no—
369#3343—6116no—
370C2×#501—611no—
371C2×#484—611no—
372C2×#482—611no—
373C2×#483—611no—
374C2×#480—611no—
375C2×#477—611no—
376C2×#478—611no—
377C2×#468—611no—
378C2×#465—611no—
379C2×#440—611no—
380C2×#435D6111yescharacteristic, complemented
381C2×#428—611no—
382C22×#107—611no—
383C2×C61—24no—
384C2×C61—42no—
385C2×C61#334314yescomplemented
386C2×C61C2×#54711yescharacteristic
387C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
388C2×C61C2×#57811yescharacteristic
389D61—82no—
390C22×#41—1221no—
391C22×SD16—611no—
392C22×M16C2×D6111yescharacteristic
393C23×C8C2×D6111yescharacteristic
394#552—618no—
395#552—1224no—
396#547—618no—
397#547—1224no—
398C2×C4⋊Q8—611no—
399C2×#126—1221no—
400C2×#125—611no—
401C2×#125—1221no—
402C2×#123—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×D4—611no—
412C2×C4×D4C2×D6111yescharacteristic
413C2×#117—611no—
414C2×#117—1221no—
415C22×C4⋊C4—611no—
416C22×C4⋊C4—611no—
417C22×C4⋊C4—611no—
418#501—618no—
419#484—618no—
420#483—618no—
421#482—618no—
422#480—618no—
423#478—618no—
424#477—618no—
425#468—618no—
426#465—618no—
427#440—618no—
428#435C2×D6118yescomplemented
429#428—618no—
430C2×#107—611no—
431C2×#107—611no—
432C2×#107—611no—
433C2×#107—611no—
434C2×#107—618no—
435C2×#107—611no—
436C2×#107—611no—
437C2×#106—611no—
438C2×#106—611no—
439C2×#106—611no—
440C2×C4⋊C8C2×D6111yescharacteristic
441C2×#103—611no—
442C2×#103—611no—
443C2×#103—611no—
444C2×#102—611no—
445C2×#102—611no—
446C2×#102—611no—
447C2×C22⋊C8C2×D6111yescharacteristic
448C2×C22⋊C8C2×D6111yescharacteristic
449C2×#97C2×D6111yescharacteristic
450C61C2×#334311yescharacteristic, complemented, Sylow
451C2×#41—1228no—
452C2×#41—2448no—
453C22×Q8—611no—
454C22×Q8—1221no—
455C22×D4—611no—
456C22×D4—1221no—
457C22×D4—1221no—
458C22×D4D24411yescharacteristic
459C23×C4—1221no—
460C23×C4—1221no—
461C23×C4—1221no—
462C23×C4—1221no—
463C23×C4C22×D6111yescharacteristic
464C23×C4C22×D6111yescharacteristic
465C2×SD16—614no—
466C2×SD16—1224no—
467C2×M16—24no—
468C2×M16C22×D6114yes—
469C22×C8—24no—
470C22×C8C22×D6111yescharacteristic
471C22×C8C22×D6114yes—
472C22×C8C22×D6111yescharacteristic
473C22×C8C22×D6111yescharacteristic
474C22×C8C22×D6111yescharacteristic
475C4⋊Q8—614no—
476C4⋊Q8—1222no—
477#126—1228no—
478#125—614no—
479#125—1228no—
480#125—1222no—
481#123—1228no—
482#123—1228no—
483#123—1228no—
484C22⋊Q8—614no—
485C22⋊Q8—614no—
486C22⋊Q8—1222no—
487C22⋊Q8—1222no—
488C22⋊Q8—1228no—
489#121—614no—
490#121—614no—
491#121—1222no—
492#121—1222no—
493C4×Q8—614no—
494C4×Q8—1222no—
495C4×D4—614no—
496C4×D4—1222no—
497C4×D4D24414yes—
498C4×D4C22×D6114yes—
499#117—614no—
500#117—1222no—
501#117—1228no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—614no—
508C2×C4⋊C4—614no—
509C2×C4⋊C4—614no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1222no—
515C2×C4⋊C4—1222no—
516C2×C4⋊C4—1222no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4D24411yescharacteristic
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4D24411yescharacteristic
531C2×C22⋊C4D24411yescharacteristic
532C2×C42—1221no—
533C2×C42—1221no—
534C2×C42C22×D6111yescharacteristic
535#107—614no—
536#107—614no—
537#107—614no—
538#107—614no—
539#107—614no—
540#107—614no—
541#106—614no—
542#106—614no—
543#106—614no—
544C4⋊C8C22×D6114yes—
545#103—614no—
546#103—614no—
547#103—614no—
548#102—614no—
549#102—614no—
550#102—614no—
551C22⋊C8C22×D6114yes—
552C22⋊C8C22×D6114yes—
553#97C22×D6114yes—
554C24—1221no—
555C24C2×D24411yescharacteristic
556C24C2×D24411yescharacteristic
557#41—24432no—
558C2×Q8—612no—
559C2×Q8—1221no—
560C2×Q8—1224no—
561C2×Q8—1222no—
562C2×Q8—1222no—
563C2×Q8—2444no—
564C2×D4—24no—
565C2×D4—612no—
566C2×D4—1224no—
567C2×D4—1224no—
568C2×D4—1221no—
569C2×D4—1222no—
570C2×D4—1222no—
571C2×D4—2444no—
572C2×D4—2444no—
573C2×D4C2×D24414yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—1224no—
579C22×C4—1224no—
580C22×C4—1224no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1224no—
589C22×C4—2444no—
590C22×C4—2444no—
591C22×C4—2444no—
592C22×C4—2444no—
593C22×C4C2×D24412yes—
594C22×C4C2×D24412yes—
595C22×C4C2×D24411yescharacteristic
596C22×C4C2×D24411yescharacteristic
597C22×C4C2×D24411yescharacteristic
598C22×C4C2×D24411yescharacteristic
599C22×C4C23×D6112yes—
600C22×C4C23×D6112yes—
601C22×C4C23×D6111yescharacteristic
602SD16—1228no—
603M16—28no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—28no—
608C2×C8#1175822414yescomplemented
609C2×C8C23×D6112yes—
610C2×C8C23×D6112yes—
611C2×C8C23×D6112yes—
612C2×C8C23×D6112yes—
613C4⋊C4—612no—
614C4⋊C4—612no—
615C4⋊C4—612no—
616C4⋊C4—612no—
617C4⋊C4—612no—
618C4⋊C4—612no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—1224no—
624C4⋊C4—1224no—
625C4⋊C4—1221no—
626C4⋊C4—1224no—
627C4⋊C4—1221no—
628C4⋊C4—1224no—
629C4⋊C4—1224no—
630C4⋊C4—1224no—
631C4⋊C4—1224no—
632C4⋊C4—1224no—
633C4⋊C4—1224no—
634C4⋊C4C2×D24414yes—
635C22⋊C4—1224no—
636C22⋊C4—1224no—
637C22⋊C4—1224no—
638C22⋊C4—1224no—
639C22⋊C4—1224no—
640C22⋊C4—1224no—
641C22⋊C4C2×D24414yes—
642C22⋊C4C2×D24414yes—
643C42—1224no—
644C42—1224no—
645C42C2×D24412yes—
646C42C23×D6112yes—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—1222no—
653C23—2442no—
654C23—2442no—
655C23—2442no—
656C23#1451980514yes—
657C23C22×D24412yes—
658C23C22×D24412yes—
659C23C22×D24411yescharacteristic
660Q8—1222no—
661Q8—1222no—
662Q8—2448no—
663Q8—2442no—
664D4—28no—
665D4—1222no—
666D4—1222no—
667D4—2448no—
668D4—2448no—
669D4—2442no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—2448no—
688C2×C4—2448no—
689C2×C4—2448no—
690C2×C4—2442no—
691C2×C4—2442no—
692C2×C4—2442no—
693C2×C4—2442no—
694C2×C4—2442no—
695C2×C4—2448no—
696C2×C4—2442no—
697C2×C4—2442no—
698C2×C4C22×D24412yes—
699C2×C4C22×D24412yes—
700C2×C4C22×D24412yes—
701C2×C4C22×D24412yes—
702C2×C4C22×D24411yescharacteristic
703C2×C4C2×#1175822412yes—
704C2×C4#1451982412yes—
705C2×C4C24×D6111yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8C2×#1175822414yescomplemented
710C22—22no—
711C22—28no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—4884no—
718C22—2442no—
719C22—2442no—
720C22—2442no—
721C22#1684041612yes—
722C22C2×#1451980514yes—
723C22C2×#1451980512yes—
724C22#1684057912yes—
725C22C23×D24411yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—2442no—
731C4—2442no—
732C4—2442no—
733C4—2442no—
734C4—2442no—
735C4—2442no—
736C4—2442no—
737C4#1684041612yes—
738C4C22×#1175822411yescharacteristic
739C4C2×#1451982411yescharacteristic
740C2—24no—
741C2—42no—
742C2—4882no—
743C2#2145826114yesdirect product factor
744C2C2×#1684041611yescharacteristic
745C2C22×#1451980511yescharacteristic
746C2C2×#1684057911yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#435C2
socleC23×C61C22×D4
prime radicalC2×#16840416C2
hypercenterC2×#435D61
hypocenterC61C2×#3343
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
1. C2×#16840452C2semidirect
3. #21458261C2direct (N × H)
4. C2×#16840171C2semidirect
5. C2×#16840098C2semidirect
6. C2×#16840087C2semidirect
7. C2×#16840093C2semidirect
8. C2×#16840076C2semidirect
9. C2×#16840058C2semidirect
10. C2×#16840063C2semidirect
11. C2×#16840008C2semidirect
12. C2×#16839991C2semidirect
13. C2×#16839864C2semidirect
14. C2×#16839804C2semidirect
15. C22×#14519711C2semidirect
16. C2×C61×#435C2semidirect
20. #16840452C22semidirect
42. #16840171C22semidirect
43. #16840098C22semidirect
44. #16840093C22semidirect
45. #16840087C22semidirect
46. #16840076C22semidirect
47. #16840063C22semidirect
48. #16840058C22semidirect
49. #16840008C22semidirect
50. #16839991C22semidirect
51. #16839864C22semidirect
52. #16839804C22semidirect
59. C2×#14519711C22semidirect
72. C61×#435C22semidirect
233. C2×C8×C61#41semidirect
335. C8×C61C2×#41semidirect
380. C2×#435D61semidirect
385. C2×C61#3343semidirect
428. #435C2×D61semidirect
450. C61C2×#3343semidirect
608. C2×C8#11758224semidirect
709. C8C2×#11758224semidirect
743. C2#21458261direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404522
C2×#168404162
#214582612
C2×#168401712
C2×#168400982
C2×#168400872
C2×#168400932
C2×#168400762
C2×#168400582
C2×#168400632
C2×#168400082
C2×#168399912
C2×#168398642
C2×#168398042
C22×#145197112
C2×C61×#4352
C2×#334361