Finite Group Databasebeta

← C2×#21458153 #30556954

Subgroups — C2×#21458153 #30556954

Order 15616.

2210 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840467C211yesmaximal, characteristic, complemented
2C2×#16840431C211yesmaximal, characteristic
3#21458153C2116yesmaximal, direct product factor
4C2×#16840107C211yesmaximal, characteristic, complemented
5C2×#16840075C211yesmaximal, characteristic, complemented
6C2×#16840074C211yesmaximal, characteristic, complemented
7C2×#16840055C211yesmaximal, characteristic, complemented
8C2×#16840008C211yesmaximal, characteristic, complemented
9C2×#16840007C211yesmaximal, characteristic, complemented
10C2×#16839961C211yesmaximal, characteristic, complemented
11C2×#16839927C211yesmaximal, characteristic, complemented
12C2×#16839924C211yesmaximal, characteristic, complemented
13C2×#16839854C211yesmaximal, characteristic, complemented
14C2×#16839838C211yesmaximal, characteristic, complemented
15C2×#16839762C211yesmaximal, characteristic, complemented
16C2×C61×#417C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758190C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×#11758189C2211yescharacteristic
22#16840467—24no—
23#16840467C2218yescomplemented
24#16840431—24no—
25#16840431C2218yes—
26C2×#14519776C2211yescharacteristic
27C2×#14519773—21no—
28C2×#14519773C2211yescharacteristic
29C2×#14519767—21no—
30C2×#14519757C2211yescharacteristic
31C2×#14519756—21no—
32C2×#14519756C2211yescharacteristic
33C2×#14519755—21no—
34C2×#14519751—21no—
35C2×#14519751C2211yescharacteristic
36C2×#14519748—21no—
37C2×#14519748C2211yescharacteristic
38C2×Q8×Dic61C2211yescharacteristic
39C2×#14519742C2211yescharacteristic
40C2×C4×C22⋊D61—21no—
41C2×C4×C22⋊D61—21no—
42C2×C4×C22⋊D61C2211yescharacteristic
43C2×C4⋊C4×D61C2211yescharacteristic
44#16840107C2218yescomplemented
45#16840075C2218yescomplemented
46#16840074C2218yescomplemented
47#16840055C2218yescomplemented
48#16840008C2218yescomplemented
49#16840007C2218yescomplemented
50#16839961C2218yescomplemented
51#16839927C2218yescomplemented
52#16839924C2218yescomplemented
53#16839854C2218yescomplemented
54#16839838C2218yescomplemented
55C2×#14519711C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519710C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59#16839762C2218yescomplemented
60C2×#14519702C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×#41×C61C2211yescharacteristic
70C22×M16×C61C2211yescharacteristic
71C22×C4⋊C4×C61C2211yescharacteristic
72C61×#417C2218yescomplemented
73C2×#103×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C2×#11758226—22no—
78C2×#11758226—24no—
79C2×#11758226—42no—
80C2×#11758226C2314yes—
81C22×Dic122—21no—
82C22×Dic122C2311yescharacteristic
83C22×D244—21no—
84C22×D244C2311yescharacteristic
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C22×C22⋊D61—21no—
88C22×C22⋊D61—21no—
89C22×C22⋊D61D411yescharacteristic
90C22×C4×D61—21no—
91C22×C4×D61—21no—
92C22×C4×D61C2311yescharacteristic
93C2×#11758202—24no—
94C2×#11758202C2314yes—
95C2×#11758190—42no—
96C2×#11758190C2314yes—
97C2×#11758200—42no—
98C2×#11758200C2314yes—
99C2×#11758189—42no—
100C2×#11758189C2314yes—
101C22×#92418C2311yescharacteristic
102C22×#92418C2311yescharacteristic
103#14519776—22no—
104#14519776C2314yes—
105#14519773—28no—
106#14519773—22no—
107#14519773C2314yes—
108#14519767—28no—
109#14519757—22no—
110#14519757C2314yes—
111#14519756—22no—
112#14519756—28no—
113#14519756C2314yes—
114#14519755—28no—
115#14519751—22no—
116#14519751—28no—
117#14519751C2314yes—
118#14519748—22no—
119#14519748—28no—
120#14519748C2314yes—
121Q8×Dic61—22no—
122Q8×Dic61C2314yes—
123#14519742—22no—
124#14519742C2314yes—
125C4×C22⋊D61—28no—
126C4×C22⋊D61—28no—
127C4×C22⋊D61D414yes—
128C4×C22⋊D61C2314yes—
129C2×C4⋊Dic61—21no—
130C2×C4⋊Dic61—21no—
131C2×C4⋊Dic61C2311yescharacteristic
132C2×C4⋊Dic61C2311yescharacteristic
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196D411yescharacteristic
138C4⋊C4×D61—22no—
139C4⋊C4×D61C2314yes—
140C2×C22⋊Dic61—21no—
141C2×C22⋊Dic61—21no—
142C2×C22⋊Dic61D411yescharacteristic
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198D411yescharacteristic
146C2×C4×Dic61—21no—
147C2×C4×Dic61—21no—
148C2×C4×Dic61C2311yescharacteristic
149#14519711C2314yes—
150#14519710C2314yes—
151#14519710C2314yes—
152#14519706C2314yes—
153#14519702C2314yes—
154#14519701C2314yes—
155#14519699C2314yes—
156#14519698C2314yes—
157#14519697C2314yes—
158#14519697C2314yes—
159C22⋊#92418C2314yes—
160#14519689C2314yes—
161C8×Dic61C2314yes—
162C2×#41×C61—22no—
163C2×#41×C61—24no—
164C2×#41×C61—42no—
165C2×#41×C61C2314yes—
166C22×Q8×C61C2311yescharacteristic
167C22×D4×C61—21no—
168C22×D4×C61C2311yescharacteristic
169C23×C4×C61—21no—
170C23×C4×C61—21no—
171C23×C4×C61C2311yescharacteristic
172C2×M16×C61—42no—
173C2×M16×C61C2314yes—
174C22×C8×C61C2311yescharacteristic
175C22×C8×C61C2311yescharacteristic
176C2×C4⋊C4×C61—22no—
177C2×C4⋊C4×C61—21no—
178C2×C4⋊C4×C61C2311yescharacteristic
179C2×C4⋊C4×C61C2314yes—
180C2×C4⋊C4×C61C2311yescharacteristic
181#103×C61C2314yes—
182#103×C61C2314yes—
183#102×C61C2314yes—
184#102×C61C2314yes—
185C24×C61—21no—
186C24×C61C2×D411yescharacteristic
187C23×D61—21no—
188C23×D61C2×D411yescharacteristic
189#41×C61—28no—
190#41×C61—44no—
191#41×C61—48no—
192C2×Q8×C61—21no—
193C2×Q8×C61—22no—
194C2×Q8×C61#4114yes—
195C2×Q8×C61C2412yes—
196C2×D4×C61—24no—
197C2×D4×C61—21no—
198C2×D4×C61—22no—
199C2×D4×C61—22no—
200C2×D4×C61—44no—
201C2×D4×C61C2412yes—
202C22×C4×C61—21no—
203C22×C4×C61—22no—
204C22×C4×C61—22no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—24no—
208C22×C4×C61—24no—
209C22×C4×C61—44no—
210C22×C4×C61—82no—
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D412yes—
213C22×C4×C61C2412yes—
214C22×C4×C61C2411yescharacteristic
215C2×C22⋊D61—24no—
216C2×C22⋊D61—24no—
217C2×C22⋊D61—24no—
218C2×C22⋊D61—24no—
219C2×C22⋊D61—24no—
220C2×C22⋊D61—44no—
221C2×C22⋊D61—82no—
222C2×C22⋊D61—82no—
223C2×C22⋊D61—82no—
224C2×C22⋊D61C2×D414yes—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61C2×D411yescharacteristic
229C22×Dic61C2×D411yescharacteristic
230C22×Dic61C2×D411yescharacteristic
231#11758226—28no—
232#11758226—44no—
233#11758226—48no—
234C2×D244—22no—
235C2×D244—22no—
236C2×D244—24no—
237C2×D244—21no—
238C2×D244—44no—
239C2×D244C2412yes—
240C2×C4×D61—22no—
241C2×C4×D61—22no—
242C2×C4×D61—24no—
243C2×C4×D61—24no—
244C2×C4×D61—44no—
245C2×C4×D61—82no—
246C2×C4×D61C2×D412yes—
247C2×C4×D61C2412yes—
248C2×Dic122—22no—
249C2×Dic122—22no—
250C2×Dic122—21no—
251C2×Dic122—24no—
252C2×Dic122—82no—
253C2×Dic122C2412yes—
254M16×C61—44no—
255C2×C8×C61—22no—
256C2×C8×C61—22no—
257C2×C8×C61C2412yes—
258C2×C8×C61C2412yes—
259C4⋊C4×C61—21no—
260C4⋊C4×C61—24no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61C2412yes—
263C4⋊C4×C61C2412yes—
264C22⋊Dic61—24no—
265C22⋊Dic61—24no—
266C22⋊Dic61C2×D414yes—
267#11758202—28no—
268#11758200—44no—
269#11758198—24no—
270#11758198—24no—
271#11758198C2×D414yes—
272C4⋊Dic61—21no—
273C4⋊Dic61—21no—
274C4⋊Dic61—24no—
275C4⋊Dic61—24no—
276C4⋊Dic61C2412yes—
277C4⋊Dic61C2412yes—
278#11758196—24no—
279#11758196—24no—
280#11758196—24no—
281#11758196—24no—
282#11758196C2×D414yes—
283C4×Dic61—24no—
284C4×Dic61—24no—
285C4×Dic61C2×D412yes—
286C4×Dic61C2412yes—
287C2×#92418—22no—
288C2×#92418—22no—
289C2×#92418C2412yes—
290C2×#92418C2412yes—
291#11758190—44no—
292#11758189—44no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—42no—
298C23×C61—42no—
299C23×C61—42no—
300C23×C61C22×D412yes—
301C23×C61C22×D411yescharacteristic
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—22no—
305C22×D61—22no—
306C22×D61—42no—
307C22×D61—42no—
308C22×D61—42no—
309C22×D61C22×D412yes—
310Q8×C61—24no—
311Q8×C61—22no—
312Q8×C61C2×#4114yes—
313D4×C61—22no—
314D4×C61—22no—
315D4×C61—48no—
316D4×C61—42no—
317C2×C4×C61—24no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—24no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—48no—
326C2×C4×C61—42no—
327C2×C4×C61—42no—
328C2×C4×C61—84no—
329C2×C4×C61C22×D412yes—
330C2×C4×C61C22×D411yescharacteristic
331C2×C4×C61C2×#4112yes—
332C2×C4×C61H(5,𝔽2)12yes—
333C2×C4×C61C2511yescharacteristic
334C22⋊D61—28no—
335C22⋊D61—48no—
336C22⋊D61—84no—
337C22⋊D61—84no—
338C22⋊D61—84no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—42no—
345C2×Dic61—42no—
346C2×Dic61—42no—
347C2×Dic61#13714yes—
348C2×Dic61C22×D412yes—
349C2×Dic61C22×D412yes—
350C2×Dic61C22×D412yes—
351D244—22no—
352D244—22no—
353D244—48no—
354D244—42no—
355C4×D61—24no—
356C4×D61—22no—
357C4×D61—22no—
358C4×D61—48no—
359C4×D61—84no—
360Dic122—22no—
361Dic122—22no—
362Dic122—42no—
363Dic122—84no—
364C8×C61—22no—
365C8×C61—22no—
366#92418—22no—
367#92418—22no—
368C2×#3333—611nomaximal, Sylow
369C22×C61—22no—
370C22×C61—22no—
371C22×C61—22no—
372C22×C61—44no—
373C22×C61—42no—
374C22×C61—42no—
375C22×C61—42no—
376C22×C61—84no—
377C22×C61#54612yes—
378C22×C61C2×#13712yes—
379C22×C61#57612yes—
380C22×C61C23×D411yescharacteristic
381C2×D61—22no—
382C2×D61—22no—
383C2×D61—22no—
384C2×D61—44no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—84no—
389C4×C61—24no—
390C4×C61—22no—
391C4×C61—42no—
392C4×C61—42no—
393C4×C61#54612yes—
394C4×C61C22×#4111yescharacteristic
395C4×C61C2×H(5,𝔽2)11yescharacteristic
396Dic61—22no—
397Dic61—22no—
398Dic61—42no—
399Dic61—42no—
400Dic61—42no—
401Dic61C2×#13714yes—
402C2×#554—611no—
403C2×#550—611no—
404#3333—6116no—
405C2×#486—611no—
406C2×#480—611no—
407C2×#480—611no—
408C2×#477—611no—
409C2×#468—611no—
410C2×#468—611no—
411C2×#460—611no—
412C2×#452—611no—
413C2×#452—611no—
414C2×C4×Q16—611no—
415C2×#436—611no—
416C2×#417—611no—
417C2×#417D6111yescharacteristic, complemented
418C2×C61—42no—
419C2×C61—82no—
420C2×C61#333314yescomplemented
421C2×C61C2×#54611yescharacteristic
422C2×C61C22×#13711yescharacteristic
423C2×C61C2×#57611yescharacteristic
424D61—42no—
425D61—82no—
426C22×#41—611no—
427C22×#41C2×D6111yescharacteristic
428C22×Q16—611no—
429C22×SD16—611no—
430C22×SD16—611no—
431C22×M16—611no—
432C22×M16C2×D6111yescharacteristic
433#554—618no—
434#554—1224no—
435#550—618no—
436#550—1224no—
437C2×C4⋊Q8—611no—
438C2×#127—611no—
439C2×#127—1221no—
440C2×#125—1221no—
441C2×C22⋊Q8—611no—
442C2×C22⋊Q8—611no—
443C2×C22⋊Q8—1221no—
444C2×C22⋊Q8—1221no—
445C2×#121—611no—
446C2×#121—611no—
447C2×#121—1221no—
448C2×#121—1221no—
449C2×C4×Q8—611no—
450C2×C4×Q8—611no—
451C2×C4×D4—611no—
452C2×C4×D4—1221no—
453C2×C4×D4—1221no—
454C22×C4⋊C4—611no—
455C22×C4⋊C4C2×D6111yescharacteristic
456#486—618no—
457#480—618no—
458#480—618no—
459#477—618no—
460#468—618no—
461#468—618no—
462#460—618no—
463#452—618no—
464#452—618no—
465C4×Q16—618no—
466#436—618no—
467C2×#107—611no—
468C2×#107—611no—
469C2×#107—611no—
470C2×C4⋊C8—611no—
471#417—618no—
472#417C2×D6118yescomplemented
473C2×#103—611no—
474C2×#103—611no—
475C2×#103C2×D6111yescharacteristic
476C2×#103C2×D6111yescharacteristic
477C2×#102—611no—
478C2×#102—611no—
479C2×#102—611no—
480C2×#102—611no—
481C2×#102C2×D6111yescharacteristic
482C2×#102C2×D6111yescharacteristic
483C2×C22⋊C8—611no—
484C2×C22⋊C8—611no—
485C2×C4×C8—611no—
486C61C2×#333311yescharacteristic, complemented, Sylow
487C2×#41—22no—
488C2×#41—24no—
489C2×#41—42no—
490C2×#41—614no—
491C2×#41—1222no—
492C2×#41—1224no—
493C2×#41—2442no—
494C2×#41C22×D6114yes—
495C22×Q8—611no—
496C22×Q8—1221no—
497C22×Q8C22×D6111yescharacteristic
498C22×D4—21no—
499C22×D4—611no—
500C22×D4—611no—
501C22×D4—1221no—
502C22×D4—1221no—
503C22×D4—1221no—
504C22×D4—1221no—
505C22×D4—1221no—
506C22×D4C22×D6111yescharacteristic
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—611no—
510C23×C4—1221no—
511C23×C4—1221no—
512C23×C4C22×D6111yescharacteristic
513C2×Q16—614no—
514C2×Q16—1224no—
515C2×SD16—614no—
516C2×SD16—614no—
517C2×SD16—2442no—
518C2×SD16—2442no—
519C2×M16—42no—
520C2×M16—614no—
521C2×M16—2442no—
522C2×M16C22×D6114yes—
523C22×C8—611no—
524C22×C8—611no—
525C22×C8C22×D6111yescharacteristic
526C22×C8C22×D6111yescharacteristic
527C4⋊Q8—614no—
528C4⋊Q8—1222no—
529#127—614no—
530#127—1222no—
531#127—1228no—
532#125—1228no—
533C22⋊Q8—614no—
534C22⋊Q8—614no—
535C22⋊Q8—1228no—
536C22⋊Q8—1228no—
537C22⋊Q8—1222no—
538C22⋊Q8—1222no—
539#121—614no—
540#121—614no—
541#121—1228no—
542#121—1228no—
543#121—1222no—
544#121—1222no—
545C4×Q8—614no—
546C4×Q8—614no—
547C4×Q8—1222no—
548C4×Q8—1222no—
549C4×D4—614no—
550C4×D4—614no—
551C4×D4—1228no—
552C4×D4—1228no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—611no—
556C2×C4⋊C4—611no—
557C2×C4⋊C4—611no—
558C2×C4⋊C4—614no—
559C2×C4⋊C4—1222no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4—1221no—
562C2×C4⋊C4—1221no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4C22×D6111yescharacteristic
567C2×C4⋊C4C22×D6111yescharacteristic
568C2×C4⋊C4C22×D6114yes—
569C2×C22⋊C4—611no—
570C2×C22⋊C4—611no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C42—611no—
576C2×C42—1221no—
577C2×C42—1221no—
578#107—614no—
579#107—614no—
580#107—614no—
581C4⋊C8—614no—
582#103—614no—
583#103—614no—
584#103C22×D6114yes—
585#103C22×D6114yes—
586#102—614no—
587#102—614no—
588#102—614no—
589#102—614no—
590#102C22×D6114yes—
591#102C22×D6114yes—
592C22⋊C8—614no—
593C22⋊C8—614no—
594C4×C8—614no—
595C24—21no—
596C24—611no—
597C24—1221no—
598C24D4×D6111yescharacteristic
599#41—28no—
600#41—44no—
601#41—48no—
602#41—1228no—
603#41—2444no—
604#41—2448no—
605C2×Q8—21no—
606C2×Q8—22no—
607C2×Q8—612no—
608C2×Q8—1224no—
609C2×Q8—1221no—
610C2×Q8—1222no—
611C2×Q8—1222no—
612C2×Q8—4882no—
613C2×Q8#1175822214yes—
614C2×Q8C23×D6112yes—
615C2×D4—24no—
616C2×D4—21no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—44no—
620C2×D4—614no—
621C2×D4—612no—
622C2×D4—1224no—
623C2×D4—1224no—
624C2×D4—1224no—
625C2×D4—1224no—
626C2×D4—1224no—
627C2×D4—1224no—
628C2×D4—1221no—
629C2×D4—1222no—
630C2×D4—1222no—
631C2×D4—4882no—
632C2×D4—4882no—
633C2×D4—4882no—
634C2×D4—2444no—
635C2×D4—2444no—
636C2×D4C23×D6112yes—
637C22×C4—21no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—44no—
645C22×C4—82no—
646C22×C4—611no—
647C22×C4—611no—
648C22×C4—611no—
649C22×C4—612no—
650C22×C4—612no—
651C22×C4—1224no—
652C22×C4—1224no—
653C22×C4—1222no—
654C22×C4—1222no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—4882no—
659C22×C4—2444no—
660C22×C4D4×D6112yes—
661C22×C4D4×D6111yescharacteristic
662C22×C4C23×D6112yes—
663C22×C4C23×D6111yescharacteristic
664Q16—1228no—
665SD16—2444no—
666SD16—2444no—
667M16—44no—
668M16—2444no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—612no—
672C2×C8—612no—
673C2×C8—1222no—
674C2×C8—1222no—
675C2×C8C23×D6112yes—
676C2×C8C23×D6112yes—
677C4⋊C4—21no—
678C4⋊C4—24no—
679C4⋊C4—21no—
680C4⋊C4—614no—
681C4⋊C4—612no—
682C4⋊C4—612no—
683C4⋊C4—1224no—
684C4⋊C4—1224no—
685C4⋊C4—1224no—
686C4⋊C4—1224no—
687C4⋊C4—1224no—
688C4⋊C4—1221no—
689C4⋊C4—1221no—
690C4⋊C4—1224no—
691C4⋊C4C23×D6112yes—
692C4⋊C4C23×D6112yes—
693C22⋊C4—614no—
694C22⋊C4—614no—
695C22⋊C4—1224no—
696C22⋊C4—1224no—
697C22⋊C4—1224no—
698C22⋊C4—1224no—
699C42—612no—
700C42—612no—
701C42—1224no—
702C42—1224no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—612no—
711C23—1222no—
712C23—1222no—
713C23—1222no—
714C23—1222no—
715C23—2442no—
716C23—2442no—
717C23—2442no—
718C23C2×D4×D6112yes—
719C23C2×D4×D6111yescharacteristic
720Q8—22no—
721Q8—24no—
722Q8—1222no—
723Q8—1222no—
724Q8—4884no—
725Q8—2442no—
726Q8C2×#1175822214yes—
727D4—22no—
728D4—22no—
729D4—48no—
730D4—42no—
731D4—1228no—
732D4—1222no—
733D4—1222no—
734D4—4884no—
735D4—4884no—
736D4—4884no—
737D4—2448no—
738D4—2448no—
739D4—2442no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—48no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—84no—
752C2×C4—614no—
753C2×C4—612no—
754C2×C4—612no—
755C2×C4—612no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1224no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—4884no—
765C2×C4—2448no—
766C2×C4—2442no—
767C2×C4—2442no—
768C2×C4—2442no—
769C2×C4C2×D4×D6112yes—
770C2×C4C2×D4×D6111yescharacteristic
771C2×C4C2×#1175822212yes—
772C2×C4#1451982212yes—
773C2×C4C24×D6111yescharacteristic
774C8—22no—
775C8—22no—
776C8—1222no—
777C8—1222no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—44no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—84no—
786C22—1222no—
787C22—1222no—
788C22—1222no—
789C22—4884no—
790C22—2442no—
791C22—2442no—
792C22—2442no—
793C22—2444no—
794C22#1684040212yes—
795C22#137×D6112yes—
796C22#1684056612yes—
797C22C22×D4×D6111yescharacteristic
798C4—22no—
799C4—24no—
800C4—42no—
801C4—42no—
802C4—614no—
803C4—1222no—
804C4—1222no—
805C4—2442no—
806C4—2442no—
807C4—2442no—
808C4#1684040212yes—
809C4C22×#1175822211yescharacteristic
810C4C2×#1451982211yescharacteristic
811C2—42no—
812C2—82no—
813C2—4882no—
814C2—2442no—
815C2#2145815314yesdirect product factor
816C2C2×#1684040211yescharacteristic
817C2C2×#137×D6111yescharacteristic
818C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#417C2
socleC23×C61C22×D4
prime radicalC2×#16840431C2
hypercenterC2×#417D61
hypocenterC61C2×#3333
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#16840467C2semidirect
3. #21458153C2direct (N × H)
4. C2×#16840107C2semidirect
5. C2×#16840075C2semidirect
6. C2×#16840074C2semidirect
7. C2×#16840055C2semidirect
8. C2×#16840008C2semidirect
9. C2×#16840007C2semidirect
10. C2×#16839961C2semidirect
11. C2×#16839927C2semidirect
12. C2×#16839924C2semidirect
13. C2×#16839854C2semidirect
14. C2×#16839838C2semidirect
15. C2×#16839762C2semidirect
16. C2×C61×#417C2semidirect
23. #16840467C22semidirect
44. #16840107C22semidirect
45. #16840075C22semidirect
46. #16840074C22semidirect
47. #16840055C22semidirect
48. #16840008C22semidirect
49. #16840007C22semidirect
50. #16839961C22semidirect
51. #16839927C22semidirect
52. #16839924C22semidirect
53. #16839854C22semidirect
54. #16839838C22semidirect
59. #16839762C22semidirect
72. C61×#417C22semidirect
417. C2×#417D61semidirect
420. C2×C61#3333semidirect
472. #417C2×D61semidirect
486. C61C2×#3333semidirect
815. C2#21458153direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404672
C2×#168404312
#214581532
C2×#168401072
C2×#168400752
C2×#168400742
C2×#168400552
C2×#168400082
C2×#168400072
C2×#168399612
C2×#168399272
C2×#168399242
C2×#168398542
C2×#168398382
C2×#168397622
C2×C61×#4172
C2×#333361