Finite Group Databasebeta

← C2×#21457941 #30556727

Subgroups — C2×#21457941 #30556727

Order 15616.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840451C211yesmaximal, characteristic, complemented
2C2×#16840431C211yesmaximal, characteristic
3#21457941C2116yesmaximal, direct product factor
4C2×#16840125C211yesmaximal, characteristic, complemented
5C2×#16840079C211yesmaximal, characteristic, complemented
6C2×#16840086C211yesmaximal, characteristic, complemented
7C2×#16840067C211yesmaximal, characteristic, complemented
8C2×#16840007C211yesmaximal, characteristic, complemented
9C2×#16839991C211yesmaximal, characteristic, complemented
10C2×#16839961C211yesmaximal, characteristic, complemented
11C2×#16839927C211yesmaximal, characteristic, complemented
12C2×#16839924C211yesmaximal, characteristic, complemented
13C2×#16839866C211yesmaximal, characteristic, complemented
14C2×#16839833C211yesmaximal, characteristic, complemented
15C2×#16839762C211yesmaximal, characteristic, complemented
16C2×C61×#416C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758190C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×#11758189C2211yescharacteristic
22#16840451—24no—
23#16840451C2218yescomplemented
24#16840431—24no—
25#16840431C2218yes—
26C2×#14519773—21no—
27C2×#14519773C2211yescharacteristic
28C2×#14519770—21no—
29C2×#14519769—21no—
30C2×#14519768C2211yescharacteristic
31C2×#14519759—21no—
32C2×#14519757C2211yescharacteristic
33C2×#14519756C2211yescharacteristic
34C2×#14519751—21no—
35C2×#14519751C2211yescharacteristic
36C2×#14519748—21no—
37C2×#14519748C2211yescharacteristic
38C2×Q8×Dic61C2211yescharacteristic
39C2×#14519742C2211yescharacteristic
40C2×C4×C22⋊D61—21no—
41C2×C4×C22⋊D61C2211yescharacteristic
42C2×#14519734—21no—
43C2×C4⋊C4×D61C2211yescharacteristic
44#16840125C2218yescomplemented
45#16840086C2218yescomplemented
46#16840079C2218yescomplemented
47#16840067C2218yescomplemented
48#16840007C2218yescomplemented
49#16839991C2218yescomplemented
50#16839961C2218yescomplemented
51#16839927C2218yescomplemented
52#16839924C2218yescomplemented
53#16839866C2218yescomplemented
54#16839833C2218yescomplemented
55C2×#14519710C2211yescharacteristic
56C2×#14519709C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59#16839762C2218yescomplemented
60C2×#14519702C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519687C2211yescharacteristic
69C22×#41×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic
71C2×#117×C61C2211yescharacteristic
72C61×#416C2218yescomplemented
73C2×#103×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C2×#11758226—22no—
78C2×#11758226—24no—
79C2×#11758226—42no—
80C2×#11758226C2314yes—
81C22×Dic122C2311yescharacteristic
82C22×D244—21no—
83C22×D244C2311yescharacteristic
84C22×C22⋊D61—21no—
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C22×C22⋊D61—21no—
88C22×C22⋊D61D411yescharacteristic
89C22×C4×D61—21no—
90C22×C4×D61—21no—
91C22×C4×D61C2311yescharacteristic
92C2×#11758202—24no—
93C2×#11758202C2314yes—
94C2×#11758190—42no—
95C2×#11758190C2314yes—
96C2×#11758200—42no—
97C2×#11758200C2314yes—
98C2×#11758189—42no—
99C2×#11758189C2314yes—
100C22×#92418C2311yescharacteristic
101C22×#92418C2311yescharacteristic
102#14519773—28no—
103#14519773—22no—
104#14519773C2314yes—
105#14519770—28no—
106#14519769—28no—
107#14519768—22no—
108#14519768C2314yes—
109#14519759—28no—
110#14519757—22no—
111#14519757C2314yes—
112#14519756—22no—
113#14519756C2314yes—
114#14519751—22no—
115#14519751—28no—
116#14519751C2314yes—
117#14519748—22no—
118#14519748—28no—
119#14519748C2314yes—
120Q8×Dic61—22no—
121Q8×Dic61C2314yes—
122#14519742—22no—
123#14519742C2314yes—
124C4×C22⋊D61—28no—
125C4×C22⋊D61D414yes—
126C4×C22⋊D61C2314yes—
127#14519734—28no—
128C2×C4⋊Dic61—21no—
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#14519710C2314yes—
150#14519709C2314yes—
151#14519708C2314yes—
152#14519706C2314yes—
153#14519702C2314yes—
154#14519701C2314yes—
155#14519699C2314yes—
156#14519698C2314yes—
157#14519697C2314yes—
158#14519697C2314yes—
159C22⋊#92418C2314yes—
160#14519689C2314yes—
161#14519687C2314yes—
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×C61C2311yescharacteristic
171C22×C8×C61—42no—
172C22×C8×C61C2311yescharacteristic
173C22×C8×C61C2311yescharacteristic
174C22×C8×C61C2314yes—
175#117×C61—22no—
176#117×C61C2314yes—
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C4⋊C4×C61C2311yescharacteristic
179C2×C22⋊C4×C61—21no—
180C2×C42×C61—21no—
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—44no—
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D412yes—
211C22×C4×C61C2412yes—
212C22×C4×C61C2411yescharacteristic
213C2×C22⋊D61—24no—
214C2×C22⋊D61—24no—
215C2×C22⋊D61—24no—
216C2×C22⋊D61—24no—
217C2×C22⋊D61—42no—
218C2×C22⋊D61—44no—
219C2×C22⋊D61—82no—
220C2×C22⋊D61—82no—
221C2×C22⋊D61—82no—
222C2×C22⋊D61C2×D414yes—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229#11758226—28no—
230#11758226—44no—
231#11758226—48no—
232C2×D244—22no—
233C2×D244—22no—
234C2×D244—24no—
235C2×D244—21no—
236C2×D244—44no—
237C2×D244C2412yes—
238C2×C4×D61—22no—
239C2×C4×D61—22no—
240C2×C4×D61—24no—
241C2×C4×D61—24no—
242C2×C4×D61—44no—
243C2×C4×D61—44no—
244C2×C4×D61C2×D412yes—
245C2×C4×D61C2412yes—
246C2×Dic122—22no—
247C2×Dic122—22no—
248C2×Dic122—21no—
249C2×Dic122C2412yes—
250C2×C8×C61—22no—
251C2×C8×C61—22no—
252C2×C8×C61—44no—
253C2×C8×C61C2412yes—
254C2×C8×C61C2412yes—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61C2412yes—
258C4⋊C4×C61C2412yes—
259C22⋊C4×C61—24no—
260C42×C61—24no—
261C22⋊Dic61—24no—
262C22⋊Dic61—24no—
263C22⋊Dic61C2×D414yes—
264#11758202—28no—
265#11758200—44no—
266#11758198—24no—
267#11758198—24no—
268#11758198C2×D414yes—
269C4⋊Dic61—21no—
270C4⋊Dic61—21no—
271C4⋊Dic61—24no—
272C4⋊Dic61—24no—
273C4⋊Dic61—24no—
274C4⋊Dic61C2412yes—
275C4⋊Dic61C2412yes—
276#11758196—24no—
277#11758196—24no—
278#11758196—24no—
279#11758196—24no—
280#11758196C2×D414yes—
281C4×Dic61—24no—
282C4×Dic61—24no—
283C4×Dic61C2×D412yes—
284C4×Dic61C2412yes—
285C2×#92418—22no—
286C2×#92418—22no—
287C2×#92418C2412yes—
288C2×#92418C2412yes—
289#11758190—44no—
290#11758189—44no—
291C23×C61—22no—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—42no—
296C23×C61—42no—
297C23×C61—42no—
298C23×C61C22×D412yes—
299C23×C61C22×D411yescharacteristic
300C22×D61—22no—
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—42no—
305C22×D61—42no—
306C22×D61—42no—
307C22×D61C22×D412yes—
308Q8×C61—24no—
309Q8×C61—22no—
310Q8×C61C2×#4114yes—
311D4×C61—22no—
312D4×C61—22no—
313D4×C61—48no—
314D4×C61—42no—
315C2×C4×C61—24no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—24no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—48no—
324C2×C4×C61—42no—
325C2×C4×C61—42no—
326C2×C4×C61C22×D412yes—
327C2×C4×C61C22×D411yescharacteristic
328C2×C4×C61C2×#4112yes—
329C2×C4×C61H(5,𝔽2)12yes—
330C2×C4×C61C2511yescharacteristic
331C22⋊D61—44no—
332C22⋊D61—48no—
333C22⋊D61—84no—
334C22⋊D61—84no—
335C22⋊D61—84no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344C2×Dic61—42no—
345C2×Dic61C22×D412yes—
346C2×Dic61C22×D412yes—
347C2×Dic61C22×D412yes—
348D244—22no—
349D244—22no—
350D244—48no—
351D244—42no—
352C4×D61—24no—
353C4×D61—22no—
354C4×D61—22no—
355C4×D61—48no—
356C4×D61—48no—
357Dic122—22no—
358Dic122—22no—
359Dic122—42no—
360C8×C61—22no—
361C8×C61—22no—
362#92418—22no—
363#92418—22no—
364C2×#3317—611nomaximal, Sylow
365C22×C61—22no—
366C22×C61—22no—
367C22×C61—22no—
368C22×C61—44no—
369C22×C61—42no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—84no—
373C22×C61#54612yes—
374C22×C61#57512yes—
375C22×C61#57712yes—
376C22×C61C23×D411yescharacteristic
377C2×D61—22no—
378C2×D61—22no—
379C2×D61—22no—
380C2×D61—44no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—84no—
385C4×C61—24no—
386C4×C61—22no—
387C4×C61—42no—
388C4×C61—42no—
389C4×C61#54612yes—
390C4×C61C22×#4111yescharacteristic
391C4×C61C2×H(5,𝔽2)11yescharacteristic
392Dic61—22no—
393Dic61—22no—
394Dic61—22no—
395Dic61—42no—
396Dic61—42no—
397Dic61—42no—
398C2×#552—611no—
399C2×#550—611no—
400#3317—6116no—
401C2×#490—611no—
402C2×#481—611no—
403C2×#482—611no—
404C2×#479—611no—
405C2×#468—611no—
406C2×#465—611no—
407C2×#460—611no—
408C2×#452—611no—
409C2×#452—611no—
410C2×#441—611no—
411C2×#435—611no—
412C2×#417—611no—
413C2×#416D6111yescharacteristic, complemented
414C2×C61—42no—
415C2×C61—82no—
416C2×C61#331714yescomplemented
417C2×C61C2×#54611yescharacteristic
418C2×C61C2×#57511yescharacteristic
419C2×C61C2×#57711yescharacteristic
420D61—42no—
421D61—82no—
422C22×#41—611no—
423C22×#41C2×D6111yescharacteristic
424C22×Q16—611no—
425C22×SD16—611no—
426C22×SD16—611no—
427C22×M16—611no—
428C23×C8C2×D6111yescharacteristic
429#552—618no—
430#552—1224no—
431#550—618no—
432#550—1224no—
433C2×#127—611no—
434C2×#127—1221no—
435C2×#126—1221no—
436C2×#125—611no—
437C2×#125—1221no—
438C2×#123—1221no—
439C2×C22⋊Q8—611no—
440C2×C22⋊Q8—611no—
441C2×#121—611no—
442C2×#121—611no—
443C2×#121—1221no—
444C2×#121—1221no—
445C2×C4×Q8—611no—
446C2×C4×Q8—611no—
447C2×C4×D4—611no—
448C2×C4×D4—1221no—
449C2×#117—1221no—
450C2×#117C2×D6111yescharacteristic
451C22×C4⋊C4—611no—
452#490—618no—
453#482—618no—
454#481—618no—
455#479—618no—
456#468—618no—
457#465—618no—
458#460—618no—
459#452—618no—
460#452—618no—
461#441—618no—
462#435—618no—
463C2×#107—611no—
464C2×#106—611no—
465C2×#106—611no—
466C2×C4⋊C8—611no—
467#417—618no—
468#416C2×D6118yescomplemented
469C2×#103—611no—
470C2×#103—611no—
471C2×#103C2×D6111yescharacteristic
472C2×#103C2×D6111yescharacteristic
473C2×#102—611no—
474C2×#102—611no—
475C2×#102—611no—
476C2×#102—611no—
477C2×#102C2×D6111yescharacteristic
478C2×#102C2×D6111yescharacteristic
479C2×C22⋊C8—611no—
480C2×C22⋊C8—611no—
481C2×#97—611no—
482C61C2×#331711yescharacteristic, complemented, Sylow
483C2×#41—22no—
484C2×#41—24no—
485C2×#41—42no—
486C2×#41—614no—
487C2×#41—1222no—
488C2×#41—1224no—
489C2×#41—2442no—
490C2×#41C22×D6114yes—
491C22×Q8—611no—
492C22×Q8C22×D6111yescharacteristic
493C22×D4—21no—
494C22×D4—611no—
495C22×D4—611no—
496C22×D4—1221no—
497C22×D4—1221no—
498C22×D4—1221no—
499C22×D4—1221no—
500C22×D4—1221no—
501C22×D4C22×D6111yescharacteristic
502C23×C4—21no—
503C23×C4—611no—
504C23×C4—1221no—
505C23×C4—1221no—
506C23×C4C22×D6111yescharacteristic
507C2×Q16—614no—
508C2×Q16—1224no—
509C2×SD16—614no—
510C2×SD16—614no—
511C2×SD16—2442no—
512C2×SD16—2442no—
513C2×M16—614no—
514C2×M16—2442no—
515C22×C8—42no—
516C22×C8—611no—
517C22×C8—611no—
518C22×C8C22×D6111yescharacteristic
519C22×C8C22×D6111yescharacteristic
520C22×C8C22×D6114yes—
521#127—614no—
522#127—1222no—
523#127—1228no—
524#126—1228no—
525#125—614no—
526#125—1228no—
527#125—1222no—
528#123—1228no—
529C22⋊Q8—614no—
530C22⋊Q8—614no—
531C22⋊Q8—1222no—
532C22⋊Q8—1222no—
533#121—614no—
534#121—614no—
535#121—1228no—
536#121—1228no—
537#121—1222no—
538#121—1222no—
539C4×Q8—614no—
540C4×Q8—614no—
541C4×Q8—1222no—
542C4×Q8—1222no—
543C4×D4—614no—
544C4×D4—614no—
545C4×D4—1228no—
546#117—22no—
547#117—1228no—
548#117C22×D6114yes—
549C2×C4⋊C4—611no—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—614no—
553C2×C4⋊C4—1222no—
554C2×C4⋊C4—1221no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4—1221no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4C22×D6111yescharacteristic
562C2×C4⋊C4C22×D6111yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—611no—
565C2×C22⋊C4—611no—
566C2×C22⋊C4—1221no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C42—21no—
571C2×C42—611no—
572C2×C42—1221no—
573C2×C42—1221no—
574#107—614no—
575#106—614no—
576#106—614no—
577C4⋊C8—614no—
578#103—614no—
579#103—614no—
580#103C22×D6114yes—
581#103C22×D6114yes—
582#102—614no—
583#102—614no—
584#102—614no—
585#102—614no—
586#102C22×D6114yes—
587#102C22×D6114yes—
588C22⋊C8—614no—
589C22⋊C8—614no—
590#97—614no—
591C24—21no—
592C24—611no—
593C24—1221no—
594C24D4×D6111yescharacteristic
595#41—28no—
596#41—44no—
597#41—48no—
598#41—1228no—
599#41—2444no—
600#41—2448no—
601C2×Q8—21no—
602C2×Q8—22no—
603C2×Q8—612no—
604C2×Q8—1221no—
605C2×Q8—1222no—
606C2×Q8—1222no—
607C2×Q8#1175822214yes—
608C2×Q8C23×D6112yes—
609C2×D4—24no—
610C2×D4—21no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—44no—
614C2×D4—614no—
615C2×D4—612no—
616C2×D4—1224no—
617C2×D4—1224no—
618C2×D4—1224no—
619C2×D4—1224no—
620C2×D4—1224no—
621C2×D4—1221no—
622C2×D4—1222no—
623C2×D4—1222no—
624C2×D4—4882no—
625C2×D4—4882no—
626C2×D4—4882no—
627C2×D4—2444no—
628C2×D4—2442no—
629C2×D4—2444no—
630C2×D4C23×D6112yes—
631C22×C4—21no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—24no—
637C22×C4—44no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—611no—
641C22×C4—612no—
642C22×C4—612no—
643C22×C4—1224no—
644C22×C4—1224no—
645C22×C4—1222no—
646C22×C4—1222no—
647C22×C4—1221no—
648C22×C4—1221no—
649C22×C4—1221no—
650C22×C4—2444no—
651C22×C4—2444no—
652C22×C4D4×D6112yes—
653C22×C4D4×D6111yescharacteristic
654C22×C4C23×D6112yes—
655C22×C4C23×D6111yescharacteristic
656Q16—1228no—
657SD16—2444no—
658SD16—2444no—
659M16—2444no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—44no—
663C2×C8—612no—
664C2×C8—612no—
665C2×C8—1222no—
666C2×C8—1222no—
667C2×C8C23×D6112yes—
668C2×C8C23×D6112yes—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—614no—
672C4⋊C4—612no—
673C4⋊C4—612no—
674C4⋊C4—1224no—
675C4⋊C4—1224no—
676C4⋊C4—1224no—
677C4⋊C4—1224no—
678C4⋊C4—1224no—
679C4⋊C4—1224no—
680C4⋊C4—1221no—
681C4⋊C4—1221no—
682C4⋊C4—1224no—
683C4⋊C4C23×D6112yes—
684C4⋊C4C23×D6112yes—
685C22⋊C4—24no—
686C22⋊C4—614no—
687C22⋊C4—614no—
688C22⋊C4—1224no—
689C22⋊C4—1224no—
690C22⋊C4—1224no—
691C22⋊C4—1224no—
692C42—24no—
693C42—612no—
694C42—612no—
695C42—1224no—
696C42—1224no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—612no—
705C23—1222no—
706C23—1222no—
707C23—1222no—
708C23—1222no—
709C23—2442no—
710C23—2442no—
711C23—2442no—
712C23C2×D4×D6112yes—
713C23C2×D4×D6111yescharacteristic
714Q8—22no—
715Q8—24no—
716Q8—1222no—
717Q8—1222no—
718Q8—2442no—
719Q8C2×#1175822214yes—
720D4—22no—
721D4—22no—
722D4—48no—
723D4—42no—
724D4—1222no—
725D4—1222no—
726D4—4884no—
727D4—4884no—
728D4—4884no—
729D4—2448no—
730D4—2444no—
731D4—2448no—
732D4—2442no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—48no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—612no—
745C2×C4—612no—
746C2×C4—612no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1224no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—2448no—
757C2×C4—2448no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4—2442no—
761C2×C4C2×D4×D6112yes—
762C2×C4C2×D4×D6111yescharacteristic
763C2×C4C2×#1175822212yes—
764C2×C4#1451982212yes—
765C2×C4C24×D6111yescharacteristic
766C8—22no—
767C8—22no—
768C8—1222no—
769C8—1222no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—44no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—84no—
778C22—1222no—
779C22—1222no—
780C22—1222no—
781C22—4884no—
782C22—2442no—
783C22—2442no—
784C22—2442no—
785C22—2444no—
786C22#1684040212yes—
787C22#1684055912yes—
788C22#1684056912yes—
789C22C22×D4×D6111yescharacteristic
790C4—22no—
791C4—24no—
792C4—42no—
793C4—42no—
794C4—1222no—
795C4—1222no—
796C4—1222no—
797C4—2442no—
798C4—2442no—
799C4—2442no—
800C4#1684040212yes—
801C4C22×#1175822211yescharacteristic
802C4C2×#1451982211yescharacteristic
803C2—42no—
804C2—82no—
805C2—4882no—
806C2—2442no—
807C2#2145794114yesdirect product factor
808C2C2×#1684040211yescharacteristic
809C2C2×#1684055911yescharacteristic
810C2C2×#1684056911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#416C2
socleC23×C61C22×D4
prime radicalC2×#16840431C2
hypercenterC2×#416D61
hypocenterC61C2×#3317
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#16840451C2semidirect
3. #21457941C2direct (N × H)
4. C2×#16840125C2semidirect
5. C2×#16840079C2semidirect
6. C2×#16840086C2semidirect
7. C2×#16840067C2semidirect
8. C2×#16840007C2semidirect
9. C2×#16839991C2semidirect
10. C2×#16839961C2semidirect
11. C2×#16839927C2semidirect
12. C2×#16839924C2semidirect
13. C2×#16839866C2semidirect
14. C2×#16839833C2semidirect
15. C2×#16839762C2semidirect
16. C2×C61×#416C2semidirect
23. #16840451C22semidirect
44. #16840125C22semidirect
45. #16840086C22semidirect
46. #16840079C22semidirect
47. #16840067C22semidirect
48. #16840007C22semidirect
49. #16839991C22semidirect
50. #16839961C22semidirect
51. #16839927C22semidirect
52. #16839924C22semidirect
53. #16839866C22semidirect
54. #16839833C22semidirect
59. #16839762C22semidirect
72. C61×#416C22semidirect
413. C2×#416D61semidirect
416. C2×C61#3317semidirect
468. #416C2×D61semidirect
482. C61C2×#3317semidirect
807. C2#21457941direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404512
C2×#168404312
#214579412
C2×#168401252
C2×#168400792
C2×#168400862
C2×#168400672
C2×#168400072
C2×#168399912
C2×#168399612
C2×#168399272
C2×#168399242
C2×#168398662
C2×#168398332
C2×#168397622
C2×C61×#4162
C2×#331761