Finite Group Databasebeta

← C2×#21458120 #30556918

Subgroups — C2×#21458120 #30556918

Order 15616.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840413C211yesmaximal, characteristic, complemented
2C2×#16840411C211yesmaximal, characteristic, complemented
3#21458120C2116yesmaximal, direct product factor
4C2×#16840111C211yesmaximal, characteristic, complemented
5C2×#16840097C211yesmaximal, characteristic, complemented
6C2×#16840096C211yesmaximal, characteristic, complemented
7C2×#16840040C211yesmaximal, characteristic, complemented
8C2×#16840011C211yesmaximal, characteristic, complemented
9C2×#16840008C211yesmaximal, characteristic, complemented
10C2×#16839966C211yesmaximal, characteristic, complemented
11C2×#16839908C211yesmaximal, characteristic, complemented
12C2×#16839907C211yesmaximal, characteristic, complemented
13C2×#16839842C211yesmaximal, characteristic, complemented
14C2×#16839838C211yesmaximal, characteristic, complemented
15C2×#16839760C211yesmaximal, characteristic, complemented
16C2×C61×#417C211yesmaximal, characteristic, complemented
17C22×#11758222—21no—
18C22×#11758224C2211yescharacteristic
19C22×#11758190C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C22×#11758199C2211yescharacteristic
22C22×#11758189C2211yescharacteristic
23#16840413—24no—
24#16840413C2218yescomplemented
25#16840411—24no—
26#16840411C2218yescomplemented
27C2×#14519776C2211yescharacteristic
28C2×#14519775C2211yescharacteristic
29C2×#14519762—21no—
30C2×#14519760—21no—
31C2×#14519760—21no—
32C2×#14519758—21no—
33C2×#14519756C2211yescharacteristic
34C2×#14519755—21no—
35C2×#14519753C2211yescharacteristic
36C2×#14519752C2211yescharacteristic
37C2×#14519751C2211yescharacteristic
38C2×#14519749—21no—
39C2×D4×Dic61C2211yescharacteristic
40C2×#14519739C2211yescharacteristic
41C2×C4×C22⋊D61C2211yescharacteristic
42C22×#11758196—21no—
43C2×C4⋊C4×D61C2211yescharacteristic
44#16840111C2218yescomplemented
45#16840097C2218yescomplemented
46#16840096C2218yescomplemented
47#16840040C2218yescomplemented
48#16840011C2218yescomplemented
49#16840008C2218yescomplemented
50#16839966C2218yescomplemented
51#16839908C2218yescomplemented
52#16839907C2218yescomplemented
53#16839842C2218yescomplemented
54#16839838C2218yescomplemented
55C2×#14519711C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519710C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59#16839760C2218yescomplemented
60C2×#14519702C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
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×#11758222—28no—
78C2×#11758222—48no—
79C2×#11758224—24no—
80C2×#11758224—22no—
81C2×#11758224—42no—
82C2×#11758224C2314yes—
83C22×Dic122—21no—
84C22×Dic122C2311yescharacteristic
85C22×D244—21no—
86C22×D244C2311yescharacteristic
87C22×C22⋊D61—21no—
88C22×C22⋊D61—21no—
89C22×C22⋊D61D411yescharacteristic
90C23×Dic61—21no—
91C23×Dic61—21no—
92C22×C4×D61—21no—
93C22×C4×D61—21no—
94C22×C4×D61C2311yescharacteristic
95C2×#11758190—42no—
96C2×#11758190C2314yes—
97C2×#11758201—42no—
98C2×#11758201C2314yes—
99C2×#11758199—24no—
100C2×#11758199C2314yes—
101C2×#11758189—42no—
102C2×#11758189C2314yes—
103C22×#92418C2311yescharacteristic
104C22×#92418C2311yescharacteristic
105#14519776—22no—
106#14519776C2314yes—
107#14519775—22no—
108#14519775C2314yes—
109#14519762—28no—
110#14519760—28no—
111#14519760—28no—
112#14519758—28no—
113#14519756—22no—
114#14519756C2314yes—
115#14519755—28no—
116#14519753—22no—
117#14519753C2314yes—
118#14519752—22no—
119#14519752C2314yes—
120#14519751—22no—
121#14519751C2314yes—
122#14519749—28no—
123D4×Dic61—22no—
124D4×Dic61C2314yes—
125#14519739—22no—
126#14519739C2314yes—
127C4×C22⋊D61D414yes—
128C4×C22⋊D61C2314yes—
129C2×C4⋊Dic61C2311yescharacteristic
130C2×C4⋊Dic61C2311yescharacteristic
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196—28no—
138C2×#11758196D411yescharacteristic
139C4⋊C4×D61—22no—
140C4⋊C4×D61C2314yes—
141C2×C22⋊Dic61—21no—
142C2×C22⋊Dic61—21no—
143C2×C22⋊Dic61D411yescharacteristic
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198D411yescharacteristic
149C2×C4×Dic61C2311yescharacteristic
150#14519711C2314yes—
151#14519710C2314yes—
152#14519710C2314yes—
153#14519706C2314yes—
154#14519702C2314yes—
155#14519701C2314yes—
156#14519700C2314yes—
157#14519700C2314yes—
158#14519699C2314yes—
159#14519698C2314yes—
160C22⋊#92418C2314yes—
161#14519689C2314yes—
162C8×Dic61C2314yes—
163C2×#41×C61—22no—
164C2×#41×C61—24no—
165C2×#41×C61—42no—
166C2×#41×C61C2314yes—
167C22×Q8×C61C2311yescharacteristic
168C22×D4×C61—21no—
169C22×D4×C61C2311yescharacteristic
170C23×C4×C61—21no—
171C23×C4×C61—21no—
172C23×C4×C61C2311yescharacteristic
173C2×M16×C61—42no—
174C2×M16×C61C2314yes—
175C22×C8×C61C2311yescharacteristic
176C22×C8×C61C2311yescharacteristic
177C2×C4⋊C4×C61—21no—
178C2×C4⋊C4×C61—22no—
179C2×C4⋊C4×C61C2311yescharacteristic
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C4⋊C4×C61C2314yes—
182#103×C61C2314yes—
183#103×C61C2314yes—
184#102×C61C2314yes—
185#102×C61C2314yes—
186C24×C61—21no—
187C24×C61C2×D411yescharacteristic
188C23×D61—21no—
189C23×D61C2×D411yescharacteristic
190#41×C61—28no—
191#41×C61—44no—
192#41×C61—48no—
193C2×Q8×C61—21no—
194C2×Q8×C61—22no—
195C2×Q8×C61—22no—
196C2×Q8×C61C2412yes—
197C2×D4×C61—24no—
198C2×D4×C61—21no—
199C2×D4×C61—22no—
200C2×D4×C61—44no—
201C2×D4×C61#4114yescomplemented
202C2×D4×C61C2412yes—
203C22×C4×C61—22no—
204C22×C4×C61—22no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—24no—
208C22×C4×C61—21no—
209C22×C4×C61—24no—
210C22×C4×C61—44no—
211C22×C4×C61—44no—
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2×D412yes—
214C22×C4×C61C2412yes—
215C22×C4×C61C2411yescharacteristic
216C2×C22⋊D61—24no—
217C2×C22⋊D61—24no—
218C2×C22⋊D61—24no—
219C2×C22⋊D61—44no—
220C2×C22⋊D61—44no—
221C2×C22⋊D61C2×D414yes—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—24no—
226C22×Dic61—24no—
227C22×Dic61—44no—
228C22×Dic61—44no—
229C22×Dic61C2×D411yescharacteristic
230C22×Dic61C2×D411yescharacteristic
231C22×Dic61C2×D411yescharacteristic
232#11758224—28no—
233#11758224—44no—
234#11758224—48no—
235#11758222—432no—
236C2×D244—22no—
237C2×D244—22no—
238C2×D244—24no—
239C2×D244—21no—
240C2×D244—44no—
241C2×D244C2412yes—
242C2×C4×D61—22no—
243C2×C4×D61—22no—
244C2×C4×D61—24no—
245C2×C4×D61—24no—
246C2×C4×D61—44no—
247C2×C4×D61—44no—
248C2×C4×D61C2×D412yes—
249C2×C4×D61C2412yes—
250C2×Dic122—22no—
251C2×Dic122—22no—
252C2×Dic122—21no—
253C2×Dic122—24no—
254C2×Dic122—44no—
255C2×Dic122C2412yes—
256M16×C61—44no—
257C2×C8×C61—22no—
258C2×C8×C61—22no—
259C2×C8×C61C2412yes—
260C2×C8×C61C2412yes—
261C4⋊C4×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61—24no—
264C4⋊C4×C61C2412yes—
265C4⋊C4×C61C2412yes—
266C22⋊Dic61—24no—
267C22⋊Dic61—24no—
268C22⋊Dic61C2×D414yes—
269#11758201—44no—
270#11758199—28no—
271#11758198—24no—
272#11758198—24no—
273#11758198—24no—
274#11758198—24no—
275#11758198C2×D414yes—
276C4⋊Dic61—21no—
277C4⋊Dic61—21no—
278C4⋊Dic61C2412yes—
279C4⋊Dic61C2412yes—
280#11758196—24no—
281#11758196—24no—
282#11758196—24no—
283#11758196—24no—
284#11758196—24no—
285#11758196—24no—
286#11758196C2×D414yes—
287C4×Dic61C2×D412yes—
288C4×Dic61C2412yes—
289C2×#92418—22no—
290C2×#92418—22no—
291C2×#92418C2412yes—
292C2×#92418C2412yes—
293#11758190—44no—
294#11758189—44no—
295C23×C61—24no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—22no—
299C23×C61—22no—
300C23×C61—42no—
301C23×C61—42no—
302C23×C61C22×D412yes—
303C23×C61C22×D411yescharacteristic
304C22×D61—22no—
305C22×D61—22no—
306C22×D61—22no—
307C22×D61—22no—
308C22×D61—42no—
309C22×D61—42no—
310C22×D61—42no—
311C22×D61C22×D412yes—
312Q8×C61—22no—
313Q8×C61—22no—
314Q8×C61—42no—
315D4×C61—24no—
316D4×C61—22no—
317D4×C61—48no—
318D4×C61C2×#4114yescomplemented
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—22no—
326C2×C4×C61—48no—
327C2×C4×C61—48no—
328C2×C4×C61—42no—
329C2×C4×C61—42no—
330C2×C4×C61—42no—
331C2×C4×C61C22×D412yes—
332C2×C4×C61C22×D411yescharacteristic
333C2×C4×C61C2×#4112yes—
334C2×C4×C61H(5,𝔽2)12yes—
335C2×C4×C61C2511yescharacteristic
336C22⋊D61—28no—
337C22⋊D61—48no—
338C22⋊D61—48no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—48no—
345C2×Dic61—42no—
346C2×Dic61—42no—
347C2×Dic61—42no—
348C2×Dic61—48no—
349C2×Dic61AGL(1,ℤ/8)14yes—
350C2×Dic61C22×D412yes—
351C2×Dic61C22×D412yes—
352C2×Dic61C22×D412yes—
353D244—22no—
354D244—22no—
355D244—48no—
356D244—42no—
357C4×D61—24no—
358C4×D61—22no—
359C4×D61—22no—
360C4×D61—48no—
361C4×D61—48no—
362Dic122—22no—
363Dic122—22no—
364Dic122—42no—
365Dic122—48no—
366C8×C61—22no—
367C8×C61—22no—
368#92418—22no—
369#92418—22no—
370C2×#3330—611nomaximal, Sylow
371C22×C61—24no—
372C22×C61—22no—
373C22×C61—22no—
374C22×C61—22no—
375C22×C61—44no—
376C22×C61—48no—
377C22×C61—42no—
378C22×C61—42no—
379C22×C61#54612yes—
380C22×C61C2×AGL(1,ℤ/8)12yes—
381C22×C61#57812yes—
382C22×C61C23×D411yescharacteristic
383C2×D61—22no—
384C2×D61—22no—
385C2×D61—22no—
386C2×D61—44no—
387C2×D61—42no—
388C2×D61—42no—
389C2×D61—42no—
390C2×D61—84no—
391C4×C61—22no—
392C4×C61—42no—
393C4×C61—42no—
394C4×C61—42no—
395C4×C61#54612yes—
396C4×C61C22×#4111yescharacteristic
397C4×C61C2×H(5,𝔽2)11yescharacteristic
398Dic61—22no—
399Dic61—22no—
400Dic61—42no—
401Dic61—42no—
402Dic61—42no—
403Dic61C2×AGL(1,ℤ/8)14yes—
404C2×#547—611no—
405C2×#547—611no—
406#3330—6116no—
407C2×#487—611no—
408C2×#484—611no—
409C2×#484—611no—
410C2×#474—611no—
411C2×#468—611no—
412C2×#468—611no—
413C2×#461—611no—
414C2×#449—611no—
415C2×#449—611no—
416C2×C4×D8—611no—
417C2×#436—611no—
418C2×#417—611no—
419C2×#417D6111yescharacteristic, complemented
420C2×C61—42no—
421C2×C61—44no—
422C2×C61#333014yescomplemented
423C2×C61C2×#54611yescharacteristic
424C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
425C2×C61C2×#57811yescharacteristic
426D61—42no—
427D61—82no—
428C22×#41—611no—
429C22×#41—1221no—
430C22×#41C2×D6111yescharacteristic
431C22×SD16—611no—
432C22×SD16—611no—
433C22×D8—611no—
434C22×M16—611no—
435C22×M16C2×D6111yescharacteristic
436#547—618no—
437#547—618no—
438#547—1224no—
439#547—1224no—
440C2×C4⋊Q8—611no—
441C2×C4⋊Q8—611no—
442C2×#123—1221no—
443C2×#123—1221no—
444C2×#123—1221no—
445C2×#123—1221no—
446C2×C22⋊Q8—611no—
447C2×C22⋊Q8—611no—
448C2×C22⋊Q8—1221no—
449C2×#121—611no—
450C2×#121—611no—
451C2×#121—1221no—
452C2×C4×D4—611no—
453C2×C4×D4—611no—
454C2×C4×D4—611no—
455C22×C4⋊C4—611no—
456C22×C4⋊C4—1221no—
457C22×C4⋊C4C2×D6111yescharacteristic
458#487—618no—
459#484—618no—
460#484—618no—
461#474—618no—
462#468—618no—
463#468—618no—
464#461—618no—
465#449—618no—
466#449—618no—
467C4×D8—618no—
468#436—618no—
469C2×#107—611no—
470C2×#107—611no—
471C2×#107—611no—
472C2×C4⋊C8—611no—
473#417—618no—
474#417C2×D6118yescomplemented
475C2×#103—611no—
476C2×#103—611no—
477C2×#103—611no—
478C2×#103—611no—
479C2×#103C2×D6111yescharacteristic
480C2×#103C2×D6111yescharacteristic
481C2×#102—611no—
482C2×#102—611no—
483C2×#102C2×D6111yescharacteristic
484C2×#102C2×D6111yescharacteristic
485C2×C22⋊C8—611no—
486C2×C22⋊C8—611no—
487C2×C4×C8—611no—
488C61C2×#333011yescharacteristic, complemented, Sylow
489C2×#41—22no—
490C2×#41—24no—
491C2×#41—42no—
492C2×#41—614no—
493C2×#41—1228no—
494C2×#41—1222no—
495C2×#41—1224no—
496C2×#41—2448no—
497C2×#41—2442no—
498C2×#41C22×D6114yes—
499C22×Q8—611no—
500C22×Q8—1221no—
501C22×Q8C22×D6111yescharacteristic
502C22×D4—21no—
503C22×D4—611no—
504C22×D4—611no—
505C22×D4—1221no—
506C22×D4—1221no—
507C22×D4—1221no—
508C22×D4C22×D6111yescharacteristic
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—611no—
512C23×C4—1221no—
513C23×C4—1221no—
514C23×C4—1221no—
515C23×C4—1221no—
516C23×C4C22×D6111yescharacteristic
517C2×SD16—614no—
518C2×SD16—614no—
519C2×SD16—2442no—
520C2×SD16—2442no—
521C2×D8—614no—
522C2×D8—1224no—
523C2×M16—42no—
524C2×M16—614no—
525C2×M16—2442no—
526C2×M16C22×D6114yes—
527C22×C8—611no—
528C22×C8—611no—
529C22×C8C22×D6111yescharacteristic
530C22×C8C22×D6111yescharacteristic
531C4⋊Q8—614no—
532C4⋊Q8—614no—
533C4⋊Q8—1222no—
534C4⋊Q8—1222no—
535#123—1228no—
536#123—1228no—
537#123—1228no—
538#123—1228no—
539C22⋊Q8—614no—
540C22⋊Q8—614no—
541C22⋊Q8—1228no—
542C22⋊Q8—1222no—
543C22⋊Q8—1222no—
544#121—614no—
545#121—614no—
546#121—1222no—
547#121—1228no—
548#121—1222no—
549C4×D4—614no—
550C4×D4—614no—
551C4×D4—614no—
552C4×D4—614no—
553C4×D4—1222no—
554C4×D4—1222no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—22no—
557C2×C4⋊C4—611no—
558C2×C4⋊C4—611no—
559C2×C4⋊C4—611no—
560C2×C4⋊C4—614no—
561C2×C4⋊C4—1222no—
562C2×C4⋊C4—1228no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4—1221no—
567C2×C4⋊C4—1221no—
568C2×C4⋊C4—1221no—
569C2×C4⋊C4C22×D6111yescharacteristic
570C2×C4⋊C4C22×D6111yescharacteristic
571C2×C4⋊C4C22×D6114yes—
572C2×C22⋊C4—611no—
573C2×C22⋊C4—611no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4—1221no—
580C2×C42—611no—
581#107—614no—
582#107—614no—
583#107—614no—
584C4⋊C8—614no—
585#103—614no—
586#103—614no—
587#103—614no—
588#103—614no—
589#103C22×D6114yes—
590#103C22×D6114yes—
591#102—614no—
592#102—614no—
593#102C22×D6114yes—
594#102C22×D6114yes—
595C22⋊C8—614no—
596C22⋊C8—614no—
597C4×C8—614no—
598C24—21no—
599C24—611no—
600C24—1221no—
601C24D4×D6111yescharacteristic
602#41—28no—
603#41—44no—
604#41—48no—
605#41—1228no—
606#41—24432no—
607#41—2444no—
608#41—2448no—
609C2×Q8—21no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—612no—
613C2×Q8—1224no—
614C2×Q8—1221no—
615C2×Q8—1222no—
616C2×Q8—1222no—
617C2×Q8—2444no—
618C2×Q8C23×D6112yes—
619C2×D4—24no—
620C2×D4—21no—
621C2×D4—22no—
622C2×D4—44no—
623C2×D4—614no—
624C2×D4—612no—
625C2×D4—1224no—
626C2×D4—1224no—
627C2×D4—1224no—
628C2×D4—1224no—
629C2×D4—1221no—
630C2×D4—1222no—
631C2×D4—1222no—
632C2×D4—2444no—
633C2×D4—2444no—
634C2×D4—2444no—
635C2×D4#1175822214yescomplemented
636C2×D4C23×D6112yes—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—24no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—611no—
647C22×C4—611no—
648C22×C4—611no—
649C22×C4—612no—
650C22×C4—612no—
651C22×C4—1224no—
652C22×C4—1224no—
653C22×C4—1224no—
654C22×C4—1224no—
655C22×C4—1222no—
656C22×C4—1222no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—2444no—
661C22×C4—2444no—
662C22×C4—2444no—
663C22×C4—2444no—
664C22×C4D4×D6112yes—
665C22×C4D4×D6111yescharacteristic
666C22×C4C23×D6112yes—
667C22×C4C23×D6111yescharacteristic
668SD16—2444no—
669SD16—2444no—
670D8—1228no—
671M16—44no—
672M16—2444no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—612no—
676C2×C8—612no—
677C2×C8—1222no—
678C2×C8—1222no—
679C2×C8C23×D6112yes—
680C2×C8C23×D6112yes—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—24no—
684C4⋊C4—614no—
685C4⋊C4—612no—
686C4⋊C4—612no—
687C4⋊C4—1224no—
688C4⋊C4—1224no—
689C4⋊C4—1224no—
690C4⋊C4—1224no—
691C4⋊C4—1224no—
692C4⋊C4—1221no—
693C4⋊C4—1221no—
694C4⋊C4—1224no—
695C4⋊C4C23×D6112yes—
696C4⋊C4C23×D6112yes—
697C22⋊C4—614no—
698C22⋊C4—614no—
699C22⋊C4—1224no—
700C22⋊C4—1224no—
701C22⋊C4—1224no—
702C22⋊C4—1224no—
703C22⋊C4—1224no—
704C22⋊C4—1224no—
705C42—612no—
706C42—612no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—24no—
712C23—42no—
713C23—42no—
714C23—612no—
715C23—1222no—
716C23—1222no—
717C23—1222no—
718C23—1222no—
719C23—2442no—
720C23—2442no—
721C23—2442no—
722C23C2×D4×D6112yes—
723C23C2×D4×D6111yescharacteristic
724Q8—22no—
725Q8—22no—
726Q8—42no—
727Q8—1222no—
728Q8—1222no—
729Q8—2448no—
730Q8—2442no—
731D4—22no—
732D4—24no—
733D4—48no—
734D4—1228no—
735D4—1222no—
736D4—1222no—
737D4—2448no—
738D4—2448no—
739D4—2448no—
740D4—2442no—
741D4C2×#1175822214yescomplemented
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—48no—
750C2×C4—48no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—614no—
755C2×C4—612no—
756C2×C4—612no—
757C2×C4—612no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1224no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—2448no—
767C2×C4—2448no—
768C2×C4—2448no—
769C2×C4—2448no—
770C2×C4—2442no—
771C2×C4—2442no—
772C2×C4—2442no—
773C2×C4C2×D4×D6112yes—
774C2×C4C2×D4×D6111yescharacteristic
775C2×C4C2×#1175822212yes—
776C2×C4#1451982212yes—
777C2×C4C24×D6111yescharacteristic
778C8—22no—
779C8—22no—
780C8—1222no—
781C8—1222no—
782C22—22no—
783C22—24no—
784C22—22no—
785C22—22no—
786C22—42no—
787C22—42no—
788C22—44no—
789C22—48no—
790C22—1222no—
791C22—1222no—
792C22—1222no—
793C22—4884no—
794C22—2442no—
795C22—2442no—
796C22—2442no—
797C22—2444no—
798C22#1684040212yes—
799C22AGL(1,ℤ/8)×D6112yes—
800C22#1684057812yes—
801C22C22×D4×D6111yescharacteristic
802C4—22no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—614no—
807C4—1222no—
808C4—1222no—
809C4—2442no—
810C4—2442no—
811C4—2442no—
812C4#1684040212yes—
813C4C22×#1175822211yescharacteristic
814C4C2×#1451982211yescharacteristic
815C2—42no—
816C2—44no—
817C2—4882no—
818C2—2442no—
819C2#2145812014yesdirect product factor
820C2C2×#1684040211yescharacteristic
821C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
822C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#417C2
socleC23×C61C22×D4
hypercenterC2×#417D61
hypocenterC61C2×#3330
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×#16840413C2semidirect
2. C2×#16840411C2semidirect
3. #21458120C2direct (N × H)
4. C2×#16840111C2semidirect
5. C2×#16840097C2semidirect
6. C2×#16840096C2semidirect
7. C2×#16840040C2semidirect
8. C2×#16840011C2semidirect
9. C2×#16840008C2semidirect
10. C2×#16839966C2semidirect
11. C2×#16839908C2semidirect
12. C2×#16839907C2semidirect
13. C2×#16839842C2semidirect
14. C2×#16839838C2semidirect
15. C2×#16839760C2semidirect
16. C2×C61×#417C2semidirect
24. #16840413C22semidirect
26. #16840411C22semidirect
44. #16840111C22semidirect
45. #16840097C22semidirect
46. #16840096C22semidirect
47. #16840040C22semidirect
48. #16840011C22semidirect
49. #16840008C22semidirect
50. #16839966C22semidirect
51. #16839908C22semidirect
52. #16839907C22semidirect
53. #16839842C22semidirect
54. #16839838C22semidirect
59. #16839760C22semidirect
72. C61×#417C22semidirect
201. C2×D4×C61#41semidirect
318. D4×C61C2×#41semidirect
419. C2×#417D61semidirect
422. C2×C61#3330semidirect
474. #417C2×D61semidirect
488. C61C2×#3330semidirect
635. C2×D4#11758222semidirect
741. D4C2×#11758222semidirect
819. C2#21458120direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404132
C2×#168404112
#214581202
C2×#168401112
C2×#168400972
C2×#168400962
C2×#168400402
C2×#168400112
C2×#168400082
C2×#168399662
C2×#168399082
C2×#168399072
C2×#168398422
C2×#168398382
C2×#168397602
C2×C61×#4172
C2×#333061