Finite Group Databasebeta

← C2×#21433164 #29453463

Subgroups — C2×#21433164 #29453463

Order 15104.

2186 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837949C211yesmaximal, characteristic
2#21433164C2116yesmaximal, direct product factor
3C2×#16837476C211yesmaximal, characteristic, complemented
4C2×#16837475C211yesmaximal, characteristic, complemented
5C2×#16837474C211yesmaximal, characteristic, complemented
6C2×#16837473C211yesmaximal, characteristic, complemented
7C2×#16837472C211yesmaximal, characteristic, complemented
8C2×#16837471C211yesmaximal, characteristic, complemented
9C2×#16837470C211yesmaximal, characteristic, complemented
10C2×#16837458C211yesmaximal, characteristic, complemented
11C2×#16837457C211yesmaximal, characteristic, complemented
12C2×#16837370C211yesmaximal, characteristic, complemented
13C2×#16837368C211yesmaximal, characteristic, complemented
14C2×#16837367C211yesmaximal, characteristic, complemented
15C2×#16837367C211yesmaximal, characteristic, complemented
16C2×C59×#435C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C22×#11745685C2211yescharacteristic
19C22×#11745664C2211yescharacteristic
20C22×#11745659C2211yescharacteristic
21C22×#11745659C2211yescharacteristic
22C23×C59⋊C8C2211yescharacteristic
23C22×C8×D59C2211yescharacteristic
24C22×C8×D59C2211yescharacteristic
25#16837949C418yes—
26#16837949C2218yes—
27C2×#14273726C411yescharacteristic
28C2×#14273723C411yescharacteristic
29C2×#14273713C411yescharacteristic
30C2×#14273713C411yescharacteristic
31C2×#14273702C411yescharacteristic
32C2×#14273700C411yescharacteristic
33C2×#14273700C411yescharacteristic
34C2×#14273698C411yescharacteristic
35C2×C4×D236C2211yescharacteristic
36C2×C4×C22⋊D59C2211yescharacteristic
37C2×C4×C22⋊D59C2211yescharacteristic
38C2×C42×D59C2211yescharacteristic
39#16837476C2218yescomplemented
40#16837475C2218yescomplemented
41#16837474C2218yescomplemented
42#16837473C2218yescomplemented
43#16837472C2218yescomplemented
44#16837471C2218yescomplemented
45#16837470C2218yescomplemented
46#16837458C2218yescomplemented
47#16837457C2218yescomplemented
48C2×C4⋊(C59⋊C8)C2211yescharacteristic
49C2×Dic59⋊C8C2211yescharacteristic
50C2×Dic59⋊C8C2211yescharacteristic
51#16837370C2218yescomplemented
52#16837368C2218yescomplemented
53#16837367C2218yescomplemented
54#16837367C2218yescomplemented
55C2×C22⋊(C59⋊C8)C2211yescharacteristic
56C2×C22⋊(C59⋊C8)C2211yescharacteristic
57C2×(C2×D59)⋊C8C2211yescharacteristic
58C2×(C2×D59)⋊C8C2211yescharacteristic
59C2×(C2×D59)⋊C8C2211yescharacteristic
60C2×(C2×D59)⋊C8C2211yescharacteristic
61C2×(C2×D59)⋊C8C2211yescharacteristic
62C2×(C2×D59)⋊C8C2211yescharacteristic
63C2×(C2×D59)⋊C8C2211yescharacteristic
64C2×(C2×D59)⋊C8C2211yescharacteristic
65C2×#14273638C2211yescharacteristic
66C2×#14273637C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
68C22×M16×C59C2211yescharacteristic
69C23×C8×C59C2211yescharacteristic
70C2×C4×D4×C59C2211yescharacteristic
71C59×#435C2218yescomplemented
72C2×C4⋊C8×C59C2211yescharacteristic
73C2×C22⋊C8×C59C2211yescharacteristic
74C2×C22⋊C8×C59C2211yescharacteristic
75C2×#97×C59C2211yescharacteristic
76C2×#11745685—42no—
77C2×#11745685—42no—
78C2×#11745685—42no—
79C2×#11745685—42no—
80C2×#11745685C2×C414yes—
81C2×#11745685C2×C414yes—
82C2×#11745685C2314yes—
83C2×#11745685C2314yes—
84C22×Dic118C2×C411yescharacteristic
85C22×Dic118C2×C411yescharacteristic
86C22×D236C2×C411yescharacteristic
87C22×D236C2×C411yescharacteristic
88C22×D236C2×C411yescharacteristic
89C22×C22⋊D59C2×C411yescharacteristic
90C22×C22⋊D59C2×C411yescharacteristic
91C22×C22⋊D59C2×C411yescharacteristic
92C22×C22⋊D59C2×C411yescharacteristic
93C22×C22⋊D59C2×C411yescharacteristic
94C22×C22⋊D59C2×C411yescharacteristic
95C22×C4×D59C2×C411yescharacteristic
96C22×C4×D59C2×C411yescharacteristic
97C22×C4×D59C2311yescharacteristic
98C22×C4×D59C2311yescharacteristic
99C22×C4×D59C2311yescharacteristic
100C2×#11745664—42no—
101C2×#11745664C2314yes—
102C2×#11745659—42no—
103C2×#11745659—42no—
104C2×#11745659C2314yes—
105C2×#11745659C2314yes—
106C22×C59⋊C8—42no—
107C22×C59⋊C8C2311yescharacteristic
108C22×C59⋊C8C2311yescharacteristic
109C22×C59⋊C8C2311yescharacteristic
110C22×C59⋊C8C2311yescharacteristic
111C22×C59⋊C8C2314yes—
112C2×C8×D59—42no—
113C2×C8×D59—42no—
114C2×C8×D59C2314yes—
115C2×C8×D59C2314yes—
116#14273726C2×C418yes—
117#14273723C2×C418yes—
118#14273713C2×C418yes—
119#14273713C2×C418yes—
120#14273702C2×C418yes—
121#14273700C2×C418yes—
122#14273700C2×C418yes—
123#14273698C2×C418yes—
124C4×D236C2×C414yes—
125C4×D236C2314yes—
126C4×C22⋊D59C2×C414yes—
127C4×C22⋊D59C2×C414yes—
128C4×C22⋊D59C2314yes—
129C4×C22⋊D59C2314yes—
130C2×C4⋊Dic59C2×C411yescharacteristic
131C2×Dic59⋊C4C2×C411yescharacteristic
132C2×Dic59⋊C4C2×C411yescharacteristic
133C2×C22⋊Dic59C2×C411yescharacteristic
134C2×C22⋊Dic59C2×C411yescharacteristic
135C2×(C2×D59)⋊C4C2×C411yescharacteristic
136C2×(C2×D59)⋊C4C2×C411yescharacteristic
137C2×(C2×D59)⋊C4C2×C411yescharacteristic
138C2×(C2×D59)⋊C4C2×C411yescharacteristic
139C2×C4×Dic59C2×C411yescharacteristic
140C2×C4×Dic59C2×C411yescharacteristic
141C2×C4×Dic59C2311yescharacteristic
142C42×D59C2×C414yes—
143C42×D59C2314yes—
144C4⋊(C59⋊C8)C2314yes—
145Dic59⋊C8C2314yes—
146Dic59⋊C8C2314yes—
147C22⋊(C59⋊C8)C2314yes—
148C22⋊(C59⋊C8)C2314yes—
149(C2×D59)⋊C8C2314yes—
150(C2×D59)⋊C8C2314yes—
151(C2×D59)⋊C8C2314yes—
152(C2×D59)⋊C8C2314yes—
153(C2×D59)⋊C8C2314yes—
154(C2×D59)⋊C8C2314yes—
155(C2×D59)⋊C8C2314yes—
156(C2×D59)⋊C8C2314yes—
157#14273638C2314yes—
158#14273637C2314yes—
159#14273637C2314yes—
160C22×D4×C59C2×C411yescharacteristic
161C23×C4×C59C2311yescharacteristic
162C23×C4×C59C2311yescharacteristic
163C2×M16×C59—42no—
164C2×M16×C59C2314yes—
165C22×C8×C59—42no—
166C22×C8×C59C2311yescharacteristic
167C22×C8×C59C2311yescharacteristic
168C22×C8×C59C2311yescharacteristic
169C22×C8×C59C2311yescharacteristic
170C22×C8×C59C2314yes—
171C4×D4×C59C2×C414yes—
172C4×D4×C59C2314yes—
173C2×C4⋊C4×C59C2×C411yescharacteristic
174C2×C22⋊C4×C59C2×C411yescharacteristic
175C2×C22⋊C4×C59C2×C411yescharacteristic
176C2×C42×C59C2311yescharacteristic
177C4⋊C8×C59C2314yes—
178C22⋊C8×C59C2314yes—
179C22⋊C8×C59C2314yes—
180#97×C59C2314yes—
181C24×C59C22×C411yescharacteristic
182C24×C59C22×C411yescharacteristic
183C23×D59C22×C411yescharacteristic
184C23×D59C22×C411yescharacteristic
185C23×D59C22×C411yescharacteristic
186C2×D4×C59—42no—
187C2×D4×C59C22×C414yes—
188C22×C4×C59—22no—
189C22×C4×C59—22no—
190C22×C4×C59—22no—
191C22×C4×C59—22no—
192C22×C4×C59C22×C411yescharacteristic
193C22×C4×C59C22×C411yescharacteristic
194C22×C4×C59C22×C411yescharacteristic
195C22×C4×C59C22×C411yescharacteristic
196C22×C4×C59C22×C412yes—
197C22×C4×C59C22×C412yes—
198C22×C4×C59C2412yes—
199C22×C4×C59C2412yes—
200C22×C4×C59C2411yescharacteristic
201C2×C22⋊D59—42no—
202C2×C22⋊D59—42no—
203C2×C22⋊D59—42no—
204C2×C22⋊D59—42no—
205C2×C22⋊D59—42no—
206C2×C22⋊D59—42no—
207C2×C22⋊D59C22×C414yes—
208C2×C22⋊D59C22×C414yes—
209C2×C22⋊D59C22×C414yes—
210C2×C22⋊D59C22×C414yes—
211C2×C22⋊D59C22×C414yes—
212C2×C22⋊D59C22×C414yes—
213C22×Dic59C22×C411yescharacteristic
214C22×Dic59C22×C411yescharacteristic
215C22×Dic59C22×C411yescharacteristic
216C22×Dic59C22×C411yescharacteristic
217C22×Dic59C22×C411yescharacteristic
218#11745685—48no—
219#11745685—48no—
220#11745685—44no—
221#11745685—44no—
222#11745685—44no—
223#11745685—44no—
224C2×D236—42no—
225C2×D236—42no—
226C2×D236—42no—
227C2×D236C22×C414yes—
228C2×D236C22×C414yes—
229C2×D236C22×C414yes—
230C2×C4×D59—22no—
231C2×C4×D59—22no—
232C2×C4×D59—22no—
233C2×C4×D59—22no—
234C2×C4×D59—22no—
235C2×C4×D59—22no—
236C2×C4×D59—42no—
237C2×C4×D59—42no—
238C2×C4×D59C22×C412yes—
239C2×C4×D59C22×C412yes—
240C2×C4×D59C22×C412yes—
241C2×C4×D59C22×C414yes—
242C2×C4×D59C22×C414yes—
243C2×C4×D59C2412yes—
244C2×C4×D59C2412yes—
245C2×C4×D59C2412yes—
246C2×Dic118—42no—
247C2×Dic118—42no—
248C2×Dic118C22×C414yes—
249C2×Dic118C22×C414yes—
250M16×C59—44no—
251C2×C8×C59—22no—
252C2×C8×C59—22no—
253C2×C8×C59—22no—
254C2×C8×C59—22no—
255C2×C8×C59—44no—
256C2×C8×C59C2412yes—
257C2×C8×C59C2412yes—
258C2×C8×C59C2412yes—
259C2×C8×C59C2412yes—
260C4⋊C4×C59C22×C414yes—
261C22⋊C4×C59C22×C414yes—
262C22⋊C4×C59C22×C414yes—
263C42×C59C22×C412yes—
264C42×C59C2412yes—
265C22⋊Dic59C22×C414yes—
266C22⋊Dic59C22×C414yes—
267(C2×D59)⋊C4C22×C414yes—
268(C2×D59)⋊C4C22×C414yes—
269(C2×D59)⋊C4C22×C414yes—
270(C2×D59)⋊C4C22×C414yes—
271C4⋊Dic59C22×C414yes—
272Dic59⋊C4C22×C414yes—
273Dic59⋊C4C22×C414yes—
274C4×Dic59C22×C412yes—
275C4×Dic59C22×C414yes—
276C4×Dic59C22×C414yes—
277C4×Dic59C2412yes—
278#11745664—44no—
279C2×C59⋊C8—22no—
280C2×C59⋊C8—22no—
281C2×C59⋊C8—22no—
282C2×C59⋊C8—22no—
283C2×C59⋊C8—44no—
284C2×C59⋊C8C2412yes—
285C2×C59⋊C8C2412yes—
286C2×C59⋊C8C2412yes—
287C2×C59⋊C8C2412yes—
288#11745659—44no—
289#11745659—44no—
290C8×D59—44no—
291C8×D59—44no—
292C23×C59—22no—
293C23×C59—22no—
294C23×C59—22no—
295C23×C59—22no—
296C23×C59—22no—
297C23×C59—22no—
298C23×C59C23×C412yes—
299C23×C59C23×C412yes—
300C23×C59C23×C411yescharacteristic
301C22×D59—22no—
302C22×D59—22no—
303C22×D59—22no—
304C22×D59—22no—
305C22×D59—22no—
306C22×D59—22no—
307C22×D59—22no—
308C22×D59—22no—
309C22×D59—22no—
310C22×D59C23×C412yes—
311C22×D59C23×C412yes—
312C22×D59C23×C412yes—
313D4×C59—44no—
314C2×C4×C59—22no—
315C2×C4×C59—22no—
316C2×C4×C59—22no—
317C2×C4×C59—22no—
318C2×C4×C59—24no—
319C2×C4×C59—24no—
320C2×C4×C59—22no—
321C2×C4×C59—22no—
322C2×C4×C59—22no—
323C2×C4×C59—22no—
324C2×C4×C59C23×C412yes—
325C2×C4×C59C23×C412yes—
326C2×C4×C59C23×C412yes—
327C2×C4×C59C23×C412yes—
328C2×C4×C59C23×C411yescharacteristic
329C2×C4×C59H(5,𝔽2)12yes—
330C2×C4×C59H(5,𝔽2)12yes—
331C2×C4×C59C2511yescharacteristic
332C22⋊D59—44no—
333C22⋊D59—44no—
334C22⋊D59—44no—
335C22⋊D59—44no—
336C22⋊D59—44no—
337C22⋊D59—44no—
338C2×Dic59—22no—
339C2×Dic59—22no—
340C2×Dic59—22no—
341C2×Dic59—22no—
342C2×Dic59—22no—
343C2×Dic59C23×C412yes—
344C2×Dic59C23×C412yes—
345C2×Dic59C23×C412yes—
346C2×Dic59C23×C412yes—
347C2×Dic59C23×C412yes—
348D236—44no—
349D236—44no—
350D236—44no—
351C4×D59—24no—
352C4×D59—24no—
353C4×D59—24no—
354C4×D59—22no—
355C4×D59—22no—
356C4×D59—22no—
357C4×D59—22no—
358C4×D59—22no—
359C4×D59—22no—
360C4×D59—44no—
361C4×D59—44no—
362Dic118—44no—
363Dic118—44no—
364C8×C59—22no—
365C8×C59—22no—
366C8×C59—22no—
367C8×C59—22no—
368C59⋊C8—22no—
369C59⋊C8—22no—
370C59⋊C8—22no—
371C59⋊C8—22no—
372C2×#2980—591nomaximal, Sylow
373C22×C59—22no—
374C22×C59—22no—
375C22×C59—22no—
376C22×C59—22no—
377C22×C59—22no—
378C22×C59—22no—
379C22×C59—44no—
380C22×C59—44no—
381C22×C59#51812yes—
382C22×C59#56812yes—
383C22×C59#56812yes—
384C22×C59C24×C411yescharacteristic
385C2×D59—22no—
386C2×D59—22no—
387C2×D59—22no—
388C2×D59—22no—
389C2×D59—22no—
390C2×D59—22no—
391C2×D59—22no—
392C2×D59—22no—
393C2×D59—22no—
394C2×D59—44no—
395C2×D59—44no—
396C2×D59—44no—
397C4×C59—22no—
398C4×C59—22no—
399C4×C59—22no—
400C4×C59—22no—
401C4×C59#51812yes—
402C4×C59C2×H(5,𝔽2)11yescharacteristic
403C4×C59C2×H(5,𝔽2)11yescharacteristic
404Dic59—22no—
405Dic59—22no—
406Dic59—22no—
407Dic59—22no—
408Dic59—22no—
409C2×#532—591no—
410#2980—5916no—
411C2×#435—591no—
412C2×#435—591no—
413C2×#435—591no—
414C2×#435—591no—
415C2×#435—591no—
416C2×#435—591no—
417C2×#435—591no—
418C2×#435D5911yescharacteristic, complemented
419C2×#432—591no—
420C2×#432—591no—
421C2×#408—591no—
422C2×#408—591no—
423C2×#408—591no—
424C2×#408—591no—
425C2×C59—42no—
426C2×C59—42no—
427C2×C59#298014yescomplemented
428C2×C59C2×#51811yescharacteristic
429C2×C59C2×#56811yescharacteristic
430C2×C59C2×#56811yescharacteristic
431D59—42no—
432D59—42no—
433D59—42no—
434C22×#41—591no—
435C22×#41—591no—
436C22×M16—591no—
437C22×M16—591no—
438C22×M16—591no—
439C22×M16C2×D5911yescharacteristic
440C23×C8—591no—
441C23×C8—591no—
442C23×C8—591no—
443C23×C8C2×D5911yescharacteristic
444#532—598no—
445#532—598no—
446C2×C4⋊Q8—591no—
447C2×#127—591no—
448C2×#124—591no—
449C2×#124—591no—
450C2×#121—591no—
451C2×#121—591no—
452C2×#121—591no—
453C2×#121—591no—
454C2×C4×D4—591no—
455C2×C4×D4—591no—
456C2×C4×D4—591no—
457C2×C4×D4C2×D5911yescharacteristic
458C22×C42—591no—
459#435—598no—
460#435—598no—
461#435—598no—
462#435—598no—
463#435—598no—
464#435—598no—
465#435—598no—
466#435C2×D5918yescomplemented
467#432—598no—
468#432—598no—
469C2×C4⋊C8—591no—
470C2×C4⋊C8—591no—
471C2×C4⋊C8—591no—
472C2×C4⋊C8C2×D5911yescharacteristic
473#408—598no—
474#408—598no—
475#408—598no—
476#408—598no—
477C2×C22⋊C8—591no—
478C2×C22⋊C8—591no—
479C2×C22⋊C8—591no—
480C2×C22⋊C8—591no—
481C2×C22⋊C8—591no—
482C2×C22⋊C8—591no—
483C2×C22⋊C8—591no—
484C2×C22⋊C8—591no—
485C2×C22⋊C8—591no—
486C2×C22⋊C8—591no—
487C2×C22⋊C8C2×D5911yescharacteristic
488C2×C22⋊C8C2×D5911yescharacteristic
489C2×#97—591no—
490C2×#97—591no—
491C2×#97—591no—
492C2×#97C2×D5911yescharacteristic
493C59C2×#298011yescharacteristic, complemented, Sylow
494C2×#41—594no—
495C2×#41—594no—
496C2×#41—594no—
497C2×#41—594no—
498C2×#41—2362no—
499C2×#41—2362no—
500C2×#41—2362no—
501C2×#41—2362no—
502C22×Q8—591no—
503C22×Q8—591no—
504C22×D4—591no—
505C22×D4—591no—
506C22×D4—591no—
507C22×D4—591no—
508C22×D4—591no—
509C22×D4—591no—
510C22×D4—591no—
511C22×D4—591no—
512C22×D4—591no—
513C22×D4C4×D5911yescharacteristic
514C23×C4—591no—
515C23×C4—591no—
516C23×C4—591no—
517C23×C4—591no—
518C23×C4—591no—
519C23×C4C22×D5911yescharacteristic
520C23×C4C22×D5911yescharacteristic
521C2×M16—42no—
522C2×M16—594no—
523C2×M16—594no—
524C2×M16—594no—
525C2×M16—2362no—
526C2×M16—2362no—
527C2×M16—2362no—
528C2×M16C22×D5914yes—
529C22×C8—42no—
530C22×C8—591no—
531C22×C8—591no—
532C22×C8—591no—
533C22×C8—591no—
534C22×C8—594no—
535C22×C8—594no—
536C22×C8—594no—
537C22×C8—2362no—
538C22×C8—2362no—
539C22×C8—2362no—
540C22×C8C22×D5911yescharacteristic
541C22×C8C22×D5911yescharacteristic
542C22×C8C22×D5911yescharacteristic
543C22×C8C22×D5911yescharacteristic
544C22×C8C22×D5914yes—
545C4⋊Q8—598no—
546#127—598no—
547#124—598no—
548#124—598no—
549#121—598no—
550#121—598no—
551#121—598no—
552#121—598no—
553C4×D4—594no—
554C4×D4—594no—
555C4×D4—594no—
556C4×D4—594no—
557C4×D4—594no—
558C4×D4—594no—
559C4×D4C4×D5914yes—
560C4×D4C22×D5914yes—
561C2×C4⋊C4—591no—
562C2×C4⋊C4—591no—
563C2×C4⋊C4—591no—
564C2×C4⋊C4C4×D5911yescharacteristic
565C2×C22⋊C4—591no—
566C2×C22⋊C4—591no—
567C2×C22⋊C4—591no—
568C2×C22⋊C4—591no—
569C2×C22⋊C4—591no—
570C2×C22⋊C4—591no—
571C2×C22⋊C4C4×D5911yescharacteristic
572C2×C22⋊C4C4×D5911yescharacteristic
573C2×C42—591no—
574C2×C42—591no—
575C2×C42—591no—
576C2×C42—594no—
577C2×C42—594no—
578C2×C42C22×D5911yescharacteristic
579C4⋊C8—594no—
580C4⋊C8—594no—
581C4⋊C8—594no—
582C4⋊C8C22×D5914yes—
583C22⋊C8—594no—
584C22⋊C8—594no—
585C22⋊C8—594no—
586C22⋊C8—594no—
587C22⋊C8—594no—
588C22⋊C8—594no—
589C22⋊C8—594no—
590C22⋊C8—594no—
591C22⋊C8—594no—
592C22⋊C8—594no—
593C22⋊C8C22×D5914yes—
594C22⋊C8C22×D5914yes—
595#97—594no—
596#97—594no—
597#97—594no—
598#97C22×D5914yes—
599C24—591no—
600C24—591no—
601C24—591no—
602C24C2×C4×D5911yescharacteristic
603C24C2×C4×D5911yescharacteristic
604#41—2364no—
605#41—2364no—
606#41—2364no—
607#41—2364no—
608#41—2368no—
609#41—2368no—
610C2×Q8—594no—
611C2×Q8—594no—
612C2×Q8—2362no—
613C2×Q8—2362no—
614C2×D4—42no—
615C2×D4—594no—
616C2×D4—594no—
617C2×D4—594no—
618C2×D4—594no—
619C2×D4—594no—
620C2×D4—594no—
621C2×D4—594no—
622C2×D4—594no—
623C2×D4—594no—
624C2×D4—2362no—
625C2×D4—2362no—
626C2×D4—2362no—
627C2×D4—2362no—
628C2×D4—2362no—
629C2×D4—2362no—
630C2×D4—2362no—
631C2×D4—2362no—
632C2×D4—2362no—
633C2×D4C2×C4×D5914yes—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—591no—
639C22×C4—591no—
640C22×C4—591no—
641C22×C4—591no—
642C22×C4—591no—
643C22×C4—592no—
644C22×C4—592no—
645C22×C4—592no—
646C22×C4—592no—
647C22×C4—592no—
648C22×C4—592no—
649C22×C4—594no—
650C22×C4—594no—
651C22×C4—1182no—
652C22×C4—1182no—
653C22×C4—1182no—
654C22×C4—1182no—
655C22×C4—1182no—
656C22×C4—1182no—
657C22×C4—2362no—
658C22×C4—2362no—
659C22×C4C2×C4×D5911yescharacteristic
660C22×C4C2×C4×D5911yescharacteristic
661C22×C4C2×C4×D5911yescharacteristic
662C22×C4C2×C4×D5911yescharacteristic
663C22×C4C2×C4×D5912yes—
664C22×C4C2×C4×D5912yes—
665C22×C4C23×D5912yes—
666C22×C4C23×D5912yes—
667C22×C4C23×D5911yescharacteristic
668M16—44no—
669M16—2364no—
670M16—2364no—
671M16—2364no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—22no—
676C2×C8—44no—
677C2×C8—592no—
678C2×C8—592no—
679C2×C8—592no—
680C2×C8—592no—
681C2×C8—1182no—
682C2×C8—1182no—
683C2×C8—1182no—
684C2×C8—1182no—
685C2×C8—2364no—
686C2×C8—2364no—
687C2×C8—2364no—
688C2×C8C23×D5912yes—
689C2×C8C23×D5912yes—
690C2×C8C23×D5912yes—
691C2×C8C23×D5912yes—
692C4⋊C4—594no—
693C4⋊C4—594no—
694C4⋊C4—594no—
695C4⋊C4C2×C4×D5914yes—
696C22⋊C4—594no—
697C22⋊C4—594no—
698C22⋊C4—594no—
699C22⋊C4—594no—
700C22⋊C4—594no—
701C22⋊C4—594no—
702C22⋊C4C2×C4×D5914yes—
703C22⋊C4C2×C4×D5914yes—
704C42—592no—
705C42—594no—
706C42—594no—
707C42—592no—
708C42C2×C4×D5912yes—
709C42C23×D5912yes—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—592no—
717C23—592no—
718C23—592no—
719C23—1182no—
720C23—1182no—
721C23—1182no—
722C23—1182no—
723C23—1182no—
724C23—1182no—
725C23—1182no—
726C23—1182no—
727C23—1182no—
728C23C22×C4×D5912yes—
729C23C22×C4×D5912yes—
730C23C22×C4×D5911yescharacteristic
731Q8—2364no—
732Q8—2364no—
733D4—44no—
734D4—2364no—
735D4—2364no—
736D4—2364no—
737D4—2364no—
738D4—2364no—
739D4—2364no—
740D4—2364no—
741D4—2364no—
742D4—2364no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—592no—
754C2×C4—592no—
755C2×C4—592no—
756C2×C4—592no—
757C2×C4—592no—
758C2×C4—1182no—
759C2×C4—1182no—
760C2×C4—1182no—
761C2×C4—1182no—
762C2×C4—1182no—
763C2×C4—1182no—
764C2×C4—1182no—
765C2×C4—1182no—
766C2×C4—1182no—
767C2×C4—1182no—
768C2×C4—1182no—
769C2×C4—1184no—
770C2×C4—1184no—
771C2×C4—1184no—
772C2×C4—2364no—
773C2×C4—2364no—
774C2×C4C22×C4×D5912yes—
775C2×C4C22×C4×D5912yes—
776C2×C4C22×C4×D5912yes—
777C2×C4C22×C4×D5912yes—
778C2×C4C22×C4×D5911yescharacteristic
779C2×C4#1427377212yes—
780C2×C4#1427377312yes—
781C2×C4C24×D5911yescharacteristic
782C8—22no—
783C8—22no—
784C8—22no—
785C8—22no—
786C8—1182no—
787C8—1182no—
788C8—1182no—
789C8—1182no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—44no—
798C22—1182no—
799C22—1182no—
800C22—1182no—
801C22—1182no—
802C22—1182no—
803C22—1182no—
804C22—1182no—
805C22—1182no—
806C22—1182no—
807C22—2364no—
808C22—2364no—
809C22—2364no—
810C22#1683787412yes—
811C22#1683816712yes—
812C22#1683816812yes—
813C22C23×C4×D5911yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—22no—
818C4—1182no—
819C4—1182no—
820C4—1182no—
821C4—1182no—
822C4—1182no—
823C4#1683787412yes—
824C4C2×#1427377211yescharacteristic
825C4C2×#1427377311yescharacteristic
826C2—42no—
827C2—42no—
828C2—2362no—
829C2—2362no—
830C2—2362no—
831C2#2143316414yesdirect product factor
832C2C2×#1683787411yescharacteristic
833C2C2×#1683816711yescharacteristic
834C2C2×#1683816811yescharacteristic
subgroupG/H
centerC22×C4C23×D59
commutatorC22×C59C24×C4
FrattiniC2×C4C24×D59
FittingC2×C59×#435C2
socleC23×C59C23×C4
prime radicalC2×#16837949C2
cosocleC2×C4×C59C25
hypercenterC2×#435D59
hypocenterC59C2×#2980
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. #21433164C2direct (N × H)
3. C2×#16837476C2semidirect
4. C2×#16837475C2semidirect
5. C2×#16837474C2semidirect
6. C2×#16837473C2semidirect
7. C2×#16837472C2semidirect
8. C2×#16837471C2semidirect
9. C2×#16837470C2semidirect
10. C2×#16837458C2semidirect
11. C2×#16837457C2semidirect
12. C2×#16837370C2semidirect
13. C2×#16837368C2semidirect
14. C2×#16837367C2semidirect
15. C2×#16837367C2semidirect
16. C2×C59×#435C2semidirect
39. #16837476C22semidirect
40. #16837475C22semidirect
41. #16837474C22semidirect
42. #16837473C22semidirect
43. #16837472C22semidirect
44. #16837471C22semidirect
45. #16837470C22semidirect
46. #16837458C22semidirect
47. #16837457C22semidirect
51. #16837370C22semidirect
52. #16837368C22semidirect
53. #16837367C22semidirect
54. #16837367C22semidirect
71. C59×#435C22semidirect
418. C2×#435D59semidirect
427. C2×C59#2980semidirect
466. #435C2×D59semidirect
493. C59C2×#2980semidirect
831. C2#21433164direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379492
#214331642
C2×#168374762
C2×#168374752
C2×#168374742
C2×#168374732
C2×#168374722
C2×#168374712
C2×#168374702
C2×#168374582
C2×#168374572
C2×#168373702
C2×#168373682
C2×#168373672
C2×C59×#4352
C2×#298059