Finite Group Databasebeta

← C2×#21435199 #29460078

Subgroups — C2×#21435199 #29460078

Order 15104.

2086 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837978C211yesmaximal, characteristic, complemented
2#21435199C2116yesmaximal, direct product factor
3C2×#16837797C211yesmaximal, characteristic, complemented
4C2×#16837784C211yesmaximal, characteristic, complemented
5C2×#16837764C211yesmaximal, characteristic, complemented
6C2×#16837754C211yesmaximal, characteristic, complemented
7C2×#16837624C211yesmaximal, characteristic, complemented
8C2×#16837612C211yesmaximal, characteristic, complemented
9C2×#16837617C211yesmaximal, characteristic, complemented
10C2×#16837607C211yesmaximal, characteristic, complemented
11C2×#16837562C211yesmaximal, characteristic, complemented
12C2×#16837545C211yesmaximal, characteristic
13C2×#16837557C211yesmaximal, characteristic, complemented
14C2×#16837540C211yesmaximal, characteristic, complemented
15C2×#16837463C211yesmaximal, characteristic, complemented
16C2×C59×#542C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C23×Dic118C2211yescharacteristic
19C22×#11745672C2211yescharacteristic
20C22×#11745672C2211yescharacteristic
21C22×#11745672C2211yescharacteristic
22C22×#11745670C2211yescharacteristic
23C22×#11745670C2211yescharacteristic
24C22×#11745670C2211yescharacteristic
25C22×#11745671C2211yescharacteristic
26C22×#11745669C2211yescharacteristic
27#16837978—24no—
28#16837978C2218yescomplemented
29C2×#14273727C2211yescharacteristic
30C2×#14273727C2211yescharacteristic
31C2×#14273715C2211yescharacteristic
32C2×#14273715C2211yescharacteristic
33C2×#14273711—21no—
34C2×#14273711—21no—
35C2×#14273707—21no—
36C2×#14273707—21no—
37#16837797C2218yescomplemented
38#16837784C2218yescomplemented
39#16837764C2218yescomplemented
40#16837754C2218yescomplemented
41#16837624C2218yescomplemented
42#16837617C2218yescomplemented
43#16837612C2218yescomplemented
44#16837607C2218yescomplemented
45#16837562C2218yescomplemented
46#16837557C2218yescomplemented
47#16837545C2218yes—
48#16837540C2218yescomplemented
49#16837463C2218yescomplemented
50C2×C4⋊(C59⋊C8)C2211yescharacteristic
51C2×C4⋊(C59⋊C8)C2211yescharacteristic
52C2×#14273650C2211yescharacteristic
53C2×#14273650C2211yescharacteristic
54C2×#14273650C2211yescharacteristic
55C2×#14273650C2211yescharacteristic
56C2×#14273650C2211yescharacteristic
57C2×#14273650C2211yescharacteristic
58C2×#14273647C2211yescharacteristic
59C2×#14273647C2211yescharacteristic
60C2×C22⋊(C59⋊C8)C2211yescharacteristic
61C2×C22⋊(C59⋊C8)C2211yescharacteristic
62C2×#14273638C2211yescharacteristic
63C2×C4×C59⋊C8C2211yescharacteristic
64C59×#542—24no—
65C59×#542C2218yescomplemented
66C2×C4⋊Q8×C59C2211yescharacteristic
67C2×#126×C59—21no—
68C2×#124×C59—21no—
69C2×#124×C59C2211yescharacteristic
70C2×#123×C59—21no—
71C2×C22⋊Q8×C59—21no—
72C2×C22⋊Q8×C59C2211yescharacteristic
73C2×#121×C59C2211yescharacteristic
74C2×C4×Q8×C59C2211yescharacteristic
75C2×C4×D4×C59C2211yescharacteristic
76C2×#117×C59C2211yescharacteristic
77C2×#11745685—22no—
78C2×#11745685—42no—
79C2×#11745685—42no—
80C2×#11745685C2314yes—
81C22×Dic118—21no—
82C22×Dic118—22no—
83C22×Dic118—42no—
84C22×Dic118—42no—
85C22×Dic118C2311yescharacteristic
86C22×Dic118C2311yescharacteristic
87C22×Dic118C2311yescharacteristic
88C22×Dic118C2314yes—
89C22×D236C2311yescharacteristic
90C22×C22⋊D59—21no—
91C23×Dic59—21no—
92C22×C4×D59—21no—
93C2×#11745672—42no—
94C2×#11745672—42no—
95C2×#11745672—42no—
96C2×#11745672C2314yes—
97C2×#11745672C2314yes—
98C2×#11745672C2314yes—
99C2×#11745670—42no—
100C2×#11745670—42no—
101C2×#11745670—42no—
102C2×#11745670C2314yes—
103C2×#11745670C2314yes—
104C2×#11745670C2314yes—
105C2×#11745671—42no—
106C2×#11745671C2314yes—
107C2×#11745669—42no—
108C2×#11745669C2314yes—
109C22×C59⋊C8C2311yescharacteristic
110C22×C59⋊C8C2311yescharacteristic
111C22×C59⋊C8C2311yescharacteristic
112C22×C59⋊C8C2311yescharacteristic
113#14273727—22no—
114#14273727—22no—
115#14273727C2314yes—
116#14273727C2314yes—
117#14273715—22no—
118#14273715—22no—
119#14273715C2314yes—
120#14273715C2314yes—
121#14273711—28no—
122#14273711—28no—
123#14273707—28no—
124#14273707—28no—
125C2×C4⋊Dic59—21no—
126C2×C4⋊Dic59—21no—
127C2×C4⋊Dic59—21no—
128C2×C4⋊Dic59—21no—
129C2×(C2×D59)⋊C4—21no—
130C2×(C2×D59)⋊C4—21no—
131C2×(C2×D59)⋊C4—21no—
132C2×(C2×D59)⋊C4—21no—
133C4⋊(C59⋊C8)C2314yes—
134C4⋊(C59⋊C8)C2314yes—
135#14273650C2314yes—
136#14273650C2314yes—
137#14273650C2314yes—
138#14273650C2314yes—
139#14273650C2314yes—
140#14273650C2314yes—
141#14273647C2314yes—
142#14273647C2314yes—
143C22⋊(C59⋊C8)C2314yes—
144C22⋊(C59⋊C8)C2314yes—
145#14273638C2314yes—
146C4×C59⋊C8C2314yes—
147C22×Q8×C59—21no—
148C22×Q8×C59C2311yescharacteristic
149C22×D4×C59—21no—
150C22×D4×C59C2311yescharacteristic
151C23×C4×C59—21no—
152C23×C4×C59C2311yescharacteristic
153C4⋊Q8×C59—22no—
154C4⋊Q8×C59C2314yes—
155#126×C59—28no—
156#124×C59—28no—
157#124×C59—22no—
158#124×C59C2314yes—
159#123×C59—28no—
160C22⋊Q8×C59—22no—
161C22⋊Q8×C59—28no—
162C22⋊Q8×C59C2314yes—
163#121×C59—22no—
164#121×C59C2314yes—
165C4×Q8×C59—22no—
166C4×Q8×C59C2314yes—
167C4×D4×C59—22no—
168C4×D4×C59C2314yes—
169#117×C59D414yes—
170#117×C59C2314yes—
171C2×C4⋊C4×C59—21no—
172C2×C4⋊C4×C59—21no—
173C2×C4⋊C4×C59—21no—
174C2×C4⋊C4×C59D411yescharacteristic
175C2×C4⋊C4×C59D411yescharacteristic
176C2×C4⋊C4×C59C2311yescharacteristic
177C2×C4⋊C4×C59C2311yescharacteristic
178C2×C22⋊C4×C59—21no—
179C2×C22⋊C4×C59—21no—
180C2×C22⋊C4×C59—21no—
181C2×C22⋊C4×C59—21no—
182C2×C22⋊C4×C59—21no—
183C2×C22⋊C4×C59D411yescharacteristic
184C2×C22⋊C4×C59D411yescharacteristic
185C2×C42×C59—21no—
186C2×C42×C59C2311yescharacteristic
187C2×C42×C59C2311yescharacteristic
188C24×C59—21no—
189C24×C59C2×D411yescharacteristic
190C23×D59—21no—
191C2×Q8×C59—21no—
192C2×Q8×C59—24no—
193C2×Q8×C59—22no—
194C2×Q8×C59—22no—
195C2×Q8×C59—82no—
196C2×Q8×C59C2412yes—
197C2×D4×C59—24no—
198C2×D4×C59—21no—
199C2×D4×C59—22no—
200C2×D4×C59—22no—
201C2×D4×C59—82no—
202C2×D4×C59C2412yes—
203C22×C4×C59—22no—
204C22×C4×C59—22no—
205C22×C4×C59—21no—
206C22×C4×C59—21no—
207C22×C4×C59—21no—
208C22×C4×C59—24no—
209C22×C4×C59—82no—
210C22×C4×C59C2×D411yescharacteristic
211C22×C4×C59C2×D411yescharacteristic
212C22×C4×C59C2×D411yescharacteristic
213C22×C4×C59C2×D411yescharacteristic
214C22×C4×C59C2×D411yescharacteristic
215C22×C4×C59C2×D412yes—
216C22×C4×C59C2412yes—
217C22×C4×C59C2411yescharacteristic
218C2×C22⋊D59—24no—
219C2×C22⋊D59—44no—
220C22×Dic59—21no—
221C22×Dic59—21no—
222C22×Dic59—21no—
223C22×Dic59—24no—
224C22×Dic59—44no—
225#11745685—44no—
226#11745685—44no—
227#11745685—48no—
228C2×D236—22no—
229C2×D236—22no—
230C2×D236—21no—
231C2×D236C2412yes—
232C2×C4×D59—24no—
233C2×C4×D59—44no—
234C2×Dic118—22no—
235C2×Dic118—22no—
236C2×Dic118—22no—
237C2×Dic118—22no—
238C2×Dic118—22no—
239C2×Dic118—22no—
240C2×Dic118—24no—
241C2×Dic118—21no—
242C2×Dic118—21no—
243C2×Dic118—21no—
244C2×Dic118—44no—
245C2×Dic118—44no—
246C2×Dic118—44no—
247C2×Dic118—48no—
248C2×Dic118C2412yes—
249C2×Dic118C2412yes—
250C2×Dic118C2412yes—
251C4⋊C4×C59—24no—
252C4⋊C4×C59—24no—
253C4⋊C4×C59—24no—
254C4⋊C4×C59—21no—
255C4⋊C4×C59—21no—
256C4⋊C4×C59C2×D414yes—
257C4⋊C4×C59C2×D414yes—
258C4⋊C4×C59C2412yes—
259C4⋊C4×C59C2412yes—
260C22⋊C4×C59—24no—
261C22⋊C4×C59—24no—
262C22⋊C4×C59—24no—
263C22⋊C4×C59—24no—
264C22⋊C4×C59—24no—
265C22⋊C4×C59C2×D414yes—
266C22⋊C4×C59C2×D414yes—
267C42×C59—24no—
268C42×C59C2×D412yes—
269C42×C59C2×D412yes—
270C42×C59C2412yes—
271C42×C59C2412yes—
272#11745672—44no—
273#11745672—44no—
274#11745672—44no—
275#11745671—44no—
276#11745670—44no—
277#11745670—44no—
278#11745670—44no—
279#11745669—44no—
280(C2×D59)⋊C4—24no—
281(C2×D59)⋊C4—24no—
282(C2×D59)⋊C4—24no—
283(C2×D59)⋊C4—24no—
284C4⋊Dic59—24no—
285C4⋊Dic59—24no—
286C4⋊Dic59—24no—
287C4⋊Dic59—24no—
288C2×C59⋊C8—22no—
289C2×C59⋊C8—22no—
290C2×C59⋊C8—22no—
291C2×C59⋊C8—22no—
292C2×C59⋊C8C2412yes—
293C2×C59⋊C8C2412yes—
294C2×C59⋊C8C2412yes—
295C2×C59⋊C8C2412yes—
296C23×C59—22no—
297C23×C59—22no—
298C23×C59—22no—
299C23×C59—22no—
300C23×C59—42no—
301C23×C59—42no—
302C23×C59—42no—
303C23×C59C22×D412yes—
304C23×C59C22×D411yescharacteristic
305C22×D59—22no—
306C22×D59—42no—
307C22×D59—42no—
308C22×D59—42no—
309Q8×C59—22no—
310Q8×C59—22no—
311Q8×C59—42no—
312Q8×C59—84no—
313D4×C59—22no—
314D4×C59—22no—
315D4×C59—42no—
316D4×C59—84no—
317C2×C4×C59—22no—
318C2×C4×C59—22no—
319C2×C4×C59—22no—
320C2×C4×C59—22no—
321C2×C4×C59—22no—
322C2×C4×C59—24no—
323C2×C4×C59—22no—
324C2×C4×C59—22no—
325C2×C4×C59—22no—
326C2×C4×C59—22no—
327C2×C4×C59—22no—
328C2×C4×C59—42no—
329C2×C4×C59—42no—
330C2×C4×C59—42no—
331C2×C4×C59—84no—
332C2×C4×C59C22×D412yes—
333C2×C4×C59C22×D412yes—
334C2×C4×C59C22×D412yes—
335C2×C4×C59C22×D412yes—
336C2×C4×C59C22×D412yes—
337C2×C4×C59C22×D411yescharacteristic
338C2×C4×C59H(5,𝔽2)12yes—
339C2×C4×C59H(5,𝔽2)12yes—
340C2×C4×C59C2511yescharacteristic
341C22⋊D59—48no—
342C2×Dic59—22no—
343C2×Dic59—22no—
344C2×Dic59—22no—
345C2×Dic59—48no—
346C2×Dic59—42no—
347C2×Dic59—42no—
348C2×Dic59—42no—
349D236—22no—
350D236—22no—
351D236—42no—
352C4×D59—48no—
353Dic118—22no—
354Dic118—22no—
355Dic118—22no—
356Dic118—22no—
357Dic118—22no—
358Dic118—22no—
359Dic118—48no—
360Dic118—42no—
361Dic118—42no—
362Dic118—42no—
363C59⋊C8—22no—
364C59⋊C8—22no—
365C59⋊C8—22no—
366C59⋊C8—22no—
367C2×#3225—591nomaximal, Sylow
368C22×C59—22no—
369C22×C59—22no—
370C22×C59—22no—
371C22×C59—44no—
372C22×C59—42no—
373C22×C59—42no—
374C22×C59—42no—
375C22×C59—84no—
376C22×C59#53512yes—
377C22×C59#57712yes—
378C22×C59#57812yes—
379C22×C59C23×D411yescharacteristic
380C2×D59—42no—
381C2×D59—42no—
382C2×D59—42no—
383C2×D59—84no—
384C4×C59—22no—
385C4×C59—22no—
386C4×C59—22no—
387C4×C59—22no—
388C4×C59—22no—
389C4×C59—42no—
390C4×C59—42no—
391C4×C59—42no—
392C4×C59#53512yes—
393C4×C59C2×H(5,𝔽2)11yescharacteristic
394C4×C59C2×H(5,𝔽2)11yescharacteristic
395Dic59—42no—
396Dic59—42no—
397Dic59—42no—
398C2×#542D5911yescharacteristic, complemented
399C2×#536—591no—
400#3225—5916no—
401C2×#497—591no—
402C2×#495—591no—
403C2×#489—591no—
404C2×#487—591no—
405C2×#464—591no—
406C2×#462—591no—
407C2×#463—591no—
408C2×#461—591no—
409C2×#452—591no—
410C2×#449—591no—
411C2×#451—591no—
412C2×#448—591no—
413C2×#433—591no—
414C2×C59—42no—
415C2×C59—82no—
416C2×C59#322514yescomplemented
417C2×C59C2×#53511yescharacteristic
418C2×C59C2×#57711yescharacteristic
419C2×C59C2×#57811yescharacteristic
420D59—82no—
421C22×#41—591no—
422C23×Q8—591no—
423C22×Q16—591no—
424C22×Q16—591no—
425C22×Q16—591no—
426C22×SD16—591no—
427C22×SD16—591no—
428C22×SD16—591no—
429C22×SD16—591no—
430C22×D8—591no—
431#542—24no—
432#542C2×D5918yescomplemented
433#536—598no—
434#536—1184no—
435C2×C4⋊Q8—591no—
436C2×C4⋊Q8—591no—
437C2×C4⋊Q8C2×D5911yescharacteristic
438C2×#126—21no—
439C2×#124—21no—
440C2×#124—591no—
441C2×#124—591no—
442C2×#124C2×D5911yescharacteristic
443C2×#123—21no—
444C2×#123—1181no—
445C2×#123—1181no—
446C2×C22⋊Q8—21no—
447C2×C22⋊Q8—1181no—
448C2×C22⋊Q8—1181no—
449C2×C22⋊Q8C2×D5911yescharacteristic
450C2×#121C2×D5911yescharacteristic
451C2×C4×Q8C2×D5911yescharacteristic
452C2×C4×D4C2×D5911yescharacteristic
453C2×#117C2×D5911yescharacteristic
454#497—598no—
455#495—598no—
456#489—598no—
457#487—598no—
458#464—598no—
459#463—598no—
460#462—598no—
461#461—598no—
462#452—598no—
463#451—598no—
464#449—598no—
465#448—598no—
466#433—598no—
467C2×C4⋊C8—591no—
468C2×C4⋊C8—591no—
469C2×#103—591no—
470C2×#103—591no—
471C2×#103—591no—
472C2×#103—591no—
473C2×#103—591no—
474C2×#103—591no—
475C2×#102—591no—
476C2×#102—591no—
477C2×C22⋊C8—591no—
478C2×C22⋊C8—591no—
479C2×#97—591no—
480C2×C4×C8—591no—
481C59C2×#322511yescharacteristic, complemented, Sylow
482C2×#41—594no—
483C2×#41—1182no—
484C2×#41—2362no—
485C2×#41—2362no—
486C22×Q8—21no—
487C22×Q8—591no—
488C22×Q8—591no—
489C22×Q8—591no—
490C22×Q8—594no—
491C22×Q8—1181no—
492C22×Q8—1182no—
493C22×Q8—2362no—
494C22×Q8—2362no—
495C22×Q8C22×D5911yescharacteristic
496C22×D4—21no—
497C22×D4—591no—
498C22×D4—1181no—
499C22×D4C22×D5911yescharacteristic
500C23×C4—21no—
501C23×C4—1181no—
502C23×C4—1181no—
503C23×C4C22×D5911yescharacteristic
504C2×Q16—594no—
505C2×Q16—594no—
506C2×Q16—594no—
507C2×Q16—2362no—
508C2×Q16—2362no—
509C2×Q16—2362no—
510C2×SD16—594no—
511C2×SD16—594no—
512C2×SD16—594no—
513C2×SD16—594no—
514C2×SD16—2362no—
515C2×SD16—2362no—
516C2×SD16—2362no—
517C2×SD16—2362no—
518C2×D8—594no—
519C2×D8—2362no—
520C22×C8—591no—
521C22×C8—591no—
522C22×C8—591no—
523C22×C8—591no—
524C4⋊Q8—22no—
525C4⋊Q8—594no—
526C4⋊Q8—594no—
527C4⋊Q8—1182no—
528C4⋊Q8—1182no—
529C4⋊Q8C22×D5914yes—
530#126—28no—
531#124—28no—
532#124—22no—
533#124—594no—
534#124—594no—
535#124—1182no—
536#124—1182no—
537#124C22×D5914yes—
538#123—28no—
539#123—1188no—
540#123—1188no—
541C22⋊Q8—22no—
542C22⋊Q8—28no—
543C22⋊Q8—1188no—
544C22⋊Q8—1188no—
545C22⋊Q8C22×D5914yes—
546#121—22no—
547#121C22×D5914yes—
548C4×Q8—22no—
549C4×Q8C22×D5914yes—
550C4×D4—22no—
551C4×D4C22×D5914yes—
552#117C22⋊D5914yes—
553#117C22×D5914yes—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—1181no—
558C2×C4⋊C4—1181no—
559C2×C4⋊C4—1181no—
560C2×C4⋊C4—1181no—
561C2×C4⋊C4C22⋊D5911yescharacteristic
562C2×C4⋊C4C22⋊D5911yescharacteristic
563C2×C4⋊C4C22×D5911yescharacteristic
564C2×C4⋊C4C22×D5911yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—1181no—
571C2×C22⋊C4—1181no—
572C2×C22⋊C4—1181no—
573C2×C22⋊C4—1181no—
574C2×C22⋊C4C22⋊D5911yescharacteristic
575C2×C22⋊C4C22⋊D5911yescharacteristic
576C2×C42—21no—
577C2×C42C22×D5911yescharacteristic
578C2×C42C22×D5911yescharacteristic
579C4⋊C8—594no—
580C4⋊C8—594no—
581#103—594no—
582#103—594no—
583#103—594no—
584#103—594no—
585#103—594no—
586#103—594no—
587#102—594no—
588#102—594no—
589C22⋊C8—594no—
590C22⋊C8—594no—
591#97—594no—
592C4×C8—594no—
593C24—21no—
594C24—1181no—
595C24C2×C22⋊D5911yescharacteristic
596#41—2364no—
597#41—2364no—
598#41—2368no—
599C2×Q8—21no—
600C2×Q8—24no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—82no—
604C2×Q8—592no—
605C2×Q8—592no—
606C2×Q8—592no—
607C2×Q8—1184no—
608C2×Q8—1181no—
609C2×Q8—1181no—
610C2×Q8—1181no—
611C2×Q8—1182no—
612C2×Q8—1182no—
613C2×Q8—1182no—
614C2×Q8—1182no—
615C2×Q8—1182no—
616C2×Q8—1182no—
617C2×Q8—2364no—
618C2×Q8—2364no—
619C2×Q8—2364no—
620C2×Q8—2368no—
621C2×Q8C23×D5912yes—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—82no—
627C2×D4—592no—
628C2×D4—1184no—
629C2×D4—1181no—
630C2×D4—1182no—
631C2×D4—1182no—
632C2×D4—2364no—
633C2×D4C23×D5912yes—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—82no—
641C22×C4—1184no—
642C22×C4—1181no—
643C22×C4—1181no—
644C22×C4—1181no—
645C22×C4—1184no—
646C22×C4—2364no—
647C22×C4—2364no—
648C22×C4C2×C22⋊D5912yes—
649C22×C4C2×C22⋊D5911yescharacteristic
650C22×C4C2×C22⋊D5911yescharacteristic
651C22×C4C2×C22⋊D5911yescharacteristic
652C22×C4C2×C22⋊D5911yescharacteristic
653C22×C4C2×C22⋊D5911yescharacteristic
654C22×C4C23×D5912yes—
655C22×C4C23×D5911yescharacteristic
656Q16—2364no—
657Q16—2364no—
658Q16—2364no—
659SD16—2364no—
660SD16—2364no—
661SD16—2364no—
662SD16—2364no—
663D8—2364no—
664C2×C8—592no—
665C2×C8—592no—
666C2×C8—592no—
667C2×C8—592no—
668C2×C8—1182no—
669C2×C8—1182no—
670C2×C8—1182no—
671C2×C8—1182no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—1184no—
678C4⋊C4—1184no—
679C4⋊C4—1184no—
680C4⋊C4—1184no—
681C4⋊C4C2×C22⋊D5914yes—
682C4⋊C4C2×C22⋊D5914yes—
683C4⋊C4C23×D5912yes—
684C4⋊C4C23×D5912yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—1184no—
691C22⋊C4—1184no—
692C22⋊C4—1184no—
693C22⋊C4—1184no—
694C22⋊C4C2×C22⋊D5914yes—
695C22⋊C4C2×C22⋊D5914yes—
696C42—24no—
697C42C2×C22⋊D5912yes—
698C42C2×C22⋊D5912yes—
699C42C23×D5912yes—
700C42C23×D5912yes—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—1182no—
709C23—2362no—
710C23—2362no—
711C23—2362no—
712C23C22×C22⋊D5912yes—
713C23C22×C22⋊D5911yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—84no—
718Q8—1182no—
719Q8—1182no—
720Q8—1182no—
721Q8—1182no—
722Q8—1182no—
723Q8—1182no—
724Q8—2368no—
725Q8—2362no—
726Q8—2362no—
727Q8—2362no—
728D4—22no—
729D4—22no—
730D4—42no—
731D4—84no—
732D4—1182no—
733D4—1182no—
734D4—2368no—
735D4—2362no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—84no—
751C2×C4—1182no—
752C2×C4—1182no—
753C2×C4—1182no—
754C2×C4—2368no—
755C2×C4—2368no—
756C2×C4—2362no—
757C2×C4—2362no—
758C2×C4—2362no—
759C2×C4C22×C22⋊D5912yes—
760C2×C4C22×C22⋊D5912yes—
761C2×C4C22×C22⋊D5912yes—
762C2×C4C22×C22⋊D5912yes—
763C2×C4C22×C22⋊D5912yes—
764C2×C4C22×C22⋊D5911yescharacteristic
765C2×C4#1427377312yes—
766C2×C4#1427377312yes—
767C2×C4C24×D5911yescharacteristic
768C8—1182no—
769C8—1182no—
770C8—1182no—
771C8—1182no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—44no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—84no—
780C22—4724no—
781C22—2362no—
782C22—2362no—
783C22—2362no—
784C22#1683796612yes—
785C22#1683821312yes—
786C22#1683821712yes—
787C22C23×C22⋊D5911yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—2362no—
797C4—2362no—
798C4—2362no—
799C4#1683796612yes—
800C4C2×#1427377311yescharacteristic
801C4C2×#1427377311yescharacteristic
802C2—42no—
803C2—82no—
804C2—4722no—
805C2#2143519914yesdirect product factor
806C2C2×#1683796611yescharacteristic
807C2C2×#1683821311yescharacteristic
808C2C2×#1683821711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#542C2
socleC23×C59C22×D4
prime radicalC2×#16837545C2
hypercenterC2×#542D59
hypocenterC59C2×#3225
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#16837978C2semidirect
2. #21435199C2direct (N × H)
3. C2×#16837797C2semidirect
4. C2×#16837784C2semidirect
5. C2×#16837764C2semidirect
6. C2×#16837754C2semidirect
7. C2×#16837624C2semidirect
8. C2×#16837612C2semidirect
9. C2×#16837617C2semidirect
10. C2×#16837607C2semidirect
11. C2×#16837562C2semidirect
13. C2×#16837557C2semidirect
14. C2×#16837540C2semidirect
15. C2×#16837463C2semidirect
16. C2×C59×#542C2semidirect
28. #16837978C22semidirect
37. #16837797C22semidirect
38. #16837784C22semidirect
39. #16837764C22semidirect
40. #16837754C22semidirect
41. #16837624C22semidirect
42. #16837617C22semidirect
43. #16837612C22semidirect
44. #16837607C22semidirect
45. #16837562C22semidirect
46. #16837557C22semidirect
48. #16837540C22semidirect
49. #16837463C22semidirect
65. C59×#542C22semidirect
398. C2×#542D59semidirect
416. C2×C59#3225semidirect
432. #542C2×D59semidirect
481. C59C2×#3225semidirect
805. C2#21435199direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379782
#214351992
C2×#168377972
C2×#168377842
C2×#168377642
C2×#168377542
C2×#168376242
C2×#168376122
C2×#168376172
C2×#168376072
C2×#168375622
C2×#168375452
C2×#168375572
C2×#168375402
C2×#168374632
C2×C59×#5422
C2×#322559