Finite Group Databasebeta

← C2×#21437041 #29469216

Subgroups — C2×#21437041 #29469216

Order 15104.

1822 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838130C211yesmaximal, characteristic, complemented
2#21437041C2116yesmaximal, direct product factor
3C2×#16837812C211yesmaximal, characteristic, complemented
4C2×#16837808C211yesmaximal, characteristic, complemented
5C2×#16837801C211yesmaximal, characteristic, complemented
6C2×#16837706C211yesmaximal, characteristic, complemented
7C2×#16837706C211yesmaximal, characteristic, complemented
8C2×#16837684C211yesmaximal, characteristic, complemented
9C2×#16837702C211yesmaximal, characteristic
10C2×#16837702C211yesmaximal, characteristic
11C2×#16837692C211yesmaximal, characteristic
12C2×#16837533C211yesmaximal, characteristic, complemented
13C2×#16837502C211yesmaximal, characteristic
14C2×#16837502C211yesmaximal, characteristic
15C2×C4×#11745670C211yesmaximal, characteristic
16C2×C59×#554C211yesmaximal, characteristic
17C22×#11745670C2211yescharacteristic
18#16838130—24no—
19#16838130C2218yescomplemented
20C2×#14273727C2211yescharacteristic
21C2×#14273725—21no—
22C2×#14273719C2211yescharacteristic
23C2×#14273719C2211yescharacteristic
24C2×#14273717—21no—
25C2×#14273717—21no—
26C2×C4×Dic118C2211yescharacteristic
27C2×C4×Dic118C2211yescharacteristic
28C2×C4×Dic118C2211yescharacteristic
29C2×#14273692—21no—
30#16837812C2218yescomplemented
31#16837808C2218yescomplemented
32#16837801C2218yescomplemented
33#16837706C2218yescomplemented
34#16837706C2218yescomplemented
35#16837702C2218yes—
36#16837702C2218yes—
37#16837692C2218yes—
38#16837684C2218yescomplemented
39#16837533C2218yescomplemented
40#16837502C2218yes—
41#16837502C2218yes—
42C4×#11745670C2218yes—
43C2×#14273660C2211yescharacteristic
44C2×#14273660C2211yescharacteristic
45C2×#14273660C2211yescharacteristic
46C2×#14273660C2211yescharacteristic
47C2×#14273658C2211yescharacteristic
48C2×#14273658C2211yescharacteristic
49C2×#14273658C2211yescharacteristic
50C2×#14273658C2211yescharacteristic
51C2×#14273658C2211yescharacteristic
52C2×C4⋊(C59⋊C8)C2211yescharacteristic
53C2×C4⋊(C59⋊C8)C2211yescharacteristic
54C2×C4⋊(C59⋊C8)C2211yescharacteristic
55C2×#14273650C2211yescharacteristic
56C2×#14273650C2211yescharacteristic
57C2×#14273650C2211yescharacteristic
58C2×#14273648C2211yescharacteristic
59C2×#14273648C2211yescharacteristic
60C2×#14273648C2211yescharacteristic
61C2×#14273638C2211yescharacteristic
62C2×#14273638C2211yescharacteristic
63C2×C4×C59⋊C8C2211yescharacteristic
64C59×#554—24no—
65C59×#554C2218yes—
66C2×C4⋊Q8×C59C2211yescharacteristic
67C2×#125×C59C2211yescharacteristic
68C2×#125×C59C2211yescharacteristic
69C2×C22⋊Q8×C59—21no—
70C2×C22⋊Q8×C59—21no—
71C2×C22⋊Q8×C59—21no—
72C2×C4×Q8×C59C2211yescharacteristic
73C2×C4×D4×C59C2211yescharacteristic
74C2×C4×D4×C59C2211yescharacteristic
75C2×C4×D4×C59C2211yescharacteristic
76C22×C4⋊C4×C59—21no—
77C22×Dic118—21no—
78C22×Dic118C2311yescharacteristic
79C2×#11745670Q818yescomplemented
80C2×#11745670C2314yes—
81C22×C59⋊C8C2311yescharacteristic
82C22×C59⋊C8C2311yescharacteristic
83C22×C59⋊C8C2311yescharacteristic
84C22×C59⋊C8C2311yescharacteristic
85#14273727—22no—
86#14273727C2314yes—
87#14273725—28no—
88#14273719—22no—
89#14273719—22no—
90#14273719C2314yes—
91#14273719C2314yes—
92#14273717—28no—
93#14273717—28no—
94C4×Dic118—22no—
95C4×Dic118—22no—
96C4×Dic118—22no—
97C4×Dic118C2314yes—
98C4×Dic118C2314yes—
99C4×Dic118C2314yes—
100#14273692—28no—
101C2×C4⋊Dic59—21no—
102C2×C4⋊Dic59C2311yescharacteristic
103C2×C4⋊Dic59C2311yescharacteristic
104C2×C4⋊Dic59C2311yescharacteristic
105C2×Dic59⋊C4—21no—
106C2×Dic59⋊C4—21no—
107C2×Dic59⋊C4—21no—
108C2×Dic59⋊C4—21no—
109C2×Dic59⋊C4—21no—
110C2×Dic59⋊C4—21no—
111C2×Dic59⋊C4—21no—
112C2×C4×Dic59—21no—
113C2×C4×Dic59—21no—
114C2×C4×Dic59—21no—
115#14273660C2314yes—
116#14273660C2314yes—
117#14273660C2314yes—
118#14273660C2314yes—
119#14273658C2314yes—
120#14273658C2314yes—
121#14273658C2314yes—
122#14273658C2314yes—
123#14273658C2314yes—
124C4⋊(C59⋊C8)C2314yes—
125C4⋊(C59⋊C8)C2314yes—
126C4⋊(C59⋊C8)C2314yes—
127#14273650C2314yes—
128#14273650C2314yes—
129#14273650C2314yes—
130#14273648C2314yes—
131#14273648C2314yes—
132#14273648C2314yes—
133#14273638C2314yes—
134#14273638C2314yes—
135C4×C59⋊C8C2314yes—
136C22×Q8×C59—21no—
137C22×Q8×C59D411yescharacteristic
138C22×D4×C59C2311yescharacteristic
139C23×C4×C59—21no—
140C23×C4×C59—21no—
141C23×C4×C59—21no—
142C4⋊Q8×C59—22no—
143C4⋊Q8×C59C2314yes—
144#125×C59—22no—
145#125×C59—22no—
146#125×C59C2314yes—
147#125×C59C2314yes—
148C22⋊Q8×C59—28no—
149C22⋊Q8×C59—28no—
150C22⋊Q8×C59—28no—
151C4×Q8×C59D414yes—
152C4×Q8×C59C2314yes—
153C4×D4×C59—22no—
154C4×D4×C59—22no—
155C4×D4×C59—22no—
156C4×D4×C59C2314yes—
157C4×D4×C59C2314yes—
158C4×D4×C59C2314yes—
159C2×C4⋊C4×C59—21no—
160C2×C4⋊C4×C59—21no—
161C2×C4⋊C4×C59—21no—
162C2×C4⋊C4×C59—21no—
163C2×C4⋊C4×C59—21no—
164C2×C4⋊C4×C59—28no—
165C2×C4⋊C4×C59D411yescharacteristic
166C2×C4⋊C4×C59D411yescharacteristic
167C2×C4⋊C4×C59D411yescharacteristic
168C2×C4⋊C4×C59C2311yescharacteristic
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C22⋊C4×C59—21no—
172C2×C22⋊C4×C59—21no—
173C2×C22⋊C4×C59—21no—
174C2×C42×C59C2311yescharacteristic
175C2×C42×C59C2311yescharacteristic
176C2×C42×C59C2311yescharacteristic
177C24×C59—21no—
178C2×Q8×C59—24no—
179C2×Q8×C59—42no—
180C2×Q8×C59—82no—
181C2×Q8×C59C2×D414yes—
182C2×D4×C59—21no—
183C2×D4×C59—22no—
184C2×D4×C59C2×Q814yes—
185C2×D4×C59C2412yes—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—24no—
190C22×C4×C59—24no—
191C22×C4×C59—24no—
192C22×C4×C59—44no—
193C22×C4×C59—82no—
194C22×C4×C59—82no—
195C22×C4×C59C2×D411yescharacteristic
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59C2×D411yescharacteristic
201C22×C4×C59C2411yescharacteristic
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59—21no—
205C22×Dic59—21no—
206C2×Dic118—21no—
207C2×Dic118—22no—
208C2×Dic118—24no—
209C2×Dic118—44no—
210C2×Dic118C2×Q814yes—
211C2×Dic118C2412yes—
212C4⋊C4×C59—24no—
213C4⋊C4×C59—24no—
214C4⋊C4×C59—24no—
215C4⋊C4×C59—24no—
216C4⋊C4×C59—24no—
217C4⋊C4×C59—21no—
218C4⋊C4×C59—21no—
219C4⋊C4×C59—21no—
220C4⋊C4×C59C2×D414yes—
221C4⋊C4×C59C2×D414yes—
222C4⋊C4×C59C2×D414yes—
223C4⋊C4×C59C2412yes—
224C4⋊C4×C59C2412yes—
225C4⋊C4×C59C2412yes—
226C22⋊C4×C59—24no—
227C22⋊C4×C59—24no—
228C22⋊C4×C59—24no—
229C42×C59C2×D412yes—
230C42×C59C2×D412yes—
231C42×C59C2×D412yes—
232C42×C59C2412yes—
233C42×C59C2412yes—
234C42×C59C2412yes—
235#11745670C2×Q8116yescomplemented
236C4⋊Dic59—24no—
237C4⋊Dic59—21no—
238C4⋊Dic59—21no—
239C4⋊Dic59—21no—
240C4⋊Dic59C2412yes—
241C4⋊Dic59C2412yes—
242C4⋊Dic59C2412yes—
243Dic59⋊C4—24no—
244Dic59⋊C4—24no—
245Dic59⋊C4—24no—
246Dic59⋊C4—24no—
247Dic59⋊C4—24no—
248Dic59⋊C4—24no—
249Dic59⋊C4—24no—
250C4×Dic59—24no—
251C4×Dic59—24no—
252C4×Dic59—24no—
253C2×C59⋊C8—22no—
254C2×C59⋊C8—22no—
255C2×C59⋊C8—22no—
256C2×C59⋊C8C2×Q814yes—
257C2×C59⋊C8C2412yes—
258C2×C59⋊C8C2412yes—
259C2×C59⋊C8C2412yes—
260C2×C59⋊C8C2412yes—
261C23×C59—24no—
262C23×C59—22no—
263C23×C59—42no—
264C23×C59—42no—
265C23×C59C22×D411yescharacteristic
266Q8×C59—44no—
267Q8×C59—84no—
268D4×C59—24no—
269D4×C59—22no—
270D4×C59C22×Q814yes—
271C2×C4×C59—22no—
272C2×C4×C59—22no—
273C2×C4×C59—22no—
274C2×C4×C59—22no—
275C2×C4×C59—22no—
276C2×C4×C59—22no—
277C2×C4×C59—22no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—48no—
281C2×C4×C59—42no—
282C2×C4×C59—42no—
283C2×C4×C59—42no—
284C2×C4×C59—84no—
285C2×C4×C59—84no—
286C2×C4×C59C22×D412yes—
287C2×C4×C59C22×D412yes—
288C2×C4×C59C22×D412yes—
289C2×C4×C59C22×D412yes—
290C2×C4×C59C22×D412yes—
291C2×C4×C59C22×D412yes—
292C2×C4×C59C22×D411yescharacteristic
293C2×C4×C59C22×Q812yes—
294C2×C4×C592−1+412yes—
295C2×C4×C59C2511yescharacteristic
296C2×Dic59—24no—
297C2×Dic59—22no—
298C2×Dic59—22no—
299C2×Dic59—22no—
300C2×Dic59—22no—
301C2×Dic59—42no—
302C2×Dic59—42no—
303C2×Dic59—42no—
304Dic118—24no—
305Dic118—22no—
306Dic118—48no—
307Dic118C22×Q814yes—
308C59⋊C8—22no—
309C59⋊C8—22no—
310C59⋊C8—22no—
311C59⋊C8C22×Q814yes—
312C2×#3388—591nomaximal, Sylow
313C22×C59—24no—
314C22×C59—48no—
315C22×C59—42no—
316C22×C59—42no—
317C22×C59D4×Q812yes—
318C22×C59#57512yes—
319C22×C59#57712yes—
320C22×C59C23×D411yescharacteristic
321C4×C59—22no—
322C4×C59—22no—
323C4×C59—22no—
324C4×C59—22no—
325C4×C59—22no—
326C4×C59—22no—
327C4×C59—42no—
328C4×C59—42no—
329C4×C59—42no—
330C4×C59D4×Q812yes—
331C4×C59C23×Q811yescharacteristic
332C4×C59C2×2−1+411yescharacteristic
333Dic59—24no—
334Dic59—42no—
335Dic59—42no—
336Dic59—42no—
337C2×#557—591no—
338C2×#554D5911yescharacteristic
339#3388—5916no—
340C2×#501—591no—
341C2×#501—591no—
342C2×#499—591no—
343C2×#479—591no—
344C2×#479—591no—
345C2×#475—591no—
346C2×#478—591no—
347C2×#478—591no—
348C2×#476—591no—
349C2×#446—591no—
350C2×#440—591no—
351C2×#440—591no—
352C2×C4×SD16—591no—
353C2×C59—44no—
354C2×C59#338814yescomplemented
355C2×C59C2×D4×Q811yescharacteristic
356C2×C59C2×#57511yescharacteristic
357C2×C59C2×#57711yescharacteristic
358C22×SD16—591no—
359#557—598no—
360#557—1184no—
361#554—24no—
362#554C2×D5918yes—
363C2×C4⋊Q8—591no—
364C2×C4⋊Q8—1181no—
365C2×C4⋊Q8C2×D5911yescharacteristic
366C2×#125—591no—
367C2×#125—591no—
368C2×#125—1181no—
369C2×#125—1181no—
370C2×#125C2×D5911yescharacteristic
371C2×#125C2×D5911yescharacteristic
372C2×C22⋊Q8—21no—
373C2×C22⋊Q8—21no—
374C2×C22⋊Q8—21no—
375C2×C4×Q8—591no—
376C2×C4×Q8—591no—
377C2×C4×Q8—591no—
378C2×C4×Q8—1181no—
379C2×C4×Q8C2×D5911yescharacteristic
380C2×C4×D4C2×D5911yescharacteristic
381C2×C4×D4C2×D5911yescharacteristic
382C2×C4×D4C2×D5911yescharacteristic
383C22×C4⋊C4—21no—
384#501—598no—
385#501—598no—
386#499—598no—
387#479—598no—
388#479—598no—
389#478—598no—
390#478—598no—
391#476—598no—
392#475—598no—
393#446—598no—
394#440—598no—
395#440—598no—
396C4×SD16—598no—
397C2×#107—591no—
398C2×#107—591no—
399C2×#107—591no—
400C2×#107—591no—
401C2×#106—591no—
402C2×#106—591no—
403C2×#106—591no—
404C2×#106—591no—
405C2×#106—591no—
406C2×C4⋊C8—591no—
407C2×C4⋊C8—591no—
408C2×C4⋊C8—591no—
409C2×#103—591no—
410C2×#103—591no—
411C2×#103—591no—
412C2×#102—591no—
413C2×#102—591no—
414C2×#102—591no—
415C2×#97—591no—
416C2×#97—591no—
417C2×C4×C8—591no—
418C59C2×#338811yescharacteristic, complemented, Sylow
419C22×Q8—21no—
420C22×Q8—591no—
421C22×Q8—1181no—
422C22×Q8C22⋊D5911yescharacteristic
423C22×D4C22×D5911yescharacteristic
424C23×C4—21no—
425C23×C4—21no—
426C23×C4—21no—
427C2×SD16—598no—
428C2×SD16—594no—
429C22×C8—591no—
430C22×C8—591no—
431C22×C8—591no—
432C22×C8—591no—
433C4⋊Q8—22no—
434C4⋊Q8—594no—
435C4⋊Q8—1188no—
436C4⋊Q8—1182no—
437C4⋊Q8C22×D5914yes—
438#125—22no—
439#125—22no—
440#125—594no—
441#125—594no—
442#125—1188no—
443#125—1188no—
444#125—1182no—
445#125—1182no—
446#125C22×D5914yes—
447#125C22×D5914yes—
448C22⋊Q8—28no—
449C22⋊Q8—28no—
450C22⋊Q8—28no—
451C4×Q8—594no—
452C4×Q8—594no—
453C4×Q8—594no—
454C4×Q8—1188no—
455C4×Q8—1182no—
456C4×Q8—1182no—
457C4×Q8—1182no—
458C4×Q8C22⋊D5914yes—
459C4×Q8C22×D5914yes—
460C4×D4—22no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4C22×D5914yes—
464C4×D4C22×D5914yes—
465C4×D4C22×D5914yes—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—28no—
472C2×C4⋊C4—591no—
473C2×C4⋊C4—591no—
474C2×C4⋊C4—591no—
475C2×C4⋊C4—1181no—
476C2×C4⋊C4—1181no—
477C2×C4⋊C4—1181no—
478C2×C4⋊C4—1181no—
479C2×C4⋊C4—1181no—
480C2×C4⋊C4—1181no—
481C2×C4⋊C4—1181no—
482C2×C4⋊C4—1181no—
483C2×C4⋊C4C22⋊D5911yescharacteristic
484C2×C4⋊C4C22⋊D5911yescharacteristic
485C2×C4⋊C4C22⋊D5911yescharacteristic
486C2×C4⋊C4C22×D5911yescharacteristic
487C2×C4⋊C4C22×D5911yescharacteristic
488C2×C4⋊C4C22×D5911yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C42—1181no—
493C2×C42—1181no—
494C2×C42—1181no—
495C2×C42C22×D5911yescharacteristic
496C2×C42C22×D5911yescharacteristic
497C2×C42C22×D5911yescharacteristic
498#107—594no—
499#107—594no—
500#107—594no—
501#107—594no—
502#106—594no—
503#106—594no—
504#106—594no—
505#106—594no—
506#106—594no—
507C4⋊C8—594no—
508C4⋊C8—594no—
509C4⋊C8—594no—
510#103—594no—
511#103—594no—
512#103—594no—
513#102—594no—
514#102—594no—
515#102—594no—
516#97—594no—
517#97—594no—
518C4×C8—594no—
519C24—21no—
520C2×Q8—24no—
521C2×Q8—42no—
522C2×Q8—82no—
523C2×Q8—594no—
524C2×Q8—592no—
525C2×Q8—1181no—
526C2×Q8—1184no—
527C2×Q8—1182no—
528C2×Q8—2364no—
529C2×Q8C2×C22⋊D5914yes—
530C2×D4—21no—
531C2×D4—22no—
532C2×D4Q8×D5914yes—
533C2×D4C23×D5912yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—44no—
541C22×C4—82no—
542C22×C4—82no—
543C22×C4—1181no—
544C22×C4—1181no—
545C22×C4—1181no—
546C22×C4—1181no—
547C22×C4C2×C22⋊D5911yescharacteristic
548C22×C4C2×C22⋊D5911yescharacteristic
549C22×C4C2×C22⋊D5911yescharacteristic
550C22×C4C2×C22⋊D5911yescharacteristic
551C22×C4C2×C22⋊D5911yescharacteristic
552C22×C4C2×C22⋊D5911yescharacteristic
553C22×C4C23×D5911yescharacteristic
554SD16—5916no—
555C2×C8—594no—
556C2×C8—592no—
557C2×C8—592no—
558C2×C8—592no—
559C2×C8—592no—
560C2×C8—1182no—
561C2×C8—1182no—
562C2×C8—1182no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—592no—
572C4⋊C4—592no—
573C4⋊C4—592no—
574C4⋊C4—1181no—
575C4⋊C4—1181no—
576C4⋊C4—1181no—
577C4⋊C4—1184no—
578C4⋊C4—1184no—
579C4⋊C4—1184no—
580C4⋊C4—1184no—
581C4⋊C4—1184no—
582C4⋊C4—1184no—
583C4⋊C4—1184no—
584C4⋊C4—1184no—
585C4⋊C4C2×C22⋊D5914yes—
586C4⋊C4C2×C22⋊D5914yes—
587C4⋊C4C2×C22⋊D5914yes—
588C4⋊C4C23×D5912yes—
589C4⋊C4C23×D5912yes—
590C4⋊C4C23×D5912yes—
591C22⋊C4—24no—
592C22⋊C4—24no—
593C22⋊C4—24no—
594C42—1184no—
595C42—1184no—
596C42—1184no—
597C42C2×C22⋊D5912yes—
598C42C2×C22⋊D5912yes—
599C42C2×C22⋊D5912yes—
600C42C23×D5912yes—
601C42C23×D5912yes—
602C42C23×D5912yes—
603C23—22no—
604C23—24no—
605C23—42no—
606C23—42no—
607C23C22×C22⋊D5911yescharacteristic
608Q8—44no—
609Q8—84no—
610Q8—594no—
611Q8—1182no—
612Q8—1184no—
613Q8—2368no—
614D4—22no—
615D4—24no—
616D4C2×Q8×D5914yes—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—48no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—84no—
631C2×C4—84no—
632C2×C4—1182no—
633C2×C4—1184no—
634C2×C4—1182no—
635C2×C4—1182no—
636C2×C4—1182no—
637C2×C4—2362no—
638C2×C4—2362no—
639C2×C4—2362no—
640C2×C4C22×C22⋊D5912yes—
641C2×C4C22×C22⋊D5912yes—
642C2×C4C22×C22⋊D5912yes—
643C2×C4C22×C22⋊D5912yes—
644C2×C4C22×C22⋊D5912yes—
645C2×C4C22×C22⋊D5912yes—
646C2×C4C22×C22⋊D5911yescharacteristic
647C2×C4C2×Q8×D5912yes—
648C2×C4#1427377512yes—
649C2×C4C24×D5911yescharacteristic
650C8—594no—
651C8—1182no—
652C8—1182no—
653C8—1182no—
654C22—24no—
655C22—48no—
656C22—42no—
657C22—42no—
658C22Q8×C22⋊D5912yes—
659C22#1683820012yes—
660C22#1683821312yes—
661C22C23×C22⋊D5911yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—22no—
666C4—22no—
667C4—22no—
668C4—42no—
669C4—42no—
670C4—42no—
671C4—1184no—
672C4—2362no—
673C4—2362no—
674C4—2362no—
675C4Q8×C22⋊D5912yes—
676C4C22×Q8×D5911yescharacteristic
677C4C2×#1427377511yescharacteristic
678C2—44no—
679C2#2143704114yesdirect product factor
680C2C2×Q8×C22⋊D5911yescharacteristic
681C2C2×#1683820011yescharacteristic
682C2C2×#1683821311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#554C2
socleC23×C59C22×D4
prime radicalC22×D4×C59C23
hypercenterC2×#554D59
hypocenterC59C2×#3388
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#16838130C2semidirect
2. #21437041C2direct (N × H)
3. C2×#16837812C2semidirect
4. C2×#16837808C2semidirect
5. C2×#16837801C2semidirect
6. C2×#16837706C2semidirect
7. C2×#16837706C2semidirect
8. C2×#16837684C2semidirect
12. C2×#16837533C2semidirect
19. #16838130C22semidirect
30. #16837812C22semidirect
31. #16837808C22semidirect
32. #16837801C22semidirect
33. #16837706C22semidirect
34. #16837706C22semidirect
38. #16837684C22semidirect
39. #16837533C22semidirect
79. C2×#11745670Q8semidirect
235. #11745670C2×Q8semidirect
354. C2×C59#3388semidirect
418. C59C2×#3388semidirect
679. C2#21437041direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381302
#214370412
C2×#168378122
C2×#168378082
C2×#168378012
C2×#168377062
C2×#168376842
C2×#168377022
C2×#168376922
C2×#168375332
C2×#168375022
C2×C4×#117456702
C2×C59×#5542
C2×#338859