Finite Group Databasebeta

← C2×#21436547 #29467232

Subgroups — C2×#21436547 #29467232

Order 15104.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838107C211yesmaximal, characteristic
2C2×#16838087C211yesmaximal, characteristic
3#21436547C2116yesmaximal, direct product factor
4C2×#16837809C211yesmaximal, characteristic, complemented
5C2×#16837737C211yesmaximal, characteristic, complemented
6C2×#16837746C211yesmaximal, characteristic, complemented
7C2×#16837734C211yesmaximal, characteristic, complemented
8C2×#16837732C211yesmaximal, characteristic, complemented
9C2×#16837712C211yesmaximal, characteristic, complemented
10C2×#16837686C211yesmaximal, characteristic, complemented
11C2×#16837661C211yesmaximal, characteristic, complemented
12C2×#16837643C211yesmaximal, characteristic, complemented
13C2×#16837508C211yesmaximal, characteristic, complemented
14C2×#16837473C211yesmaximal, characteristic
15C2×#16837441C211yesmaximal, characteristic, complemented
16C22×#106×C59C211yesmaximal, characteristic, complemented
17C22×Dic236C2211yescharacteristic
18C22×#11745659C2211yescharacteristic
19#16838107—24no—
20#16838107C2218yes—
21#16838087—24no—
22#16838087C2218yes—
23C2×#14273726C2211yescharacteristic
24C2×#14273722—21no—
25C2×#14273718C2211yescharacteristic
26C2×#14273717—21no—
27C2×#14273717—21no—
28C2×#14273710—21no—
29C2×#14273707C2211yescharacteristic
30C2×#14273707C2211yescharacteristic
31C2×#14273706—21no—
32C2×#14273706C2211yescharacteristic
33C2×#14273706C2211yescharacteristic
34C2×#14273705—21no—
35C2×#14273692C2211yescharacteristic
36C2×#14273692C2211yescharacteristic
37C2×C4×C22⋊D59—21no—
38C2×C4×C22⋊D59C2211yescharacteristic
39C2×#14273686—21no—
40C2×#14273685C2211yescharacteristic
41C2×C4⋊C4×D59C2211yescharacteristic
42#16837809C2218yescomplemented
43#16837746C2218yescomplemented
44#16837737C2218yescomplemented
45#16837734C2218yescomplemented
46#16837732C2218yescomplemented
47#16837712C2218yescomplemented
48#16837686C2218yescomplemented
49#16837661C2218yescomplemented
50#16837643C2218yescomplemented
51#16837508C2218yescomplemented
52#16837473C2218yes—
53#16837441C2218yescomplemented
54C2×#14273661C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×#14273658C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273652C2211yescharacteristic
62C2×#14273650C2211yescharacteristic
63C2×#14273650C2211yescharacteristic
64C2×#14273650C2211yescharacteristic
65C2×#14273650C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×#14273637C2211yescharacteristic
69C23×C8×C59C2211yescharacteristic
70C22×C4⋊C4×C59C2211yescharacteristic
71C22×C4⋊C4×C59C2211yescharacteristic
72C2×#106×C59C2211yescharacteristic
73C2×#106×C59C2211yescharacteristic
74C2×#106×C59C2211yescharacteristic
75C2×#106×C59C2211yescharacteristic
76C2×#106×C59C2218yescomplemented
77C22×Dic118—21no—
78C22×Dic118C2311yescharacteristic
79C22×Dic118C2311yescharacteristic
80C22×C22⋊D59D411yescharacteristic
81C22×C4×D59—21no—
82C22×C4×D59C2311yescharacteristic
83C2×Dic236—24no—
84C2×Dic236C2314yes—
85C2×#11745659—24no—
86C2×#11745659C2314yes—
87C22×C59⋊C8C2311yescharacteristic
88C22×C59⋊C8C2311yescharacteristic
89#14273726—22no—
90#14273726C2314yes—
91#14273722—28no—
92#14273718—22no—
93#14273718C2314yes—
94#14273717—28no—
95#14273717—28no—
96#14273710—28no—
97#14273707—22no—
98#14273707—22no—
99#14273707C2314yes—
100#14273707C2314yes—
101#14273706—22no—
102#14273706—22no—
103#14273706—28no—
104#14273706C2314yes—
105#14273706C2314yes—
106#14273705—28no—
107#14273692—22no—
108#14273692—22no—
109#14273692C2314yes—
110#14273692C2314yes—
111C4×C22⋊D59—28no—
112C4×C22⋊D59D414yes—
113C4×C22⋊D59C2314yes—
114#14273686—28no—
115#14273685—22no—
116#14273685C2314yes—
117C2×C4⋊Dic59—21no—
118C2×C4⋊Dic59—21no—
119C2×C4⋊Dic59—21no—
120C2×C4⋊Dic59C2311yescharacteristic
121C2×C4⋊Dic59C2311yescharacteristic
122C2×Dic59⋊C4—21no—
123C2×Dic59⋊C4—21no—
124C2×Dic59⋊C4—21no—
125C2×Dic59⋊C4—21no—
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4D411yescharacteristic
130C4⋊C4×D59—22no—
131C4⋊C4×D59C2314yes—
132C2×C22⋊Dic59—21no—
133C2×C22⋊Dic59—21no—
134C2×C22⋊Dic59D411yescharacteristic
135C2×(C2×D59)⋊C4—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4D411yescharacteristic
139C2×C4×Dic59—21no—
140C2×C4×Dic59—21no—
141C2×C4×Dic59—21no—
142C2×C4×Dic59C2311yescharacteristic
143#14273661C2314yes—
144#14273660C2314yes—
145#14273660C2314yes—
146#14273658C2314yes—
147#14273658C2314yes—
148Dic59⋊C8C2314yes—
149#14273652C2314yes—
150#14273652C2314yes—
151#14273650C2314yes—
152#14273650C2314yes—
153#14273650C2314yes—
154#14273650C2314yes—
155C22⋊(C59⋊C8)C2314yes—
156(C2×D59)⋊C8C2314yes—
157#14273637C2314yes—
158C23×C4×C59—21no—
159C23×C4×C59—21no—
160C23×C4×C59C2311yescharacteristic
161C22×C8×C59—24no—
162C22×C8×C59C2314yes—
163C22×C8×C59C2311yescharacteristic
164C22×C8×C59C2311yescharacteristic
165C2×C4⋊C4×C59—21no—
166C2×C4⋊C4×C59—21no—
167C2×C4⋊C4×C59—22no—
168C2×C4⋊C4×C59—22no—
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C4⋊C4×C59C2314yes—
174C2×C4⋊C4×C59C2314yes—
175#106×C59C2314yes—
176#106×C59C2314yes—
177#106×C59C2314yes—
178#106×C59C2314yes—
179C24×C59C2×D411yescharacteristic
180C23×D59C2×D411yescharacteristic
181C22×C4×C59—22no—
182C22×C4×C59—22no—
183C22×C4×C59—21no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—24no—
188C22×C4×C59—24no—
189C22×C4×C59—44no—
190C22×C4×C59—82no—
191C22×C4×C59C2×D411yescharacteristic
192C22×C4×C59C2×D412yes—
193C22×C4×C59C2412yes—
194C22×C4×C59C2411yescharacteristic
195C2×C22⋊D59—24no—
196C2×C22⋊D59C2×D414yes—
197C22×Dic59—21no—
198C22×Dic59—21no—
199C22×Dic59—21no—
200C22×Dic59—21no—
201C22×Dic59C2×D411yescharacteristic
202C22×Dic59C2×D411yescharacteristic
203C22×Dic59C2×D411yescharacteristic
204C2×C4×D59—22no—
205C2×C4×D59—22no—
206C2×C4×D59—24no—
207C2×C4×D59—82no—
208C2×C4×D59C2×D412yes—
209C2×C4×D59C2412yes—
210C2×Dic118—22no—
211C2×Dic118—22no—
212C2×Dic118—22no—
213C2×Dic118—22no—
214C2×Dic118—21no—
215C2×Dic118—21no—
216C2×Dic118—24no—
217C2×Dic118—82no—
218C2×Dic118C2412yes—
219C2×Dic118C2412yes—
220C2×C8×C59—22no—
221C2×C8×C59—28no—
222C2×C8×C59#4114yes—
223C2×C8×C59C2412yes—
224C2×C8×C59C2412yes—
225C4⋊C4×C59—21no—
226C4⋊C4×C59—21no—
227C4⋊C4×C59—24no—
228C4⋊C4×C59—21no—
229C4⋊C4×C59—21no—
230C4⋊C4×C59—24no—
231C4⋊C4×C59C2412yes—
232C4⋊C4×C59C2412yes—
233C4⋊C4×C59C2412yes—
234C4⋊C4×C59C2412yes—
235C22⋊Dic59—24no—
236C22⋊Dic59—24no—
237C22⋊Dic59C2×D414yes—
238(C2×D59)⋊C4—24no—
239(C2×D59)⋊C4—24no—
240(C2×D59)⋊C4—24no—
241(C2×D59)⋊C4C2×D414yes—
242C4⋊Dic59—21no—
243C4⋊Dic59—21no—
244C4⋊Dic59—24no—
245C4⋊Dic59—24no—
246C4⋊Dic59—24no—
247C4⋊Dic59C2412yes—
248C4⋊Dic59C2412yes—
249Dic59⋊C4—24no—
250Dic59⋊C4—24no—
251Dic59⋊C4—24no—
252Dic59⋊C4—24no—
253Dic59⋊C4—24no—
254Dic59⋊C4—24no—
255Dic59⋊C4—24no—
256Dic59⋊C4C2×D414yes—
257C4×Dic59—24no—
258C4×Dic59—24no—
259C4×Dic59—24no—
260C4×Dic59C2×D412yes—
261C4×Dic59C2412yes—
262C2×C59⋊C8—22no—
263C2×C59⋊C8—22no—
264C2×C59⋊C8C2412yes—
265C2×C59⋊C8C2412yes—
266Dic236—28no—
267#11745659—28no—
268C23×C59—22no—
269C23×C59—22no—
270C23×C59#13714yes—
271C23×C59C22×D412yes—
272C23×C59C22×D411yescharacteristic
273C22×D59—22no—
274C22×D59—22no—
275C22×D59—22no—
276C22×D59C22×D412yes—
277C2×C4×C59—22no—
278C2×C4×C59—24no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—48no—
286C2×C4×C59—42no—
287C2×C4×C59—42no—
288C2×C4×C59—42no—
289C2×C4×C59—42no—
290C2×C4×C59—84no—
291C2×C4×C59C22×D412yes—
292C2×C4×C59C22×D411yescharacteristic
293C2×C4×C59C2×#4112yes—
294C2×C4×C592−1+412yes—
295C2×C4×C59C2511yescharacteristic
296C22⋊D59—28no—
297C2×Dic59—22no—
298C2×Dic59—22no—
299C2×Dic59—22no—
300C2×Dic59—22no—
301C2×Dic59—22no—
302C2×Dic59—22no—
303C2×Dic59—22no—
304C2×Dic59—42no—
305C2×Dic59—42no—
306C2×Dic59—42no—
307C2×Dic59—42no—
308C2×Dic59C22×D412yes—
309C2×Dic59C22×D412yes—
310C2×Dic59C22×D412yes—
311C4×D59—24no—
312C4×D59—22no—
313C4×D59—22no—
314C4×D59—84no—
315Dic118—22no—
316Dic118—22no—
317Dic118—22no—
318Dic118—22no—
319Dic118—42no—
320Dic118—42no—
321Dic118—84no—
322C8×C59—22no—
323C8×C59C2×#4114yes—
324C59⋊C8—22no—
325C59⋊C8—22no—
326C2×#3344—591nomaximal, Sylow
327C22×C59—28no—
328C22×C59—22no—
329C22×C59—22no—
330C22×C59#54712yes—
331C22×C59C2×#13714yes—
332C22×C59C2×#13712yes—
333C22×C59#57712yes—
334C22×C59C23×D411yescharacteristic
335C2×D59—22no—
336C2×D59—22no—
337C2×D59—22no—
338C2×D59—44no—
339C4×C59—22no—
340C4×C59—42no—
341C4×C59—42no—
342C4×C59—42no—
343C4×C59—42no—
344C4×C59#54712yes—
345C4×C59C22×#4111yescharacteristic
346C4×C59C2×2−1+411yescharacteristic
347Dic59—22no—
348Dic59—22no—
349Dic59—22no—
350Dic59—42no—
351Dic59—42no—
352Dic59—42no—
353Dic59—42no—
354C2×#554—591no—
355C2×#552—591no—
356#3344—5916no—
357C2×#501—591no—
358C2×#484—591no—
359C2×#485—591no—
360C2×#483—591no—
361C2×#483—591no—
362C2×#479—591no—
363C2×#475—591no—
364C2×#470—591no—
365C2×#467—591no—
366C2×#441—591no—
367C2×#435—591no—
368C2×#428—591no—
369C22×#106D5911yescharacteristic, complemented
370C2×C59—24no—
371C2×C59#334414yescomplemented
372C2×C59C2×#54711yescharacteristic
373C2×C59C22×#13711yescharacteristic
374C2×C59C2×#57711yescharacteristic
375D59—42no—
376C22×Q16—591no—
377C22×M16—591no—
378C23×C8C2×D5911yescharacteristic
379#554—598no—
380#554—1184no—
381#552—598no—
382#552—1184no—
383C2×C4⋊Q8—591no—
384C2×#126—1181no—
385C2×#125—591no—
386C2×#125—1181no—
387C2×#125—1181no—
388C2×#123—1181no—
389C2×C22⋊Q8—591no—
390C2×C22⋊Q8—591no—
391C2×C22⋊Q8—591no—
392C2×C22⋊Q8—591no—
393C2×C22⋊Q8—1181no—
394C2×C22⋊Q8—1181no—
395C2×C4×Q8—591no—
396C2×C4×Q8—591no—
397C2×C4×D4—591no—
398C2×C4×D4—1181no—
399C2×#117—591no—
400C2×#117—1181no—
401C22×C4⋊C4—591no—
402C22×C4⋊C4C2×D5911yescharacteristic
403C22×C4⋊C4C2×D5911yescharacteristic
404#501—598no—
405#485—598no—
406#484—598no—
407#483—598no—
408#483—598no—
409#479—598no—
410#475—598no—
411#470—598no—
412#467—598no—
413#441—598no—
414#435—598no—
415#428—598no—
416C2×#107—591no—
417C2×#107—591no—
418C2×#107—591no—
419C2×#106—591no—
420C2×#106—591no—
421C2×#106C2×D5911yescharacteristic
422C2×#106C2×D5911yescharacteristic
423C2×#106C2×D5911yescharacteristic
424C2×#106C2×D5911yescharacteristic
425C2×#106C2×D5918yescomplemented
426C2×C4⋊C8—591no—
427C2×#103—591no—
428C2×#103—591no—
429C2×#103—591no—
430C2×#103—591no—
431C2×#103—591no—
432C2×#103—591no—
433C2×C22⋊C8—591no—
434C2×C22⋊C8—591no—
435C2×#97—591no—
436C59C2×#334411yescharacteristic, complemented, Sylow
437C22×Q8—591no—
438C22×Q8—591no—
439C22×Q8—1181no—
440C22×D4—591no—
441C23×C4—21no—
442C23×C4—21no—
443C23×C4—591no—
444C23×C4—1181no—
445C23×C4C22×D5911yescharacteristic
446C2×Q16—594no—
447C2×Q16—1184no—
448C2×M16—594no—
449C2×M16—1184no—
450C22×C8—24no—
451C22×C8—591no—
452C22×C8—591no—
453C22×C8C22×D5911yescharacteristic
454C22×C8C22×D5914yes—
455C22×C8C22×D5911yescharacteristic
456C4⋊Q8—594no—
457C4⋊Q8—1182no—
458#126—1188no—
459#125—594no—
460#125—1182no—
461#125—1188no—
462#125—1188no—
463#123—1188no—
464C22⋊Q8—594no—
465C22⋊Q8—594no—
466C22⋊Q8—594no—
467C22⋊Q8—594no—
468C22⋊Q8—1188no—
469C22⋊Q8—1188no—
470C22⋊Q8—1182no—
471C22⋊Q8—1182no—
472C22⋊Q8—1182no—
473C22⋊Q8—1182no—
474C4×Q8—594no—
475C4×Q8—594no—
476C4×Q8—1182no—
477C4×Q8—1182no—
478C4×D4—594no—
479C4×D4—594no—
480C4×D4—1188no—
481#117—594no—
482#117—1188no—
483#117—1182no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—591no—
489C2×C4⋊C4—591no—
490C2×C4⋊C4—591no—
491C2×C4⋊C4—594no—
492C2×C4⋊C4—1182no—
493C2×C4⋊C4—1181no—
494C2×C4⋊C4—1181no—
495C2×C4⋊C4—1181no—
496C2×C4⋊C4—1181no—
497C2×C4⋊C4—1181no—
498C2×C4⋊C4—1181no—
499C2×C4⋊C4—1181no—
500C2×C4⋊C4—1181no—
501C2×C4⋊C4—1181no—
502C2×C4⋊C4—1181no—
503C2×C4⋊C4C22×D5911yescharacteristic
504C2×C4⋊C4C22×D5911yescharacteristic
505C2×C4⋊C4C22×D5911yescharacteristic
506C2×C4⋊C4C22×D5911yescharacteristic
507C2×C4⋊C4C22×D5914yes—
508C2×C4⋊C4C22×D5914yes—
509C2×C22⋊C4—591no—
510C2×C22⋊C4—591no—
511C2×C22⋊C4—1181no—
512C2×C22⋊C4—1181no—
513C2×C22⋊C4—1181no—
514C2×C22⋊C4—1181no—
515C2×C22⋊C4—1181no—
516C2×C42—591no—
517C2×C42—1181no—
518C2×C42—1181no—
519C2×C42—1181no—
520#107—594no—
521#107—594no—
522#107—594no—
523#106—594no—
524#106—594no—
525#106C22×D5914yes—
526#106C22×D5914yes—
527#106C22×D5914yes—
528#106C22×D5914yes—
529C4⋊C8—594no—
530#103—594no—
531#103—594no—
532#103—594no—
533#103—594no—
534#103—594no—
535#103—594no—
536C22⋊C8—594no—
537C22⋊C8—594no—
538#97—594no—
539C24—591no—
540C24D4×D5911yescharacteristic
541C2×Q8—592no—
542C2×Q8—592no—
543C2×Q8—1184no—
544C2×Q8—1181no—
545C2×Q8—1181no—
546C2×Q8—1182no—
547C2×Q8—1182no—
548C2×Q8—1182no—
549C2×Q8—1182no—
550C2×Q8—4722no—
551C2×D4—594no—
552C2×D4—1184no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—24no—
561C22×C4—44no—
562C22×C4—82no—
563C22×C4—591no—
564C22×C4—591no—
565C22×C4—591no—
566C22×C4—592no—
567C22×C4—592no—
568C22×C4—1184no—
569C22×C4—1182no—
570C22×C4—1182no—
571C22×C4—1181no—
572C22×C4—1181no—
573C22×C4—1181no—
574C22×C4—1181no—
575C22×C4—4722no—
576C22×C4D4×D5912yes—
577C22×C4D4×D5911yescharacteristic
578C22×C4C23×D5912yes—
579C22×C4C23×D5911yescharacteristic
580Q16—1188no—
581M16—1188no—
582C2×C8—22no—
583C2×C8—28no—
584C2×C8—592no—
585C2×C8—592no—
586C2×C8—1182no—
587C2×C8—1182no—
588C2×C8#1174568514yes—
589C2×C8C23×D5912yes—
590C2×C8C23×D5912yes—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—24no—
597C4⋊C4—594no—
598C4⋊C4—592no—
599C4⋊C4—592no—
600C4⋊C4—1184no—
601C4⋊C4—1184no—
602C4⋊C4—1184no—
603C4⋊C4—1184no—
604C4⋊C4—1184no—
605C4⋊C4—1184no—
606C4⋊C4—1184no—
607C4⋊C4—1184no—
608C4⋊C4—1181no—
609C4⋊C4—1181no—
610C4⋊C4—1184no—
611C4⋊C4—1184no—
612C4⋊C4C23×D5912yes—
613C4⋊C4C23×D5912yes—
614C4⋊C4C23×D5912yes—
615C4⋊C4C23×D5912yes—
616C22⋊C4—594no—
617C22⋊C4—594no—
618C22⋊C4—1184no—
619C22⋊C4—1184no—
620C22⋊C4—1184no—
621C22⋊C4—1184no—
622C22⋊C4—1184no—
623C42—592no—
624C42—592no—
625C42—1184no—
626C42—1184no—
627C42—1184no—
628C23—22no—
629C23—22no—
630C23—592no—
631C23—1182no—
632C23—1182no—
633C23—1182no—
634C23#1427375614yes—
635C23C2×D4×D5912yes—
636C23C2×D4×D5911yescharacteristic
637Q8—1182no—
638Q8—1182no—
639Q8—1182no—
640Q8—1182no—
641Q8—4724no—
642Q8—2362no—
643Q8—2362no—
644D4—1188no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—24no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—48no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—84no—
659C2×C4—592no—
660C2×C4—592no—
661C2×C4—592no—
662C2×C4—1182no—
663C2×C4—1182no—
664C2×C4—1182no—
665C2×C4—1182no—
666C2×C4—1182no—
667C2×C4—1184no—
668C2×C4—1182no—
669C2×C4—1182no—
670C2×C4—1182no—
671C2×C4—1182no—
672C2×C4—4724no—
673C2×C4—2362no—
674C2×C4—2362no—
675C2×C4—2362no—
676C2×C4—2362no—
677C2×C4C2×D4×D5912yes—
678C2×C4C2×D4×D5911yescharacteristic
679C2×C4C2×#1174568512yes—
680C2×C4#1427377512yes—
681C2×C4C24×D5911yescharacteristic
682C8—22no—
683C8—1182no—
684C8—1182no—
685C8C2×#1174568514yes—
686C22—22no—
687C22—28no—
688C22—22no—
689C22—1182no—
690C22—1182no—
691C22—1182no—
692C22—2364no—
693C22#1683805312yes—
694C22C2×#1427375614yes—
695C22C2×#1427375612yes—
696C22#1683820812yes—
697C22C22×D4×D5911yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—1182no—
704C4—1182no—
705C4—1182no—
706C4—2362no—
707C4—2362no—
708C4—2362no—
709C4—2362no—
710C4#1683805312yes—
711C4C22×#1174568511yescharacteristic
712C4C2×#1427377511yescharacteristic
713C2—24no—
714C2—2362no—
715C2#2143654714yesdirect product factor
716C2C2×#1683805311yescharacteristic
717C2C22×#1427375611yescharacteristic
718C2C2×#1683820811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC22×#106×C59C2
socleC23×C59C22×D4
prime radicalC22×C22⋊D59D4
hypercenterC22×#106D59
hypocenterC59C2×#3344
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
3. #21436547C2direct (N × H)
4. C2×#16837809C2semidirect
5. C2×#16837737C2semidirect
6. C2×#16837746C2semidirect
7. C2×#16837734C2semidirect
8. C2×#16837732C2semidirect
9. C2×#16837712C2semidirect
10. C2×#16837686C2semidirect
11. C2×#16837661C2semidirect
12. C2×#16837643C2semidirect
13. C2×#16837508C2semidirect
15. C2×#16837441C2semidirect
16. C22×#106×C59C2semidirect
42. #16837809C22semidirect
43. #16837746C22semidirect
44. #16837737C22semidirect
45. #16837734C22semidirect
46. #16837732C22semidirect
47. #16837712C22semidirect
48. #16837686C22semidirect
49. #16837661C22semidirect
50. #16837643C22semidirect
51. #16837508C22semidirect
53. #16837441C22semidirect
76. C2×#106×C59C22semidirect
369. C22×#106D59semidirect
371. C2×C59#3344semidirect
425. C2×#106C2×D59semidirect
436. C59C2×#3344semidirect
715. C2#21436547direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381072
C2×#168380872
#214365472
C2×#168378092
C2×#168377372
C2×#168377462
C2×#168377342
C2×#168377322
C2×#168377122
C2×#168376862
C2×#168376612
C2×#168376432
C2×#168375082
C2×#168374732
C2×#168374412
C22×#106×C592
C2×#334459