Finite Group Databasebeta

← C2×#21436449 #29467108

Subgroups — C2×#21436449 #29467108

Order 15104.

2158 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838107C211yesmaximal, characteristic, complemented
2C2×#16838053C211yesmaximal, characteristic
3#21436449C2116yesmaximal, direct product factor
4C2×#16837799C211yesmaximal, characteristic, complemented
5C2×#16837722C211yesmaximal, characteristic, complemented
6C2×#16837720C211yesmaximal, characteristic, complemented
7C2×#16837734C211yesmaximal, characteristic, complemented
8C2×#16837732C211yesmaximal, characteristic, complemented
9C2×#16837686C211yesmaximal, characteristic, complemented
10C2×#16837691C211yesmaximal, characteristic, complemented
11C2×#16837632C211yesmaximal, characteristic, complemented
12C2×#16837631C211yesmaximal, characteristic, complemented
13C2×#16837489C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D59C211yesmaximal, characteristic, complemented
15C2×#106×D59C211yesmaximal, characteristic, complemented
16C22×#106×C59C211yesmaximal, characteristic, complemented
17C22×#11745685—21no—
18C22×#11745660C2211yescharacteristic
19C22×C8×D59C2211yescharacteristic
20#16838107—24no—
21#16838107C2218yescomplemented
22#16838053—24no—
23#16838053C2218yes—
24C2×#14273726C2211yescharacteristic
25C2×#14273726C2211yescharacteristic
26C2×#14273717—21no—
27C2×#14273712—21no—
28C2×#14273710—21no—
29C2×#14273707C2211yescharacteristic
30C2×#14273706—21no—
31C2×#14273706C2211yescharacteristic
32C2×#14273705—21no—
33C2×#14273705—21no—
34C2×#14273702C2211yescharacteristic
35C2×#14273701C2211yescharacteristic
36C2×#14273692C2211yescharacteristic
37C2×#14273689C2211yescharacteristic
38C2×C4×C22⋊D59—21no—
39C2×C4×C22⋊D59C2211yescharacteristic
40C2×C4⋊C4×D59C2211yescharacteristic
41C2×C4⋊C4×D59C2211yescharacteristic
42#16837799C2218yescomplemented
43#16837734C2218yescomplemented
44#16837732C2218yescomplemented
45#16837722C2218yescomplemented
46#16837720C2218yescomplemented
47#16837691C2218yescomplemented
48#16837686C2218yescomplemented
49#16837632C2218yescomplemented
50#16837631C2218yescomplemented
51#16837489C2218yescomplemented
52C8×C22⋊D59C2218yescomplemented
53C2×#14273659C2211yescharacteristic
54C2×#14273658C2211yescharacteristic
55C2×#14273658C2211yescharacteristic
56C2×#14273658C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58#106×D59C2218yescomplemented
59C2×Dic59⋊C8C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273650C2211yescharacteristic
62C2×#14273650C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
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
77C2×#11745685—28no—
78C2×#11745685—48no—
79C22×Dic118—21no—
80C22×Dic118—21no—
81C22×Dic118C2311yescharacteristic
82C22×D236—21no—
83C22×D236C2311yescharacteristic
84C22×C22⋊D59—21no—
85C22×C22⋊D59D411yescharacteristic
86C22×C4×D59—21no—
87C22×C4×D59—21no—
88C22×C4×D59—21no—
89C22×C4×D59C2311yescharacteristic
90C2×#11745660—24no—
91C2×#11745660C2314yes—
92C22×C59⋊C8C2311yescharacteristic
93C22×C59⋊C8C2311yescharacteristic
94C2×C8×D59—24no—
95C2×C8×D59C2314yes—
96#14273726—22no—
97#14273726—22no—
98#14273726C2314yes—
99#14273726C2314yes—
100#14273717—28no—
101#14273712—28no—
102#14273710—28no—
103#14273707—22no—
104#14273707C2314yes—
105#14273706—22no—
106#14273706—28no—
107#14273706C2314yes—
108#14273705—28no—
109#14273705—28no—
110#14273702—22no—
111#14273702C2314yes—
112#14273701—22no—
113#14273701C2314yes—
114#14273692—22no—
115#14273692C2314yes—
116#14273689—22no—
117#14273689C2314yes—
118C4×C22⋊D59—28no—
119C4×C22⋊D59D414yes—
120C4×C22⋊D59C2314yes—
121C2×C4⋊Dic59—21no—
122C2×C4⋊Dic59C2311yescharacteristic
123C2×C4⋊Dic59C2311yescharacteristic
124C2×Dic59⋊C4—21no—
125C2×Dic59⋊C4—21no—
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4D411yescharacteristic
131C4⋊C4×D59—22no—
132C4⋊C4×D59—22no—
133C4⋊C4×D59C2314yes—
134C4⋊C4×D59C2314yes—
135C2×C22⋊Dic59—21no—
136C2×C22⋊Dic59D411yescharacteristic
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4D411yescharacteristic
142C2×C4×Dic59—21no—
143C2×C4×Dic59C2311yescharacteristic
144#14273659C2314yes—
145#14273658C2314yes—
146#14273658C2314yes—
147#14273658C2314yes—
148#14273658C2314yes—
149Dic59⋊C8C2314yes—
150#14273652C2314yes—
151#14273650C2314yes—
152#14273650C2314yes—
153#14273649C2314yes—
154#14273647C2314yes—
155#14273647C2314yes—
156C22⋊(C59⋊C8)C2314yes—
157(C2×D59)⋊C8C2314yes—
158C8×Dic59C2314yes—
159C23×C4×C59—21no—
160C23×C4×C59—21no—
161C23×C4×C59C2311yescharacteristic
162C22×C8×C59—24no—
163C22×C8×C59C2311yescharacteristic
164C22×C8×C59C2314yes—
165C22×C8×C59C2311yescharacteristic
166C2×C4⋊C4×C59—21no—
167C2×C4⋊C4×C59—21no—
168C2×C4⋊C4×C59—22no—
169C2×C4⋊C4×C59—22no—
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C4⋊C4×C59C2314yes—
175C2×C4⋊C4×C59C2314yes—
176#106×C59C2314yes—
177#106×C59C2314yes—
178#106×C59C2314yes—
179#106×C59C2314yes—
180C24×C59C2×D411yescharacteristic
181C23×D59—21no—
182C23×D59C2×D411yescharacteristic
183C22×C4×C59—22no—
184C22×C4×C59—22no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—24no—
190C22×C4×C59—24no—
191C22×C4×C59—44no—
192C22×C4×C59—82no—
193C22×C4×C59C2×D411yescharacteristic
194C22×C4×C59C2×D412yes—
195C22×C4×C59C2412yes—
196C22×C4×C59C2411yescharacteristic
197C2×C22⋊D59—24no—
198C2×C22⋊D59—44no—
199C2×C22⋊D59SD1618yescomplemented
200C2×C22⋊D59C2×D414yes—
201C22×Dic59—21no—
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59C2×D411yescharacteristic
205C22×Dic59C2×D411yescharacteristic
206C22×Dic59C2×D411yescharacteristic
207#11745685—432no—
208C2×D236—22no—
209C2×D236—22no—
210C2×D236—24no—
211C2×D236—21no—
212C2×D236—44no—
213C2×D236C2412yes—
214C2×C4×D59—22no—
215C2×C4×D59—22no—
216C2×C4×D59—24no—
217C2×C4×D59—24no—
218C2×C4×D59—24no—
219C2×C4×D59—44no—
220C2×C4×D59—44no—
221C2×C4×D59—82no—
222C2×C4×D59C2×D412yes—
223C2×C4×D59C2412yes—
224C2×Dic118—22no—
225C2×Dic118—22no—
226C2×Dic118—21no—
227C2×Dic118—24no—
228C2×Dic118—24no—
229C2×Dic118—44no—
230C2×Dic118—82no—
231C2×Dic118C2412yes—
232C2×C8×C59—22no—
233C2×C8×C59—28no—
234C2×C8×C59#4114yescomplemented
235C2×C8×C59C2412yes—
236C2×C8×C59C2412yes—
237C4⋊C4×C59—21no—
238C4⋊C4×C59—21no—
239C4⋊C4×C59—21no—
240C4⋊C4×C59—24no—
241C4⋊C4×C59—24no—
242C4⋊C4×C59—21no—
243C4⋊C4×C59C2412yes—
244C4⋊C4×C59C2412yes—
245C4⋊C4×C59C2412yes—
246C4⋊C4×C59C2412yes—
247C22⋊Dic59—24no—
248C22⋊Dic59C2×D414yes—
249(C2×D59)⋊C4—24no—
250(C2×D59)⋊C4—24no—
251(C2×D59)⋊C4—24no—
252(C2×D59)⋊C4—24no—
253(C2×D59)⋊C4C2×D414yes—
254C4⋊Dic59—21no—
255C4⋊Dic59—21no—
256C4⋊Dic59—24no—
257C4⋊Dic59C2412yes—
258C4⋊Dic59C2412yes—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261Dic59⋊C4—24no—
262Dic59⋊C4—24no—
263Dic59⋊C4—24no—
264Dic59⋊C4—24no—
265Dic59⋊C4C2×D414yes—
266C4×Dic59—24no—
267C4×Dic59C2×D412yes—
268C4×Dic59C2412yes—
269C2×C59⋊C8—22no—
270C2×C59⋊C8—22no—
271C2×C59⋊C8C2412yes—
272C2×C59⋊C8C2412yes—
273#11745660—28no—
274C8×D59—28no—
275C23×C59—22no—
276C23×C59—22no—
277C23×C59C2×SD1614yes—
278C23×C59C22×D412yes—
279C23×C59C22×D411yescharacteristic
280C22×D59—22no—
281C22×D59—22no—
282C22×D59—22no—
283C22×D59—42no—
284C22×D59—42no—
285C22×D59—42no—
286C22×D59C2×SD1614yes—
287C22×D59C22×D412yes—
288C2×C4×C59—22no—
289C2×C4×C59—24no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—42no—
297C2×C4×C59—42no—
298C2×C4×C59—48no—
299C2×C4×C59—42no—
300C2×C4×C59—42no—
301C2×C4×C59—84no—
302C2×C4×C59C22×D412yes—
303C2×C4×C59C22×D411yescharacteristic
304C2×C4×C59C2×#4112yes—
305C2×C4×C592−1+412yes—
306C2×C4×C59C2511yescharacteristic
307C22⋊D59—48no—
308C22⋊D59C2×SD16116yescomplemented
309C2×Dic59—22no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—42no—
315C2×Dic59—42no—
316C2×Dic59—42no—
317C2×Dic59C2×SD1614yes—
318C2×Dic59C22×D412yes—
319C2×Dic59C22×D412yes—
320C2×Dic59C22×D412yes—
321D236—22no—
322D236—22no—
323D236—48no—
324D236—42no—
325C4×D59—24no—
326C4×D59—22no—
327C4×D59—22no—
328C4×D59—48no—
329C4×D59—48no—
330C4×D59—84no—
331Dic118—22no—
332Dic118—22no—
333Dic118—42no—
334Dic118—48no—
335Dic118—84no—
336C8×C59—22no—
337C8×C59C2×#4114yescomplemented
338C59⋊C8—22no—
339C59⋊C8—22no—
340C2×#3335—591nomaximal, Sylow
341C22×C59—28no—
342C22×C59—22no—
343C22×C59—22no—
344C22×C59#54712yes—
345C22×C59C22×SD1614yes—
346C22×C59C22×SD1612yes—
347C22×C59#57712yes—
348C22×C59C23×D411yescharacteristic
349C2×D59—28no—
350C2×D59—22no—
351C2×D59—22no—
352C2×D59—42no—
353C2×D59—42no—
354C2×D59—42no—
355C2×D59—84no—
356C2×D59C22×SD1614yes—
357C4×C59—22no—
358C4×C59—42no—
359C4×C59—42no—
360C4×C59—42no—
361C4×C59—42no—
362C4×C59#54712yes—
363C4×C59C22×#4111yescharacteristic
364C4×C59C2×2−1+411yescharacteristic
365Dic59—22no—
366Dic59—22no—
367Dic59—42no—
368Dic59—42no—
369Dic59—42no—
370Dic59C22×SD1614yes—
371C2×#554—591no—
372C2×#547—591no—
373#3335—5916no—
374C2×#498—591no—
375C2×#481—591no—
376C2×#481—591no—
377C2×#483—591no—
378C2×#483—591no—
379C2×#475—591no—
380C2×#476—591no—
381C2×#465—591no—
382C2×#465—591no—
383C2×C4×SD16—591no—
384C2×C8×D4—591no—
385C22×#106—591no—
386C22×#106D5911yescharacteristic, complemented
387C2×C59—24no—
388C2×C59#333514yescomplemented
389C2×C59C2×#54711yescharacteristic
390C2×C59C23×SD1611yescharacteristic
391C2×C59C2×#57711yescharacteristic
392D59—24no—
393D59—82no—
394C22×#41—1181no—
395C22×SD16—591no—
396C23×C8—591no—
397C23×C8C2×D5911yescharacteristic
398#554—598no—
399#554—1184no—
400#547—598no—
401#547—1184no—
402C2×C4⋊Q8—591no—
403C2×C4⋊Q8—591no—
404C2×#125—1181no—
405C2×#123—1181no—
406C2×#123—1181no—
407C2×C22⋊Q8—591no—
408C2×C22⋊Q8—591no—
409C2×C22⋊Q8—1181no—
410C2×C22⋊Q8—1181no—
411C2×C22⋊Q8—1181no—
412C2×#121—591no—
413C2×#121—591no—
414C2×C4×Q8—591no—
415C2×C4×D4—591no—
416C2×C4×D4—591no—
417C2×C4×D4—1181no—
418C22×C4⋊C4—591no—
419C22×C4⋊C4—591no—
420C22×C4⋊C4C2×D5911yescharacteristic
421C22×C4⋊C4C2×D5911yescharacteristic
422#498—598no—
423#483—598no—
424#483—598no—
425#481—598no—
426#481—598no—
427#476—598no—
428#475—598no—
429#465—598no—
430#465—598no—
431C4×SD16—598no—
432C8×D4—598no—
433C2×#106—591no—
434C2×#106—591no—
435C2×#106—591no—
436C2×#106—591no—
437C2×#106—591no—
438C2×#106—598no—
439C2×#106C2×D5911yescharacteristic
440C2×#106C2×D5911yescharacteristic
441C2×#106C2×D5911yescharacteristic
442C2×#106C2×D5911yescharacteristic
443C2×#106C2×D5918yescomplemented
444C2×C4⋊C8—591no—
445C2×#103—591no—
446C2×#103—591no—
447C2×#103—591no—
448C2×#102—591no—
449C2×#102—591no—
450C2×#102—591no—
451C2×C22⋊C8—591no—
452C2×C22⋊C8—591no—
453C2×C4×C8—591no—
454C59C2×#333511yescharacteristic, complemented, Sylow
455C2×#41—1188no—
456C2×#41—2368no—
457C22×Q8—591no—
458C22×Q8—1181no—
459C22×Q8—1181no—
460C22×D4—591no—
461C22×D4—591no—
462C22×D4—1181no—
463C22×D4—1181no—
464C23×C4—21no—
465C23×C4—21no—
466C23×C4—591no—
467C23×C4—1181no—
468C23×C4—1181no—
469C23×C4—1181no—
470C23×C4C22×D5911yescharacteristic
471C2×SD16—594no—
472C2×SD16—1184no—
473C22×C8—24no—
474C22×C8—591no—
475C22×C8—591no—
476C22×C8—594no—
477C22×C8—1184no—
478C22×C8C22×D5911yescharacteristic
479C22×C8C22×D5914yes—
480C22×C8C22×D5911yescharacteristic
481C4⋊Q8—594no—
482C4⋊Q8—594no—
483C4⋊Q8—1182no—
484C4⋊Q8—1182no—
485#125—1188no—
486#123—1188no—
487#123—1188no—
488C22⋊Q8—594no—
489C22⋊Q8—594no—
490C22⋊Q8—1188no—
491C22⋊Q8—1188no—
492C22⋊Q8—1188no—
493C22⋊Q8—1182no—
494C22⋊Q8—1182no—
495#121—594no—
496#121—594no—
497#121—1182no—
498#121—1182no—
499C4×Q8—594no—
500C4×Q8—1182no—
501C4×D4—594no—
502C4×D4—594no—
503C4×D4—594no—
504C4×D4—1182no—
505C4×D4—1188no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—591no—
511C2×C4⋊C4—591no—
512C2×C4⋊C4—591no—
513C2×C4⋊C4—594no—
514C2×C4⋊C4—594no—
515C2×C4⋊C4—1182no—
516C2×C4⋊C4—1182no—
517C2×C4⋊C4—1181no—
518C2×C4⋊C4—1181no—
519C2×C4⋊C4—1181no—
520C2×C4⋊C4—1181no—
521C2×C4⋊C4—1181no—
522C2×C4⋊C4—1181no—
523C2×C4⋊C4—1181no—
524C2×C4⋊C4C22×D5911yescharacteristic
525C2×C4⋊C4C22×D5911yescharacteristic
526C2×C4⋊C4C22×D5911yescharacteristic
527C2×C4⋊C4C22×D5911yescharacteristic
528C2×C4⋊C4C22×D5914yes—
529C2×C4⋊C4C22×D5914yes—
530C2×C22⋊C4—591no—
531C2×C22⋊C4—591no—
532C2×C22⋊C4—1181no—
533C2×C22⋊C4—1181no—
534C2×C22⋊C4—1181no—
535C2×C22⋊C4—1181no—
536C2×C22⋊C4—1181no—
537C2×C42—591no—
538C2×C42—1181no—
539#106—594no—
540#106—594no—
541#106—594no—
542#106—594no—
543#106—594no—
544#106C22×D5914yes—
545#106C22×D5914yes—
546#106C22×D5914yes—
547#106C22×D5914yes—
548C4⋊C8—594no—
549#103—594no—
550#103—594no—
551#103—594no—
552#102—594no—
553#102—594no—
554#102—594no—
555C22⋊C8—594no—
556C22⋊C8—594no—
557C4×C8—594no—
558C24—591no—
559C24—1181no—
560C24D4×D5911yescharacteristic
561#41—23632no—
562C2×Q8—592no—
563C2×Q8—1184no—
564C2×Q8—1184no—
565C2×Q8—1181no—
566C2×Q8—1182no—
567C2×Q8—1182no—
568C2×Q8—4722no—
569C2×Q8—2364no—
570C2×D4—598no—
571C2×D4—594no—
572C2×D4—592no—
573C2×D4—1184no—
574C2×D4—1184no—
575C2×D4—1181no—
576C2×D4—1182no—
577C2×D4—1182no—
578C2×D4—2364no—
579C2×D4—2364no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—24no—
588C22×C4—44no—
589C22×C4—82no—
590C22×C4—591no—
591C22×C4—591no—
592C22×C4—591no—
593C22×C4—592no—
594C22×C4—592no—
595C22×C4—1184no—
596C22×C4—1184no—
597C22×C4—1184no—
598C22×C4—1182no—
599C22×C4—1182no—
600C22×C4—1181no—
601C22×C4—1181no—
602C22×C4—1181no—
603C22×C4—4722no—
604C22×C4—2364no—
605C22×C4—2364no—
606C22×C4D4×D5912yes—
607C22×C4D4×D5911yescharacteristic
608C22×C4C23×D5912yes—
609C22×C4C23×D5911yescharacteristic
610SD16—1188no—
611C2×C8—22no—
612C2×C8—28no—
613C2×C8—592no—
614C2×C8—592no—
615C2×C8—1182no—
616C2×C8—1182no—
617C2×C8—1188no—
618C2×C8#1174568514yescomplemented
619C2×C8C23×D5912yes—
620C2×C8C23×D5912yes—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—594no—
628C4⋊C4—592no—
629C4⋊C4—592no—
630C4⋊C4—1184no—
631C4⋊C4—1184no—
632C4⋊C4—1184no—
633C4⋊C4—1184no—
634C4⋊C4—1184no—
635C4⋊C4—1184no—
636C4⋊C4—1181no—
637C4⋊C4—1181no—
638C4⋊C4—1184no—
639C4⋊C4C23×D5912yes—
640C4⋊C4C23×D5912yes—
641C4⋊C4C23×D5912yes—
642C4⋊C4C23×D5912yes—
643C22⋊C4—594no—
644C22⋊C4—594no—
645C22⋊C4—1184no—
646C22⋊C4—1184no—
647C22⋊C4—1184no—
648C22⋊C4—1184no—
649C22⋊C4—1184no—
650C42—592no—
651C42—592no—
652C42—1184no—
653C23—22no—
654C23—22no—
655C23—594no—
656C23—592no—
657C23—1182no—
658C23—1182no—
659C23—1182no—
660C23—2362no—
661C23—2362no—
662C23—2362no—
663C23SD16×D5914yes—
664C23C2×D4×D5912yes—
665C23C2×D4×D5911yescharacteristic
666Q8—1182no—
667Q8—1182no—
668Q8—4724no—
669Q8—2368no—
670Q8—2362no—
671D4—5916no—
672D4—1182no—
673D4—1182no—
674D4—2368no—
675D4—2368no—
676D4—2362no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—48no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—84no—
691C2×C4—594no—
692C2×C4—592no—
693C2×C4—592no—
694C2×C4—592no—
695C2×C4—1182no—
696C2×C4—1182no—
697C2×C4—1182no—
698C2×C4—1182no—
699C2×C4—1184no—
700C2×C4—1182no—
701C2×C4—1182no—
702C2×C4—1182no—
703C2×C4—4724no—
704C2×C4—2368no—
705C2×C4—2368no—
706C2×C4—2362no—
707C2×C4—2362no—
708C2×C4—2362no—
709C2×C4C2×D4×D5912yes—
710C2×C4C2×D4×D5911yescharacteristic
711C2×C4C2×#1174568512yes—
712C2×C4#1427377512yes—
713C2×C4C24×D5911yescharacteristic
714C8—22no—
715C8—1182no—
716C8—1182no—
717C8C2×#1174568514yescomplemented
718C22—28no—
719C22—22no—
720C22—22no—
721C22—594no—
722C22—1188no—
723C22—1182no—
724C22—1182no—
725C22—4724no—
726C22—2362no—
727C22—2362no—
728C22—2362no—
729C22#1683805312yes—
730C22C2×SD16×D5914yes—
731C22C2×SD16×D5912yes—
732C22#1683820812yes—
733C22C22×D4×D5911yescharacteristic
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—594no—
740C4—1182no—
741C4—1182no—
742C4—2362no—
743C4—2362no—
744C4—2362no—
745C4#1683805312yes—
746C4C22×#1174568511yescharacteristic
747C4C2×#1427377511yescharacteristic
748C2—24no—
749C2—1184no—
750C2—4722no—
751C2#2143644914yesdirect product factor
752C2C2×#1683805311yescharacteristic
753C2C22×SD16×D5911yescharacteristic
754C2C2×#1683820811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC22×#106×C59C2
socleC23×C59C22×D4
prime radicalC2×#16838053C2
hypercenterC22×#106D59
hypocenterC59C2×#3335
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
1. C2×#16838107C2semidirect
3. #21436449C2direct (N × H)
4. C2×#16837799C2semidirect
5. C2×#16837722C2semidirect
6. C2×#16837720C2semidirect
7. C2×#16837734C2semidirect
8. C2×#16837732C2semidirect
9. C2×#16837686C2semidirect
10. C2×#16837691C2semidirect
11. C2×#16837632C2semidirect
12. C2×#16837631C2semidirect
13. C2×#16837489C2semidirect
14. C2×C8×C22⋊D59C2semidirect
15. C2×#106×D59C2semidirect
16. C22×#106×C59C2semidirect
21. #16838107C22semidirect
42. #16837799C22semidirect
43. #16837734C22semidirect
44. #16837732C22semidirect
45. #16837722C22semidirect
46. #16837720C22semidirect
47. #16837691C22semidirect
48. #16837686C22semidirect
49. #16837632C22semidirect
50. #16837631C22semidirect
51. #16837489C22semidirect
52. C8×C22⋊D59C22semidirect
58. #106×D59C22semidirect
76. C2×#106×C59C22semidirect
199. C2×C22⋊D59SD16semidirect
234. C2×C8×C59#41semidirect
308. C22⋊D59C2×SD16semidirect
337. C8×C59C2×#41semidirect
386. C22×#106D59semidirect
388. C2×C59#3335semidirect
443. C2×#106C2×D59semidirect
454. C59C2×#3335semidirect
618. C2×C8#11745685semidirect
717. C8C2×#11745685semidirect
751. C2#21436449direct (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×#168380532
#214364492
C2×#168377992
C2×#168377222
C2×#168377202
C2×#168377342
C2×#168377322
C2×#168376862
C2×#168376912
C2×#168376322
C2×#168376312
C2×#168374892
C2×C8×C22⋊D592
C2×#106×D592
C22×#106×C592
C2×#333559