Finite Group Databasebeta

← C2×#22621229 #33958221

Subgroups — C2×#22621229 #33958221

Order 18688.

1742 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989208C211yesmaximal, characteristic
2#22621229C2116yesmaximal, direct product factor
3C2×#17988997C211yesmaximal, characteristic, complemented
4C2×#17988983C211yesmaximal, characteristic, complemented
5C2×#17988949C211yesmaximal, characteristic, complemented
6C2×#17988944C211yesmaximal, characteristic, complemented
7C2×#17988905C211yesmaximal, characteristic
8C2×#17988928C211yesmaximal, characteristic, complemented
9C2×#17988911C211yesmaximal, characteristic
10C2×#17988917C211yesmaximal, characteristic, complemented
11C2×#17988891C211yesmaximal, characteristic, complemented
12C2×#17988869C211yesmaximal, characteristic, complemented
13C2×#17988884C211yesmaximal, characteristic, complemented
14C2×#17988874C211yesmaximal, characteristic, complemented
15C2×#17988648C211yesmaximal, characteristic, complemented
16C2×#544×C73C211yesmaximal, characteristic, complemented
17#17989208—24no—
18#17989208C2218yes—
19C2×#14556591C2211yescharacteristic
20C2×#14556586—21no—
21C2×#14556579C2211yescharacteristic
22C2×#14556577—21no—
23C2×#14556573—21no—
24C2×#14556570C2211yescharacteristic
25C2×#14556569—21no—
26C2×#14556565C2211yescharacteristic
27C2×C4×Dic146C2211yescharacteristic
28C2×C4×D292C2211yescharacteristic
29#17988997C2218yescomplemented
30#17988983C2218yescomplemented
31#17988949C2218yescomplemented
32#17988944C2218yescomplemented
33#17988928C2218yescomplemented
34#17988917C2218yescomplemented
35#17988911C2218yes—
36#17988905C2218yes—
37#17988891C2218yescomplemented
38#17988884C2218yescomplemented
39#17988874C2218yescomplemented
40#17988869C2218yescomplemented
41#17988648C2218yescomplemented
42C2×#14556524C2211yescharacteristic
43C2×#14556524C2211yescharacteristic
44C2×#14556522C2211yescharacteristic
45C2×#14556522C2211yescharacteristic
46C2×#14556522C2211yescharacteristic
47C2×#14556522C2211yescharacteristic
48C2×#14556522C2211yescharacteristic
49C2×#14556522C2211yescharacteristic
50C2×C4⋊#10596831C2211yescharacteristic
51C2×C4⋊#10596831C2211yescharacteristic
52C2×#14556514C2211yescharacteristic
53C2×#14556514C2211yescharacteristic
54C2×#14556514C2211yescharacteristic
55C2×#14556514C2211yescharacteristic
56C2×#14556511C2211yescharacteristic
57C2×#14556511C2211yescharacteristic
58C2×#14556511C2211yescharacteristic
59C2×#14556511C2211yescharacteristic
60C2×C22⋊#10596831C2211yescharacteristic
61C2×C22⋊#10596831C2211yescharacteristic
62C2×#14556502C2211yescharacteristic
63C2×C4×#10596831C2211yescharacteristic
64#544×C73—24no—
65#544×C73C2218yescomplemented
66C2×C4⋊Q8×C73—21no—
67C2×C4⋊Q8×C73C2211yescharacteristic
68C2×C4⋊Q8×C73C2211yescharacteristic
69C2×#125×C73—21no—
70C2×#125×C73C2211yescharacteristic
71C2×#125×C73C2211yescharacteristic
72C2×C22⋊Q8×C73—21no—
73C2×C22⋊Q8×C73—21no—
74C2×#117×C73C2211yescharacteristic
75C2×#117×C73C2211yescharacteristic
76C22×C4⋊C4×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146C2311yescharacteristic
79C22×D292C2311yescharacteristic
80C22×C22⋊D73—21no—
81C22×C4×D73—21no—
82C22×#10596831C2311yescharacteristic
83C22×#10596831C2311yescharacteristic
84C22×#10596831C2311yescharacteristic
85C22×#10596831C2311yescharacteristic
86#14556591—22no—
87#14556591C2314yes—
88#14556586—28no—
89#14556579—22no—
90#14556579C2314yes—
91#14556577—28no—
92#14556573—28no—
93#14556570—22no—
94#14556570C2314yes—
95#14556569—28no—
96#14556565—22no—
97#14556565C2314yes—
98C4×Dic146—22no—
99C4×Dic146C2314yes—
100C4×D292—22no—
101C4×D292C2314yes—
102C2×C4⋊Dic73—21no—
103C2×C4⋊Dic73C2311yescharacteristic
104C2×C4⋊Dic73C2311yescharacteristic
105C2×#11924007—21no—
106C2×#11924007—21no—
107C2×C22⋊Dic73—21no—
108C2×#11924005—21no—
109C2×#11924005—21no—
110C2×#11924005—21no—
111C2×#11924005—21no—
112C2×C4×Dic73—21no—
113#14556524C2314yes—
114#14556524C2314yes—
115#14556522C2314yes—
116#14556522C2314yes—
117#14556522C2314yes—
118#14556522C2314yes—
119#14556522C2314yes—
120#14556522C2314yes—
121C4⋊#10596831C2314yes—
122C4⋊#10596831C2314yes—
123#14556514C2314yes—
124#14556514C2314yes—
125#14556514C2314yes—
126#14556514C2314yes—
127#14556511C2314yes—
128#14556511C2314yes—
129#14556511C2314yes—
130#14556511C2314yes—
131C22⋊#10596831C2314yes—
132C22⋊#10596831C2314yes—
133#14556502C2314yes—
134C4×#10596831C2314yes—
135C22×Q8×C73—21no—
136C22×Q8×C73—21no—
137C23×C4×C73—21no—
138C23×C4×C73C2311yescharacteristic
139C4⋊Q8×C73—28no—
140C4⋊Q8×C73—22no—
141C4⋊Q8×C73—22no—
142C4⋊Q8×C73C2314yes—
143C4⋊Q8×C73C2314yes—
144#125×C73—28no—
145#125×C73—22no—
146#125×C73—22no—
147#125×C73C2314yes—
148#125×C73C2314yes—
149C22⋊Q8×C73—28no—
150C22⋊Q8×C73—28no—
151#117×C73—22no—
152#117×C73D414yes—
153#117×C73C2314yes—
154#117×C73C2314yes—
155C2×C4⋊C4×C73—21no—
156C2×C4⋊C4×C73—22no—
157C2×C4⋊C4×C73—21no—
158C2×C4⋊C4×C73—21no—
159C2×C4⋊C4×C73—21no—
160C2×C4⋊C4×C73—21no—
161C2×C4⋊C4×C73—21no—
162C2×C4⋊C4×C73—21no—
163C2×C4⋊C4×C73D411yescharacteristic
164C2×C4⋊C4×C73D411yescharacteristic
165C2×C4⋊C4×C73C2311yescharacteristic
166C2×C4⋊C4×C73C2311yescharacteristic
167C2×C4⋊C4×C73C2311yescharacteristic
168C2×C4⋊C4×C73C2311yescharacteristic
169C2×C4⋊C4×C73C2314yes—
170C2×C22⋊C4×C73—21no—
171C2×C22⋊C4×C73D411yescharacteristic
172C2×C22⋊C4×C73D411yescharacteristic
173C2×C42×C73—21no—
174C2×C42×C73C2311yescharacteristic
175C2×C42×C73C2311yescharacteristic
176C23×D73—21no—
177C2×Dic146—22no—
178C2×Dic146—22no—
179C2×Dic146—21no—
180C2×Dic146—24no—
181C2×Dic146—82no—
182C2×Dic146C2412yes—
183C2×D292—22no—
184C2×D292—22no—
185C2×D292—21no—
186C2×D292C2412yes—
187C2×C22⋊D73—24no—
188C2×C22⋊D73—82no—
189C22×Dic73—21no—
190C22×Dic73—21no—
191C22×Dic73—21no—
192C2×C4×D73—24no—
193C2×C4×D73—82no—
194C2×#10596831—22no—
195C2×#10596831—22no—
196C2×#10596831—22no—
197C2×#10596831—22no—
198C2×#10596831C2412yes—
199C2×#10596831C2412yes—
200C2×#10596831C2412yes—
201C2×#10596831C2412yes—
202C4⋊Dic73—24no—
203C4⋊Dic73—21no—
204C4⋊Dic73—21no—
205C4⋊Dic73C2412yes—
206C4⋊Dic73C2412yes—
207#11924007—24no—
208#11924007—24no—
209C22⋊Dic73—24no—
210#11924005—24no—
211#11924005—24no—
212#11924005—24no—
213#11924005—24no—
214C4×Dic73—24no—
215C24×C73C2×D411yescharacteristic
216C2×Q8×C73—24no—
217C2×Q8×C73—24no—
218C2×Q8×C73—82no—
219C2×Q8×C73—82no—
220C22×C4×C73—22no—
221C22×C4×C73—22no—
222C22×C4×C73—21no—
223C22×C4×C73—21no—
224C22×C4×C73—21no—
225C22×C4×C73—21no—
226C22×C4×C73—24no—
227C22×C4×C73—82no—
228C22×C4×C73C2×D411yescharacteristic
229C22×C4×C73C2×D411yescharacteristic
230C22×C4×C73C2×D411yescharacteristic
231C22×C4×C73C2×D411yescharacteristic
232C22×C4×C73C2×D411yescharacteristic
233C22×C4×C73C2×D412yes—
234C22×C4×C73C2412yes—
235C22×C4×C73C2411yescharacteristic
236C4⋊C4×C73—24no—
237C4⋊C4×C73—21no—
238C4⋊C4×C73—21no—
239C4⋊C4×C73—24no—
240C4⋊C4×C73—24no—
241C4⋊C4×C73—24no—
242C4⋊C4×C73—24no—
243C4⋊C4×C73—24no—
244C4⋊C4×C73—24no—
245C4⋊C4×C73—21no—
246C4⋊C4×C73—21no—
247C4⋊C4×C73C2×D414yes—
248C4⋊C4×C73C2×D414yes—
249C4⋊C4×C73C2412yes—
250C4⋊C4×C73C2412yes—
251C4⋊C4×C73C2412yes—
252C4⋊C4×C73C2412yes—
253C22⋊C4×C73—24no—
254C22⋊C4×C73C2×D414yes—
255C22⋊C4×C73C2×D414yes—
256C42×C73—24no—
257C42×C73C2×D412yes—
258C42×C73C2×D412yes—
259C42×C73C2412yes—
260C42×C73C2412yes—
261C23×C73—22no—
262C23×C73—22no—
263C23×C73—22no—
264C23×C73C22×D412yes—
265C23×C73C22×D411yescharacteristic
266C22×D73—22no—
267C22×D73—42no—
268C22×D73—42no—
269C22×D73—42no—
270Q8×C73—84no—
271Q8×C73—84no—
272C2×C4×C73—22no—
273C2×C4×C73—22no—
274C2×C4×C73—22no—
275C2×C4×C73—22no—
276C2×C4×C73—22no—
277C2×C4×C73—24no—
278C2×C4×C73—22no—
279C2×C4×C73—22no—
280C2×C4×C73—22no—
281C2×C4×C73—22no—
282C2×C4×C73—22no—
283C2×C4×C73—22no—
284C2×C4×C73—42no—
285C2×C4×C73—42no—
286C2×C4×C73—42no—
287C2×C4×C73—42no—
288C2×C4×C73—84no—
289C2×C4×C73C22×D412yes—
290C2×C4×C73C22×D412yes—
291C2×C4×C73C22×D412yes—
292C2×C4×C73C22×D412yes—
293C2×C4×C73C22×D412yes—
294C2×C4×C73C22×D411yescharacteristic
295C2×C4×C732−1+412yes—
296C2×C4×C732−1+412yes—
297C2×C4×C73C2511yescharacteristic
298C22⋊D73—84no—
299C2×Dic73—22no—
300C2×Dic73—22no—
301C2×Dic73—22no—
302C2×Dic73—42no—
303C2×Dic73—42no—
304C2×Dic73—42no—
305D292—22no—
306D292—22no—
307D292—42no—
308C4×D73—84no—
309Dic146—22no—
310Dic146—22no—
311Dic146—42no—
312Dic146—84no—
313#10596831—22no—
314#10596831—22no—
315#10596831—22no—
316#10596831—22no—
317C22×C73—22no—
318C22×C73—22no—
319C22×C73—22no—
320C22×C73—44no—
321C22×C73#53612yes—
322C22×C73#57712yes—
323C22×C73#57712yes—
324C22×C73C23×D411yescharacteristic
325C2×D73—42no—
326C2×D73—42no—
327C2×D73—42no—
328C2×D73—84no—
329C4×C73—22no—
330C4×C73—22no—
331C4×C73—22no—
332C4×C73—22no—
333C4×C73—22no—
334C4×C73—42no—
335C4×C73—42no—
336C4×C73—42no—
337C4×C73—42no—
338C4×C73#53612yes—
339C4×C73C2×2−1+411yescharacteristic
340C4×C73C2×2−1+411yescharacteristic
341Dic73—42no—
342Dic73—42no—
343Dic73—42no—
344C2×#3244—731nomaximal, Sylow
345C2×C73—42no—
346C2×C73#324414yescomplemented
347C2×C73C2×#53611yescharacteristic
348C2×C73C2×#57711yescharacteristic
349C2×C73C2×#57711yescharacteristic
350D73—82no—
351C2×#544D7311yescharacteristic, complemented
352C2×#542—731no—
353#3244—7316no—
354C2×#501—731no—
355C2×#498—731no—
356C2×#489—731no—
357C2×#488—731no—
358C2×#481—731no—
359C2×#485—731no—
360C2×#482—731no—
361C2×#483—731no—
362C2×#479—731no—
363C2×#475—731no—
364C2×#478—731no—
365C2×#476—731no—
366C2×#433—731no—
367C73C2×#324411yescharacteristic, complemented, Sylow
368#544—24no—
369#544C2×D7318yescomplemented
370#542—738no—
371#542—1464no—
372C2×C4⋊Q8—21no—
373C2×C4⋊Q8—731no—
374C2×C4⋊Q8C2×D7311yescharacteristic
375C2×C4⋊Q8C2×D7311yescharacteristic
376C2×#126—1461no—
377C2×#125—21no—
378C2×#125C2×D7311yescharacteristic
379C2×#125C2×D7311yescharacteristic
380C2×#124—731no—
381C2×#124—1461no—
382C2×#123—1461no—
383C2×C22⋊Q8—21no—
384C2×C22⋊Q8—21no—
385C2×C22⋊Q8—731no—
386C2×C22⋊Q8—1461no—
387C2×#121—731no—
388C2×C4×Q8—731no—
389C2×C4×D4—731no—
390C2×#117C2×D7311yescharacteristic
391C2×#117C2×D7311yescharacteristic
392C22×C4⋊C4C2×D7311yescharacteristic
393#501—738no—
394#498—738no—
395#489—738no—
396#488—738no—
397#485—738no—
398#483—738no—
399#482—738no—
400#481—738no—
401#479—738no—
402#478—738no—
403#476—738no—
404#475—738no—
405#433—738no—
406C2×#107—731no—
407C2×#107—731no—
408C2×#106—731no—
409C2×#106—731no—
410C2×#106—731no—
411C2×#106—731no—
412C2×#106—731no—
413C2×#106—731no—
414C2×C4⋊C8—731no—
415C2×C4⋊C8—731no—
416C2×#103—731no—
417C2×#103—731no—
418C2×#103—731no—
419C2×#103—731no—
420C2×#102—731no—
421C2×#102—731no—
422C2×#102—731no—
423C2×#102—731no—
424C2×C22⋊C8—731no—
425C2×C22⋊C8—731no—
426C2×#97—731no—
427C2×C4×C8—731no—
428C22×Q8—21no—
429C22×Q8—21no—
430C22×Q8—731no—
431C22×Q8—1461no—
432C22×D4—731no—
433C22×D4—1461no—
434C23×C4—21no—
435C23×C4—1461no—
436C23×C4C22×D7311yescharacteristic
437C22×C8—731no—
438C22×C8—731no—
439C22×C8—731no—
440C22×C8—731no—
441C4⋊Q8—28no—
442C4⋊Q8—22no—
443C4⋊Q8—22no—
444C4⋊Q8—734no—
445C4⋊Q8—1462no—
446C4⋊Q8C22×D7314yes—
447C4⋊Q8C22×D7314yes—
448#126—1468no—
449#125—28no—
450#125—22no—
451#125—22no—
452#125C22×D7314yes—
453#125C22×D7314yes—
454#124—734no—
455#124—1468no—
456#124—1462no—
457#123—1468no—
458C22⋊Q8—28no—
459C22⋊Q8—28no—
460C22⋊Q8—734no—
461C22⋊Q8—1462no—
462C22⋊Q8—1468no—
463#121—734no—
464#121—1462no—
465C4×Q8—734no—
466C4×Q8—1462no—
467C4×D4—734no—
468C4×D4—1462no—
469#117—22no—
470#117C22⋊D7314yes—
471#117C22×D7314yes—
472#117C22×D7314yes—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—731no—
482C2×C4⋊C4—731no—
483C2×C4⋊C4—1461no—
484C2×C4⋊C4—1461no—
485C2×C4⋊C4—1461no—
486C2×C4⋊C4C22⋊D7311yescharacteristic
487C2×C4⋊C4C22⋊D7311yescharacteristic
488C2×C4⋊C4C22×D7311yescharacteristic
489C2×C4⋊C4C22×D7311yescharacteristic
490C2×C4⋊C4C22×D7314yes—
491C2×C4⋊C4C22×D7311yescharacteristic
492C2×C4⋊C4C22×D7311yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—1461no—
495C2×C22⋊C4—1461no—
496C2×C22⋊C4—1461no—
497C2×C22⋊C4—1461no—
498C2×C22⋊C4—1461no—
499C2×C22⋊C4C22⋊D7311yescharacteristic
500C2×C22⋊C4C22⋊D7311yescharacteristic
501C2×C42—21no—
502C2×C42—1461no—
503C2×C42C22×D7311yescharacteristic
504C2×C42C22×D7311yescharacteristic
505#107—734no—
506#107—734no—
507#106—734no—
508#106—734no—
509#106—734no—
510#106—734no—
511#106—734no—
512#106—734no—
513C4⋊C8—734no—
514C4⋊C8—734no—
515#103—734no—
516#103—734no—
517#103—734no—
518#103—734no—
519#102—734no—
520#102—734no—
521#102—734no—
522#102—734no—
523C22⋊C8—734no—
524C22⋊C8—734no—
525#97—734no—
526C4×C8—734no—
527C24—1461no—
528C24C2×C22⋊D7311yescharacteristic
529C2×Q8—24no—
530C2×Q8—24no—
531C2×Q8—82no—
532C2×Q8—82no—
533C2×Q8—5842no—
534C2×Q8—732no—
535C2×Q8—1462no—
536C2×Q8—1462no—
537C2×Q8—1461no—
538C2×Q8—1464no—
539C2×D4—5842no—
540C2×D4—732no—
541C2×D4—1464no—
542C2×D4—1461no—
543C2×D4—1462no—
544C2×D4—1462no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—24no—
552C22×C4—82no—
553C22×C4—5842no—
554C22×C4—1461no—
555C22×C4—1461no—
556C22×C4—1461no—
557C22×C4—1464no—
558C22×C4C2×C22⋊D7312yes—
559C22×C4C2×C22⋊D7311yescharacteristic
560C22×C4C2×C22⋊D7311yescharacteristic
561C22×C4C2×C22⋊D7311yescharacteristic
562C22×C4C2×C22⋊D7311yescharacteristic
563C22×C4C2×C22⋊D7311yescharacteristic
564C22×C4C23×D7312yes—
565C22×C4C23×D7311yescharacteristic
566C2×C8—732no—
567C2×C8—732no—
568C2×C8—732no—
569C2×C8—732no—
570C2×C8—1462no—
571C2×C8—1462no—
572C2×C8—1462no—
573C2×C8—1462no—
574C4⋊C4—24no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—732no—
586C4⋊C4—732no—
587C4⋊C4—1464no—
588C4⋊C4—1464no—
589C4⋊C4—1461no—
590C4⋊C4—1461no—
591C4⋊C4—1464no—
592C4⋊C4C2×C22⋊D7314yes—
593C4⋊C4C2×C22⋊D7314yes—
594C4⋊C4C23×D7312yes—
595C4⋊C4C23×D7312yes—
596C4⋊C4C23×D7312yes—
597C4⋊C4C23×D7312yes—
598C22⋊C4—24no—
599C22⋊C4—1464no—
600C22⋊C4—1464no—
601C22⋊C4—1464no—
602C22⋊C4—1464no—
603C22⋊C4—1464no—
604C22⋊C4C2×C22⋊D7314yes—
605C22⋊C4C2×C22⋊D7314yes—
606C42—24no—
607C42—1464no—
608C42C2×C22⋊D7312yes—
609C42C2×C22⋊D7312yes—
610C42C23×D7312yes—
611C42C23×D7312yes—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—2922no—
616C23—2922no—
617C23—2922no—
618C23—1462no—
619C23C22×C22⋊D7312yes—
620C23C22×C22⋊D7311yescharacteristic
621Q8—84no—
622Q8—84no—
623Q8—2922no—
624Q8—5844no—
625Q8—1462no—
626Q8—1462no—
627D4—2922no—
628D4—5844no—
629D4—1462no—
630D4—1462no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—84no—
648C2×C4—2922no—
649C2×C4—2922no—
650C2×C4—2922no—
651C2×C4—5844no—
652C2×C4—1462no—
653C2×C4—1462no—
654C2×C4—1462no—
655C2×C4C22×C22⋊D7312yes—
656C2×C4C22×C22⋊D7312yes—
657C2×C4C22×C22⋊D7312yes—
658C2×C4C22×C22⋊D7312yes—
659C2×C4C22×C22⋊D7312yes—
660C2×C4C22×C22⋊D7311yescharacteristic
661C2×C4#1455663912yes—
662C2×C4#1455663912yes—
663C2×C4C24×D7311yescharacteristic
664C8—1462no—
665C8—1462no—
666C8—1462no—
667C8—1462no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—44no—
672C22—2922no—
673C22—2922no—
674C22—2922no—
675C22—5844no—
676C22#1798916112yes—
677C22#1798939512yes—
678C22#1798939812yes—
679C22C23×C22⋊D7311yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—42no—
689C4—2922no—
690C4—2922no—
691C4—2922no—
692C4#1798916112yes—
693C4C2×#1455663911yescharacteristic
694C4C2×#1455663911yescharacteristic
695C2—42no—
696C2—5842no—
697C2#2262122914yesdirect product factor
698C2C2×#1798916111yescharacteristic
699C2C2×#1798939511yescharacteristic
700C2C2×#1798939811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#544×C73C2
socleC23×C73C22×D4
prime radicalC2×#14556565C22
hypercenterC2×#544D73
hypocenterC73C2×#3244
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #22621229C2direct (N × H)
3. C2×#17988997C2semidirect
4. C2×#17988983C2semidirect
5. C2×#17988949C2semidirect
6. C2×#17988944C2semidirect
8. C2×#17988928C2semidirect
10. C2×#17988917C2semidirect
11. C2×#17988891C2semidirect
12. C2×#17988869C2semidirect
13. C2×#17988884C2semidirect
14. C2×#17988874C2semidirect
15. C2×#17988648C2semidirect
16. C2×#544×C73C2semidirect
29. #17988997C22semidirect
30. #17988983C22semidirect
31. #17988949C22semidirect
32. #17988944C22semidirect
33. #17988928C22semidirect
34. #17988917C22semidirect
37. #17988891C22semidirect
38. #17988884C22semidirect
39. #17988874C22semidirect
40. #17988869C22semidirect
41. #17988648C22semidirect
65. #544×C73C22semidirect
346. C2×C73#3244semidirect
351. C2×#544D73semidirect
367. C73C2×#3244semidirect
369. #544C2×D73semidirect
697. C2#22621229direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892082
#226212292
C2×#179889972
C2×#179889832
C2×#179889492
C2×#179889442
C2×#179889052
C2×#179889282
C2×#179889112
C2×#179889172
C2×#179888912
C2×#179888692
C2×#179888842
C2×#179888742
C2×#179886482
C2×#544×C732
C2×#324473