Finite Group Databasebeta

← C2×#22620599 #33955852

Subgroups — C2×#22620599 #33955852

Order 18688.

1906 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989208C211yesmaximal, characteristic
2C2×#17989199C211yesmaximal, characteristic, complemented
3#22620599C2116yesmaximal, direct product factor
4C2×#17988996C211yesmaximal, characteristic, complemented
5C2×#17988981C211yesmaximal, characteristic, complemented
6C2×#17988942C211yesmaximal, characteristic, complemented
7C2×#17988938C211yesmaximal, characteristic, complemented
8C2×#17988845C211yesmaximal, characteristic, complemented
9C2×#17988833C211yesmaximal, characteristic
10C2×#17988828C211yesmaximal, characteristic, complemented
11C2×#17988816C211yesmaximal, characteristic
12C2×#17988695C211yesmaximal, characteristic, complemented
13C2×#17988689C211yesmaximal, characteristic, complemented
14C2×C4×Dic292C211yesmaximal, characteristic, complemented
15C2×C4×#11924017C211yesmaximal, characteristic, complemented
16C2×#405×C73C211yesmaximal, characteristic, complemented
17C22×Dic292C2211yescharacteristic
18C22×Dic292C2211yescharacteristic
19C22×#11924017C2211yescharacteristic
20C22×#11924017C2211yescharacteristic
21#17989208—24no—
22#17989208C2218yes—
23#17989199—24no—
24#17989199C2218yescomplemented
25C2×#14556591C2211yescharacteristic
26C2×#14556591C2211yescharacteristic
27C2×#14556586—21no—
28C2×#14556584—21no—
29C2×#14556584—21no—
30C2×#14556583C2211yescharacteristic
31C2×#14556581—21no—
32C2×#14556581—21no—
33C2×#14556579C2211yescharacteristic
34C2×#14556577—21no—
35C2×#14556573—21no—
36C2×#14556570C2211yescharacteristic
37C2×#14556570C2211yescharacteristic
38C2×#14556570C2211yescharacteristic
39C2×#14556569—21no—
40C2×#14556565C2211yescharacteristic
41C2×C4×Dic146C2211yescharacteristic
42C2×C4×Dic146C2211yescharacteristic
43C2×C4×Dic146C2211yescharacteristic
44C2×C4×D292C2211yescharacteristic
45#17988996C2218yescomplemented
46#17988981C2218yescomplemented
47#17988942C2218yescomplemented
48#17988938C2218yescomplemented
49#17988845C2218yescomplemented
50#17988833C2218yes—
51#17988828C2218yescomplemented
52#17988816C2218yes—
53#17988695C2218yescomplemented
54#17988689C2218yescomplemented
55C4×Dic292C2218yescomplemented
56C4×#11924017C2218yescomplemented
57C2×#14556525C2211yescharacteristic
58C2×#14556525C2211yescharacteristic
59C2×#14556523C2211yescharacteristic
60C2×#14556523C2211yescharacteristic
61C2×#14556516C2211yescharacteristic
62C2×#14556516C2211yescharacteristic
63C2×#14556516C2211yescharacteristic
64C2×#14556516C2211yescharacteristic
65C2×#14556516C2211yescharacteristic
66C2×#14556516C2211yescharacteristic
67C2×#14556513C2211yescharacteristic
68C2×#14556513C2211yescharacteristic
69C22×M16×C73C2211yescharacteristic
70C23×C8×C73C2211yescharacteristic
71C2×#117×C73C2211yescharacteristic
72#405×C73C2218yescomplemented
73C2×#97×C73C2211yescharacteristic
74C2×#97×C73C2211yescharacteristic
75C2×C4×C8×C73C2211yescharacteristic
76C2×C4×C8×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146C2311yescharacteristic
79C22×Dic146C2311yescharacteristic
80C22×Dic146C2311yescharacteristic
81C22×D292C2311yescharacteristic
82C22×C22⋊D73—21no—
83C22×C4×D73—21no—
84C2×Dic292—24no—
85C2×Dic292—24no—
86C2×Dic292C2314yes—
87C2×Dic292C2314yes—
88C2×#11924017—24no—
89C2×#11924017—24no—
90C2×#11924017C2314yes—
91C2×#11924017C2314yes—
92#14556591—22no—
93#14556591—22no—
94#14556591C2314yes—
95#14556591C2314yes—
96#14556586—28no—
97#14556584—28no—
98#14556584—28no—
99#14556583—22no—
100#14556583C2314yes—
101#14556581—28no—
102#14556581—28no—
103#14556579—22no—
104#14556579C2314yes—
105#14556577—28no—
106#14556573—28no—
107#14556570—22no—
108#14556570—22no—
109#14556570—22no—
110#14556570C2314yes—
111#14556570C2314yes—
112#14556570C2314yes—
113#14556569—28no—
114#14556565—22no—
115#14556565C2314yes—
116C4×Dic146—22no—
117C4×Dic146—22no—
118C4×Dic146—22no—
119C4×Dic146C2314yes—
120C4×Dic146C2314yes—
121C4×Dic146C2314yes—
122C4×D292—22no—
123C4×D292C2314yes—
124C2×C4⋊Dic73—21no—
125C2×C4⋊Dic73—21no—
126C2×C4⋊Dic73—21no—
127C2×C4⋊Dic73C2311yescharacteristic
128C2×C4⋊Dic73C2311yescharacteristic
129C2×C4⋊Dic73C2311yescharacteristic
130C2×C4⋊Dic73C2311yescharacteristic
131C2×#11924007—21no—
132C2×#11924007—21no—
133C2×#11924007—21no—
134C2×#11924007—21no—
135C2×#11924007—21no—
136C2×#11924007—21no—
137C2×#11924007—21no—
138C2×#11924007—21no—
139C2×C22⋊Dic73—21no—
140C2×C22⋊Dic73—21no—
141C2×C22⋊Dic73—21no—
142C2×#11924005—21no—
143C2×#11924005—21no—
144C2×#11924005—21no—
145C2×#11924005—21no—
146C2×C4×Dic73—21no—
147C2×C4×Dic73—21no—
148C2×C4×Dic73—21no—
149#14556525C2314yes—
150#14556525C2314yes—
151#14556523C2314yes—
152#14556523C2314yes—
153#14556516C2314yes—
154#14556516C2314yes—
155#14556516C2314yes—
156#14556516C2314yes—
157#14556516C2314yes—
158#14556516C2314yes—
159#14556513C2314yes—
160#14556513C2314yes—
161C23×C4×C73C2311yescharacteristic
162C2×M16×C73—24no—
163C2×M16×C73C2314yes—
164C22×C8×C73—24no—
165C22×C8×C73C2311yescharacteristic
166C22×C8×C73C2311yescharacteristic
167C22×C8×C73C2314yes—
168C22×C8×C73C2311yescharacteristic
169C22×C8×C73C2311yescharacteristic
170#117×C73D414yes—
171#117×C73C2314yes—
172C2×C4⋊C4×C73D411yescharacteristic
173C2×C4⋊C4×C73D411yescharacteristic
174C2×C22⋊C4×C73D411yescharacteristic
175C2×C22⋊C4×C73D411yescharacteristic
176C2×C42×C73C2311yescharacteristic
177C2×C42×C73C2311yescharacteristic
178#97×C73C2314yes—
179#97×C73C2314yes—
180C4×C8×C73C2314yes—
181C4×C8×C73C2314yes—
182C23×D73—21no—
183C2×Dic146—22no—
184C2×Dic146—22no—
185C2×Dic146—22no—
186C2×Dic146—22no—
187C2×Dic146—22no—
188C2×Dic146—22no—
189C2×Dic146—21no—
190C2×Dic146—21no—
191C2×Dic146—21no—
192C2×Dic146—24no—
193C2×Dic146—82no—
194C2×Dic146C2412yes—
195C2×Dic146C2412yes—
196C2×Dic146C2412yes—
197C2×D292—22no—
198C2×D292—22no—
199C2×D292—21no—
200C2×D292C2412yes—
201C2×C22⋊D73—24no—
202C2×C22⋊D73—82no—
203C22×Dic73—21no—
204C22×Dic73—21no—
205C22×Dic73—21no—
206C22×Dic73—21no—
207C22×Dic73—21no—
208C22×Dic73—21no—
209C22×Dic73—21no—
210C2×C4×D73—24no—
211C2×C4×D73—82no—
212Dic292—28no—
213Dic292—28no—
214#11924017—28no—
215#11924017—28no—
216C4⋊Dic73—24no—
217C4⋊Dic73—24no—
218C4⋊Dic73—24no—
219C4⋊Dic73—21no—
220C4⋊Dic73—21no—
221C4⋊Dic73—21no—
222C4⋊Dic73—21no—
223C4⋊Dic73C2412yes—
224C4⋊Dic73C2412yes—
225C4⋊Dic73C2412yes—
226C4⋊Dic73C2412yes—
227#11924007—24no—
228#11924007—24no—
229#11924007—24no—
230#11924007—24no—
231#11924007—24no—
232#11924007—24no—
233#11924007—24no—
234#11924007—24no—
235C22⋊Dic73—24no—
236C22⋊Dic73—24no—
237C22⋊Dic73—24no—
238#11924005—24no—
239#11924005—24no—
240#11924005—24no—
241#11924005—24no—
242C4×Dic73—24no—
243C4×Dic73—24no—
244C4×Dic73—24no—
245C24×C73C2×D411yescharacteristic
246C22×C4×C73—22no—
247C22×C4×C73—22no—
248C22×C4×C73C2×D411yescharacteristic
249C22×C4×C73C2×D411yescharacteristic
250C22×C4×C73C2×D411yescharacteristic
251C22×C4×C73C2×D411yescharacteristic
252C22×C4×C73C2×D411yescharacteristic
253C22×C4×C73C2×D412yes—
254C22×C4×C73C2412yes—
255C22×C4×C73C2411yescharacteristic
256M16×C73—28no—
257C2×C8×C73—22no—
258C2×C8×C73—22no—
259C2×C8×C73—28no—
260C2×C8×C73#4114yes—
261C2×C8×C73#4114yes—
262C2×C8×C73C2412yes—
263C2×C8×C73C2412yes—
264C2×C8×C73C2412yes—
265C2×C8×C73C2412yes—
266C4⋊C4×C73C2×D414yes—
267C4⋊C4×C73C2×D414yes—
268C22⋊C4×C73C2×D414yes—
269C22⋊C4×C73C2×D414yes—
270C42×C73C2×D412yes—
271C42×C73C2×D412yes—
272C42×C73C2412yes—
273C42×C73C2412yes—
274C23×C73—22no—
275C23×C73—22no—
276C23×C73—22no—
277C23×C73C22×D412yes—
278C23×C73C22×D411yescharacteristic
279C22×D73—22no—
280C22×D73—42no—
281C22×D73—42no—
282C22×D73—42no—
283C2×C4×C73—22no—
284C2×C4×C73—22no—
285C2×C4×C73—22no—
286C2×C4×C73—22no—
287C2×C4×C73—22no—
288C2×C4×C73—24no—
289C2×C4×C73—22no—
290C2×C4×C73—22no—
291C2×C4×C73C22×D412yes—
292C2×C4×C73C22×D412yes—
293C2×C4×C73C22×D412yes—
294C2×C4×C73C22×D412yes—
295C2×C4×C73C22×D412yes—
296C2×C4×C73C22×D411yescharacteristic
297C2×C4×C73C2×#4112yes—
298C2×C4×C73C2×#4112yes—
299C2×C4×C73C2511yescharacteristic
300C22⋊D73—84no—
301C2×Dic73—22no—
302C2×Dic73—22no—
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—22no—
307C2×Dic73—22no—
308C2×Dic73—42no—
309C2×Dic73—42no—
310C2×Dic73—42no—
311C2×Dic73—42no—
312C2×Dic73—42no—
313C2×Dic73—42no—
314C2×Dic73—42no—
315D292—22no—
316D292—22no—
317D292—42no—
318C4×D73—84no—
319Dic146—22no—
320Dic146—22no—
321Dic146—22no—
322Dic146—22no—
323Dic146—22no—
324Dic146—22no—
325Dic146—42no—
326Dic146—42no—
327Dic146—42no—
328Dic146—84no—
329C8×C73—22no—
330C8×C73—22no—
331C8×C73C2×#4114yes—
332C8×C73C2×#4114yes—
333C22×C73—22no—
334C22×C73—22no—
335C22×C73—22no—
336C22×C73—44no—
337C22×C73#53212yes—
338C22×C73#57712yes—
339C22×C73#57812yes—
340C22×C73C23×D411yescharacteristic
341C2×D73—42no—
342C2×D73—42no—
343C2×D73—42no—
344C2×D73—84no—
345C4×C73—22no—
346C4×C73—22no—
347C4×C73—22no—
348C4×C73—22no—
349C4×C73—22no—
350C4×C73#53212yes—
351C4×C73C22×#4111yescharacteristic
352C4×C73C22×#4111yescharacteristic
353Dic73—42no—
354Dic73—42no—
355Dic73—42no—
356Dic73—42no—
357Dic73—42no—
358Dic73—42no—
359Dic73—42no—
360C2×#3178—731nomaximal, Sylow
361C2×C73—42no—
362C2×C73#317814yescomplemented
363C2×C73C2×#53211yescharacteristic
364C2×C73C2×#57711yescharacteristic
365C2×C73C2×#57811yescharacteristic
366D73—82no—
367C2×#542—731no—
368C2×#541—731no—
369#3178—7316no—
370C2×#501—731no—
371C2×#497—731no—
372C2×#488—731no—
373C2×#487—731no—
374C2×#470—731no—
375C2×#468—731no—
376C2×#467—731no—
377C2×#465—731no—
378C2×#441—731no—
379C2×#440—731no—
380C2×C4×Q16—731no—
381C2×C4×SD16—731no—
382C2×#405D7311yescharacteristic, complemented
383C73C2×#317811yescharacteristic, complemented, Sylow
384C22×Q16—731no—
385C22×Q16—731no—
386C22×SD16—731no—
387C22×SD16—731no—
388C22×M16C2×D7311yescharacteristic
389C23×C8C2×D7311yescharacteristic
390#542—738no—
391#542—1464no—
392#541—738no—
393#541—1464no—
394C2×C4⋊Q8—731no—
395C2×C4⋊Q8—731no—
396C2×#126—1461no—
397C2×#126—1461no—
398C2×#126—1461no—
399C2×#125—731no—
400C2×#125—1461no—
401C2×#125—1461no—
402C2×#124—731no—
403C2×#124—1461no—
404C2×#123—1461no—
405C2×C22⋊Q8—731no—
406C2×C22⋊Q8—731no—
407C2×C22⋊Q8—731no—
408C2×C22⋊Q8—1461no—
409C2×#121—731no—
410C2×C4×Q8—731no—
411C2×C4×Q8—731no—
412C2×C4×Q8—731no—
413C2×C4×D4—731no—
414C2×#117C2×D7311yescharacteristic
415#501—738no—
416#497—738no—
417#488—738no—
418#487—738no—
419#470—738no—
420#468—738no—
421#467—738no—
422#465—738no—
423#441—738no—
424#440—738no—
425C4×Q16—738no—
426C4×SD16—738no—
427C2×#107—731no—
428C2×#107—731no—
429C2×#106—731no—
430C2×#106—731no—
431C2×#103—731no—
432C2×#103—731no—
433C2×#103—731no—
434C2×#103—731no—
435C2×#103—731no—
436C2×#103—731no—
437C2×#102—731no—
438C2×#102—731no—
439#405C2×D7318yescomplemented
440C2×#97C2×D7311yescharacteristic
441C2×#97C2×D7311yescharacteristic
442C2×C4×C8C2×D7311yescharacteristic
443C2×C4×C8C2×D7311yescharacteristic
444C22×Q8—731no—
445C22×Q8—731no—
446C22×Q8—731no—
447C22×Q8—1461no—
448C22×D4—731no—
449C22×D4—1461no—
450C23×C4—1461no—
451C23×C4C22×D7311yescharacteristic
452C2×Q16—734no—
453C2×Q16—734no—
454C2×Q16—1464no—
455C2×Q16—1464no—
456C2×SD16—734no—
457C2×SD16—734no—
458C2×SD16—1464no—
459C2×SD16—1464no—
460C2×M16—24no—
461C2×M16C22×D7314yes—
462C22×C8—24no—
463C22×C8C22×D7311yescharacteristic
464C22×C8C22×D7314yes—
465C22×C8C22×D7311yescharacteristic
466C22×C8C22×D7311yescharacteristic
467C22×C8C22×D7311yescharacteristic
468C4⋊Q8—734no—
469C4⋊Q8—734no—
470C4⋊Q8—1462no—
471C4⋊Q8—1462no—
472#126—1468no—
473#126—1468no—
474#126—1468no—
475#125—734no—
476#125—1468no—
477#125—1468no—
478#125—1462no—
479#124—734no—
480#124—1468no—
481#124—1462no—
482#123—1468no—
483C22⋊Q8—734no—
484C22⋊Q8—734no—
485C22⋊Q8—734no—
486C22⋊Q8—1462no—
487C22⋊Q8—1462no—
488C22⋊Q8—1462no—
489C22⋊Q8—1468no—
490#121—734no—
491#121—1462no—
492C4×Q8—734no—
493C4×Q8—734no—
494C4×Q8—734no—
495C4×Q8—1462no—
496C4×Q8—1462no—
497C4×Q8—1462no—
498C4×D4—734no—
499C4×D4—1462no—
500#117D29214yes—
501#117C22×D7314yes—
502C2×C4⋊C4—731no—
503C2×C4⋊C4—731no—
504C2×C4⋊C4—731no—
505C2×C4⋊C4—731no—
506C2×C4⋊C4—1461no—
507C2×C4⋊C4—1461no—
508C2×C4⋊C4—1461no—
509C2×C4⋊C4—1461no—
510C2×C4⋊C4—1461no—
511C2×C4⋊C4—1461no—
512C2×C4⋊C4—1461no—
513C2×C4⋊C4—1461no—
514C2×C4⋊C4—1461no—
515C2×C4⋊C4—1461no—
516C2×C4⋊C4—1461no—
517C2×C4⋊C4D29211yescharacteristic
518C2×C4⋊C4D29211yescharacteristic
519C2×C22⋊C4—1461no—
520C2×C22⋊C4—1461no—
521C2×C22⋊C4—1461no—
522C2×C22⋊C4—1461no—
523C2×C22⋊C4—1461no—
524C2×C22⋊C4—1461no—
525C2×C22⋊C4—1461no—
526C2×C22⋊C4D29211yescharacteristic
527C2×C22⋊C4D29211yescharacteristic
528C2×C42—1461no—
529C2×C42—1461no—
530C2×C42—1461no—
531C2×C42C22×D7311yescharacteristic
532C2×C42C22×D7311yescharacteristic
533#107—734no—
534#107—734no—
535#106—734no—
536#106—734no—
537#103—734no—
538#103—734no—
539#103—734no—
540#103—734no—
541#103—734no—
542#103—734no—
543#102—734no—
544#102—734no—
545#97C22×D7314yes—
546#97C22×D7314yes—
547C4×C8C22×D7314yes—
548C4×C8C22×D7314yes—
549C24—1461no—
550C24C2×D29211yescharacteristic
551C2×Q8—5842no—
552C2×Q8—732no—
553C2×Q8—732no—
554C2×Q8—732no—
555C2×Q8—1462no—
556C2×Q8—1462no—
557C2×Q8—1462no—
558C2×Q8—1462no—
559C2×Q8—1462no—
560C2×Q8—1462no—
561C2×Q8—1461no—
562C2×Q8—1461no—
563C2×Q8—1461no—
564C2×Q8—1464no—
565C2×D4—5842no—
566C2×D4—732no—
567C2×D4—1464no—
568C2×D4—1461no—
569C2×D4—1462no—
570C2×D4—1462no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—5842no—
574C22×C4—1461no—
575C22×C4—1461no—
576C22×C4—1461no—
577C22×C4—1461no—
578C22×C4—1461no—
579C22×C4—1461no—
580C22×C4—1461no—
581C22×C4—1464no—
582C22×C4C2×D29212yes—
583C22×C4C2×D29211yescharacteristic
584C22×C4C2×D29211yescharacteristic
585C22×C4C2×D29211yescharacteristic
586C22×C4C2×D29211yescharacteristic
587C22×C4C2×D29211yescharacteristic
588C22×C4C23×D7312yes—
589C22×C4C23×D7311yescharacteristic
590Q16—1468no—
591Q16—1468no—
592SD16—1468no—
593SD16—1468no—
594M16—28no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—28no—
598C2×C8#1192402814yes—
599C2×C8#1192402814yes—
600C2×C8C23×D7312yes—
601C2×C8C23×D7312yes—
602C2×C8C23×D7312yes—
603C2×C8C23×D7312yes—
604C4⋊C4—732no—
605C4⋊C4—732no—
606C4⋊C4—732no—
607C4⋊C4—732no—
608C4⋊C4—1464no—
609C4⋊C4—1464no—
610C4⋊C4—1464no—
611C4⋊C4—1464no—
612C4⋊C4—1464no—
613C4⋊C4—1464no—
614C4⋊C4—1464no—
615C4⋊C4—1464no—
616C4⋊C4—1461no—
617C4⋊C4—1461no—
618C4⋊C4—1461no—
619C4⋊C4—1461no—
620C4⋊C4—1464no—
621C4⋊C4—1464no—
622C4⋊C4—1464no—
623C4⋊C4C2×D29214yes—
624C4⋊C4C2×D29214yes—
625C22⋊C4—1464no—
626C22⋊C4—1464no—
627C22⋊C4—1464no—
628C22⋊C4—1464no—
629C22⋊C4—1464no—
630C22⋊C4—1464no—
631C22⋊C4—1464no—
632C22⋊C4C2×D29214yes—
633C22⋊C4C2×D29214yes—
634C42—1464no—
635C42—1464no—
636C42—1464no—
637C42C2×D29212yes—
638C42C2×D29212yes—
639C42C23×D7312yes—
640C42C23×D7312yes—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—2922no—
645C23—2922no—
646C23—2922no—
647C23—1462no—
648C23C22×D29212yes—
649C23C22×D29211yescharacteristic
650Q8—2922no—
651Q8—2922no—
652Q8—2922no—
653Q8—5844no—
654Q8—1462no—
655Q8—1462no—
656Q8—1462no—
657Q8—1462no—
658Q8—1462no—
659Q8—1462no—
660D4—2922no—
661D4—5844no—
662D4—1462no—
663D4—1462no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—2922no—
673C2×C4—2922no—
674C2×C4—2922no—
675C2×C4—2922no—
676C2×C4—2922no—
677C2×C4—2922no—
678C2×C4—2922no—
679C2×C4—5844no—
680C2×C4—1462no—
681C2×C4—1462no—
682C2×C4—1462no—
683C2×C4—1462no—
684C2×C4—1462no—
685C2×C4—1462no—
686C2×C4—1462no—
687C2×C4C22×D29212yes—
688C2×C4C22×D29212yes—
689C2×C4C22×D29212yes—
690C2×C4C22×D29212yes—
691C2×C4C22×D29212yes—
692C2×C4C22×D29211yescharacteristic
693C2×C4C2×#1192402812yes—
694C2×C4C2×#1192402812yes—
695C2×C4C24×D7311yescharacteristic
696C8—22no—
697C8—22no—
698C8C2×#1192402814yes—
699C8C2×#1192402814yes—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—2922no—
705C22—2922no—
706C22—2922no—
707C22—5844no—
708C22#1798913712yes—
709C22#1798939912yes—
710C22#1798940412yes—
711C22C23×D29211yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—2922no—
718C4—2922no—
719C4—2922no—
720C4—2922no—
721C4—2922no—
722C4—2922no—
723C4—2922no—
724C4#1798913712yes—
725C4C22×#1192402811yescharacteristic
726C4C22×#1192402811yescharacteristic
727C2—42no—
728C2—5842no—
729C2#2262059914yesdirect product factor
730C2C2×#1798913711yescharacteristic
731C2C2×#1798939911yescharacteristic
732C2C2×#1798940411yescharacteristic
subgroupG/H
centerC23C22×D292
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#405×C73C2
socleC23×C73C22×D4
prime radicalC2×#14556565C22
hypercenterC2×#405D73
hypocenterC73C2×#3178
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
2. C2×#17989199C2semidirect
3. #22620599C2direct (N × H)
4. C2×#17988996C2semidirect
5. C2×#17988981C2semidirect
6. C2×#17988942C2semidirect
7. C2×#17988938C2semidirect
8. C2×#17988845C2semidirect
10. C2×#17988828C2semidirect
12. C2×#17988695C2semidirect
13. C2×#17988689C2semidirect
14. C2×C4×Dic292C2semidirect
15. C2×C4×#11924017C2semidirect
16. C2×#405×C73C2semidirect
24. #17989199C22semidirect
45. #17988996C22semidirect
46. #17988981C22semidirect
47. #17988942C22semidirect
48. #17988938C22semidirect
49. #17988845C22semidirect
51. #17988828C22semidirect
53. #17988695C22semidirect
54. #17988689C22semidirect
55. C4×Dic292C22semidirect
56. C4×#11924017C22semidirect
72. #405×C73C22semidirect
362. C2×C73#3178semidirect
382. C2×#405D73semidirect
383. C73C2×#3178semidirect
439. #405C2×D73semidirect
729. C2#22620599direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892082
C2×#179891992
#226205992
C2×#179889962
C2×#179889812
C2×#179889422
C2×#179889382
C2×#179888452
C2×#179888332
C2×#179888282
C2×#179888162
C2×#179886952
C2×#179886892
C2×C4×Dic2922
C2×C4×#119240172
C2×#405×C732
C2×#317873