Finite Group Databasebeta

← C2×#22620604 #33955857

Subgroups — C2×#22620604 #33955857

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×#17989211C211yesmaximal, characteristic
2C2×#17989200C211yesmaximal, characteristic, complemented
3#22620604C2116yesmaximal, direct product factor
4C2×#17988981C211yesmaximal, characteristic, complemented
5C2×#17988944C211yesmaximal, characteristic, complemented
6C2×#17988939C211yesmaximal, characteristic, complemented
7C2×#17988846C211yesmaximal, characteristic, complemented
8C2×#17988834C211yesmaximal, characteristic
9C2×#17988829C211yesmaximal, characteristic, complemented
10C2×#17988817C211yesmaximal, characteristic
11C2×#17988693C211yesmaximal, characteristic, complemented
12C2×#17988686C211yesmaximal, characteristic, complemented
13C2×#17988681C211yesmaximal, characteristic, complemented
14C2×#17988674C211yesmaximal, characteristic, complemented
15C2×#17988544C211yesmaximal, characteristic, complemented
16C2×#501×C73C211yesmaximal, characteristic, complemented
17C22×Dic292C2211yescharacteristic
18C22×Dic292C2211yescharacteristic
19C22×#11924017C2211yescharacteristic
20C22×#11924017C2211yescharacteristic
21C22×#11924011C2211yescharacteristic
22C22×C8×D73C2211yescharacteristic
23#17989211—24no—
24#17989211C2218yes—
25#17989200—24no—
26#17989200C2218yescomplemented
27C2×#14556591C2211yescharacteristic
28C2×#14556586—21no—
29C2×#14556586—21no—
30C2×#14556586—21no—
31C2×#14556582—21no—
32C2×#14556582—21no—
33C2×#14556580—21no—
34C2×#14556579C2211yescharacteristic
35C2×#14556576—21no—
36C2×#14556571C2211yescharacteristic
37C2×#14556571C2211yescharacteristic
38C2×#14556571C2211yescharacteristic
39C2×#14556567—21no—
40C2×#14556566C2211yescharacteristic
41C2×#14556556C2211yescharacteristic
42C2×#14556556C2211yescharacteristic
43C2×#14556556C2211yescharacteristic
44C2×#14556553C2211yescharacteristic
45C2×#14556548C2211yescharacteristic
46#17988981C2218yescomplemented
47#17988944C2218yescomplemented
48#17988939C2218yescomplemented
49#17988846C2218yescomplemented
50#17988834C2218yes—
51#17988829C2218yescomplemented
52#17988817C2218yes—
53#17988693C2218yescomplemented
54#17988686C2218yescomplemented
55#17988681C2218yescomplemented
56#17988674C2218yescomplemented
57C2×#14556514C2211yescharacteristic
58C2×#14556514C2211yescharacteristic
59C2×#14556514C2211yescharacteristic
60C2×#14556514C2211yescharacteristic
61C2×#14556514C2211yescharacteristic
62C2×#14556514C2211yescharacteristic
63C2×#14556511C2211yescharacteristic
64C2×#14556511C2211yescharacteristic
65#17988544C2218yescomplemented
66C2×#14556501C2211yescharacteristic
67C2×C4×#10596831C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C2×C4⋊Q8×C73C2211yescharacteristic
70C2×#125×C73C2211yescharacteristic
71#501×C73C2218yescomplemented
72C2×#107×C73C2211yescharacteristic
73C2×#107×C73C2211yescharacteristic
74C2×#106×C73C2211yescharacteristic
75C2×#106×C73C2211yescharacteristic
76C2×#97×C73C2211yescharacteristic
77C22×Dic146C2311yescharacteristic
78C22×Dic146C2311yescharacteristic
79C22×Dic146C2311yescharacteristic
80C22×D292—21no—
81C22×D292C2311yescharacteristic
82C22×C4×D73—21no—
83C22×C4×D73C2311yescharacteristic
84C2×Dic292—24no—
85C2×Dic292—24no—
86C2×Dic292C2314yes—
87C2×Dic292C2314yes—
88C2×#11924017—24no—
89C2×#11924017—24no—
90C2×#11924017C2314yes—
91C2×#11924017C2314yes—
92C2×#11924011—24no—
93C2×#11924011C2314yes—
94C22×#10596831C2311yescharacteristic
95C22×#10596831C2311yescharacteristic
96C2×C8×D73—24no—
97C2×C8×D73C2314yes—
98#14556591—22no—
99#14556591C2314yes—
100#14556586—28no—
101#14556586—28no—
102#14556586—28no—
103#14556582—28no—
104#14556582—28no—
105#14556580—28no—
106#14556579—22no—
107#14556579C2314yes—
108#14556576—28no—
109#14556571—22no—
110#14556571—22no—
111#14556571—22no—
112#14556571C2314yes—
113#14556571C2314yes—
114#14556571C2314yes—
115#14556567—28no—
116#14556566—22no—
117#14556566C2314yes—
118#14556556—22no—
119#14556556—22no—
120#14556556—22no—
121#14556556C2314yes—
122#14556556C2314yes—
123#14556556C2314yes—
124#14556553—22no—
125#14556553C2314yes—
126#14556548D414yes—
127#14556548C2314yes—
128C2×C4⋊Dic73—21no—
129C2×C4⋊Dic73—21no—
130C2×C4⋊Dic73—21no—
131C2×C4⋊Dic73—21no—
132C2×C4⋊Dic73—21no—
133C2×#11924007—21no—
134C2×#11924007—21no—
135C2×#11924007—21no—
136C2×#11924007D411yescharacteristic
137C2×#11924007D411yescharacteristic
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×#11924005—21no—
141C2×#11924005—21no—
142C2×#11924005—21no—
143C2×#11924005—21no—
144C2×#11924005—21no—
145C2×#11924005D411yescharacteristic
146C2×#11924005D411yescharacteristic
147C2×C4×Dic73—21no—
148C2×C4×Dic73—21no—
149C2×C4×Dic73—21no—
150C2×C4×Dic73C2311yescharacteristic
151#14556514C2314yes—
152#14556514C2314yes—
153#14556514C2314yes—
154#14556514C2314yes—
155#14556514C2314yes—
156#14556514C2314yes—
157#14556511C2314yes—
158#14556511C2314yes—
159#14556501C2314yes—
160C4×#10596831C2314yes—
161C8×Dic73C2314yes—
162C22×Q8×C73—21no—
163C22×C8×C73C2311yescharacteristic
164C22×C8×C73C2311yescharacteristic
165C4⋊Q8×C73—22no—
166C4⋊Q8×C73C2314yes—
167#125×C73—22no—
168#125×C73C2314yes—
169C2×C4⋊C4×C73—21no—
170C2×C4⋊C4×C73—21no—
171C2×C4⋊C4×C73—21no—
172C2×C4⋊C4×C73C2311yescharacteristic
173C2×C4⋊C4×C73C2311yescharacteristic
174C2×C4⋊C4×C73C2311yescharacteristic
175C2×C4⋊C4×C73C2311yescharacteristic
176C2×C42×C73C2311yescharacteristic
177#107×C73C2314yes—
178#107×C73C2314yes—
179#106×C73C2314yes—
180#106×C73C2314yes—
181#97×C73C2314yes—
182C23×D73—21no—
183C23×D73C2×D411yescharacteristic
184C2×Dic146—22no—
185C2×Dic146—22no—
186C2×Dic146—22no—
187C2×Dic146—22no—
188C2×Dic146—22no—
189C2×Dic146—22no—
190C2×Dic146—21no—
191C2×Dic146—21no—
192C2×Dic146—21no—
193C2×Dic146C2412yes—
194C2×Dic146C2412yes—
195C2×Dic146C2412yes—
196C2×D292—22no—
197C2×D292—22no—
198C2×D292—21no—
199C2×D292—24no—
200C2×D292—82no—
201C2×D292C2412yes—
202C22×Dic73—21no—
203C22×Dic73—21no—
204C22×Dic73—21no—
205C22×Dic73C2×D411yescharacteristic
206C22×Dic73C2×D411yescharacteristic
207C22×Dic73C2×D411yescharacteristic
208C2×C4×D73—22no—
209C2×C4×D73—22no—
210C2×C4×D73—24no—
211C2×C4×D73—82no—
212C2×C4×D73C2×D412yes—
213C2×C4×D73C2412yes—
214Dic292—28no—
215Dic292—28no—
216#11924017—28no—
217#11924017—28no—
218#11924011—28no—
219C2×#10596831—22no—
220C2×#10596831—22no—
221C2×#10596831C2412yes—
222C2×#10596831C2412yes—
223C8×D73—28no—
224C4⋊Dic73—24no—
225C4⋊Dic73—24no—
226C4⋊Dic73—24no—
227C4⋊Dic73—24no—
228C4⋊Dic73—24no—
229#11924007—24no—
230#11924007—24no—
231#11924007—24no—
232#11924007C2×D414yes—
233#11924007C2×D414yes—
234#11924005—24no—
235#11924005—24no—
236#11924005—24no—
237#11924005—24no—
238#11924005—24no—
239#11924005—24no—
240#11924005—24no—
241#11924005C2×D414yes—
242#11924005C2×D414yes—
243C4×Dic73—24no—
244C4×Dic73—24no—
245C4×Dic73—24no—
246C4×Dic73C2×D412yes—
247C4×Dic73C2412yes—
248C2×Q8×C73—24no—
249C2×Q8×C73—82no—
250C22×C4×C73—21no—
251C22×C4×C73—21no—
252C22×C4×C73—21no—
253C22×C4×C73—21no—
254C22×C4×C73C2×D411yescharacteristic
255C22×C4×C73C2×D411yescharacteristic
256C22×C4×C73C2411yescharacteristic
257C2×C8×C73#4114yes—
258C2×C8×C73#4114yes—
259C2×C8×C73C2412yes—
260C2×C8×C73C2412yes—
261C4⋊C4×C73—24no—
262C4⋊C4×C73—24no—
263C4⋊C4×C73—24no—
264C4⋊C4×C73—21no—
265C4⋊C4×C73—21no—
266C4⋊C4×C73—21no—
267C4⋊C4×C73—21no—
268C4⋊C4×C73C2412yes—
269C4⋊C4×C73C2412yes—
270C4⋊C4×C73C2412yes—
271C4⋊C4×C73C2412yes—
272C42×C73C2×D412yes—
273C42×C73C2412yes—
274C23×C73C22×D411yescharacteristic
275C22×D73—22no—
276C22×D73—22no—
277C22×D73—22no—
278C22×D73—22no—
279C22×D73—42no—
280C22×D73—42no—
281C22×D73—42no—
282C22×D73C22×D412yes—
283Q8×C73—84no—
284C2×C4×C73—22no—
285C2×C4×C73—22no—
286C2×C4×C73—22no—
287C2×C4×C73—22no—
288C2×C4×C73—22no—
289C2×C4×C73—22no—
290C2×C4×C73—42no—
291C2×C4×C73—42no—
292C2×C4×C73—42no—
293C2×C4×C73—42no—
294C2×C4×C73C22×D412yes—
295C2×C4×C73C22×D412yes—
296C2×C4×C73C22×D411yescharacteristic
297C2×C4×C73C2×#4112yes—
298C2×C4×C73C2×#4112yes—
299C2×C4×C73C2511yescharacteristic
300C2×Dic73—22no—
301C2×Dic73—22no—
302C2×Dic73—22no—
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—42no—
307C2×Dic73—42no—
308C2×Dic73—42no—
309C2×Dic73C22×D412yes—
310C2×Dic73C22×D412yes—
311C2×Dic73C22×D412yes—
312D292—22no—
313D292—22no—
314D292—42no—
315D292—84no—
316C4×D73—24no—
317C4×D73—22no—
318C4×D73—22no—
319C4×D73—84no—
320Dic146—22no—
321Dic146—22no—
322Dic146—22no—
323Dic146—22no—
324Dic146—22no—
325Dic146—22no—
326Dic146—42no—
327Dic146—42no—
328Dic146—42no—
329C8×C73C2×#4114yes—
330C8×C73C2×#4114yes—
331#10596831—22no—
332#10596831—22no—
333C22×C73#53212yes—
334C22×C73#57712yes—
335C22×C73#57812yes—
336C22×C73C23×D411yescharacteristic
337C2×D73—22no—
338C2×D73—22no—
339C2×D73—22no—
340C2×D73—44no—
341C2×D73—42no—
342C2×D73—42no—
343C2×D73—42no—
344C2×D73—84no—
345C4×C73—22no—
346C4×C73—22no—
347C4×C73—42no—
348C4×C73—42no—
349C4×C73—42no—
350C4×C73—42no—
351C4×C73#53212yes—
352C4×C73C22×#4111yescharacteristic
353C4×C73C22×#4111yescharacteristic
354Dic73—22no—
355Dic73—22no—
356Dic73—22no—
357Dic73—42no—
358Dic73—42no—
359Dic73—42no—
360C2×#3178—731nomaximal, Sylow
361C2×C73#317814yescomplemented
362C2×C73C2×#53211yescharacteristic
363C2×C73C2×#57711yescharacteristic
364C2×C73C2×#57811yescharacteristic
365D73—42no—
366D73—82no—
367C2×#542—731no—
368C2×#541—731no—
369#3178—7316no—
370C2×#501D7311yescharacteristic, complemented
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×#405—731no—
383C73C2×#317811yescharacteristic, complemented, Sylow
384C22×Q16—731no—
385C22×Q16—731no—
386C22×SD16—731no—
387C22×SD16—731no—
388C22×M16—731no—
389C23×C8—731no—
390#542—738no—
391#542—1464no—
392#541—738no—
393#541—1464no—
394C2×C4⋊Q8—731no—
395C2×C4⋊Q8C2×D7311yescharacteristic
396C2×#126—1461no—
397C2×#126—1461no—
398C2×#126—1461no—
399C2×#125—1461no—
400C2×#125—1461no—
401C2×#125C2×D7311yescharacteristic
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×#117—731no—
415#501C2×D7318yescomplemented
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×#107C2×D7311yescharacteristic
428C2×#107C2×D7311yescharacteristic
429C2×#106C2×D7311yescharacteristic
430C2×#106C2×D7311yescharacteristic
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#405—738no—
440C2×#97—731no—
441C2×#97C2×D7311yescharacteristic
442C2×C4×C8—731no—
443C2×C4×C8—731no—
444C22×Q8—21no—
445C22×Q8—731no—
446C22×Q8—731no—
447C22×Q8—731no—
448C22×D4—731no—
449C22×D4—1461no—
450C23×C4—731no—
451C23×C4—1461no—
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—734no—
461C2×M16—1464no—
462C22×C8—731no—
463C22×C8—731no—
464C22×C8—734no—
465C22×C8—1464no—
466C22×C8C22×D7311yescharacteristic
467C22×C8C22×D7311yescharacteristic
468C4⋊Q8—22no—
469C4⋊Q8—734no—
470C4⋊Q8—1462no—
471C4⋊Q8C22×D7314yes—
472#126—1468no—
473#126—1468no—
474#126—1468no—
475#125—22no—
476#125—1468no—
477#125—1468no—
478#125C22×D7314yes—
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#117—734no—
501#117—734no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—731no—
506C2×C4⋊C4—731no—
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⋊C4C22×D7311yescharacteristic
516C2×C4⋊C4C22×D7311yescharacteristic
517C2×C4⋊C4C22×D7311yescharacteristic
518C2×C4⋊C4C22×D7311yescharacteristic
519C2×C22⋊C4—731no—
520C2×C22⋊C4—731no—
521C2×C22⋊C4—1461no—
522C2×C22⋊C4—1461no—
523C2×C22⋊C4—1461no—
524C2×C22⋊C4—1461no—
525C2×C22⋊C4—1461no—
526C2×C22⋊C4—1461no—
527C2×C22⋊C4—1461no—
528C2×C42—731no—
529C2×C42—1461no—
530C2×C42—1461no—
531C2×C42—1461no—
532C2×C42C22×D7311yescharacteristic
533#107C22×D7314yes—
534#107C22×D7314yes—
535#106C22×D7314yes—
536#106C22×D7314yes—
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#97—734no—
546#97C22×D7314yes—
547C4×C8—734no—
548C4×C8—734no—
549C24—731no—
550C24—1461no—
551C2×Q8—24no—
552C2×Q8—82no—
553C2×Q8—732no—
554C2×Q8—732no—
555C2×Q8—732no—
556C2×Q8—1462no—
557C2×Q8—1462no—
558C2×Q8—1462no—
559C2×Q8—1462no—
560C2×Q8—1462no—
561C2×Q8—1462no—
562C2×Q8—1461no—
563C2×Q8—1461no—
564C2×Q8—1461no—
565C2×D4—5842no—
566C2×D4—732no—
567C2×D4—1464no—
568C2×D4—1461no—
569C2×D4—1462no—
570C2×D4—1462no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—5842no—
576C22×C4—731no—
577C22×C4—731no—
578C22×C4—731no—
579C22×C4—732no—
580C22×C4—732no—
581C22×C4—1464no—
582C22×C4—1461no—
583C22×C4—1461no—
584C22×C4—1461no—
585C22×C4—1462no—
586C22×C4—1462no—
587C22×C4D4×D7311yescharacteristic
588C22×C4D4×D7311yescharacteristic
589C22×C4C23×D7311yescharacteristic
590Q16—1468no—
591Q16—1468no—
592SD16—1468no—
593SD16—1468no—
594M16—1468no—
595C2×C8—732no—
596C2×C8—732no—
597C2×C8—1462no—
598C2×C8—1462no—
599C2×C8—1468no—
600C2×C8#1192402914yes—
601C2×C8#1192402914yes—
602C2×C8C23×D7312yes—
603C2×C8C23×D7312yes—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—734no—
612C4⋊C4—734no—
613C4⋊C4—1464no—
614C4⋊C4—1464no—
615C4⋊C4—1464no—
616C4⋊C4—1464no—
617C4⋊C4—1464no—
618C4⋊C4—1464no—
619C4⋊C4—1464no—
620C4⋊C4—1464no—
621C4⋊C4C23×D7312yes—
622C4⋊C4C23×D7312yes—
623C4⋊C4C23×D7312yes—
624C4⋊C4C23×D7312yes—
625C22⋊C4—734no—
626C22⋊C4—734no—
627C22⋊C4—1464no—
628C22⋊C4—1464no—
629C22⋊C4—1464no—
630C22⋊C4—1464no—
631C22⋊C4—1464no—
632C22⋊C4—1464no—
633C22⋊C4—1464no—
634C42—732no—
635C42—732no—
636C42—1464no—
637C42—1464no—
638C42—1464no—
639C42D4×D7312yes—
640C42C23×D7312yes—
641C23—2922no—
642C23—2922no—
643C23—2922no—
644C23—732no—
645C23—1462no—
646C23—1462no—
647C23—1462no—
648C23—1462no—
649C23C2×D4×D7311yescharacteristic
650Q8—84no—
651Q8—2922no—
652Q8—2922no—
653Q8—2922no—
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—22no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—2922no—
675C2×C4—2922no—
676C2×C4—2922no—
677C2×C4—5844no—
678C2×C4—732no—
679C2×C4—732no—
680C2×C4—732no—
681C2×C4—1462no—
682C2×C4—1462no—
683C2×C4—1462no—
684C2×C4—1462no—
685C2×C4—1462no—
686C2×C4—1462no—
687C2×C4—1464no—
688C2×C4—1462no—
689C2×C4—1462no—
690C2×C4C2×D4×D7312yes—
691C2×C4C2×D4×D7312yes—
692C2×C4C2×D4×D7311yescharacteristic
693C2×C4C2×#1192402912yes—
694C2×C4C2×#1192402912yes—
695C2×C4C24×D7311yescharacteristic
696C8—1462no—
697C8—1462no—
698C8C2×#1192402914yes—
699C8C2×#1192402914yes—
700C22—2924no—
701C22—2922no—
702C22—2922no—
703C22—2922no—
704C22—5844no—
705C22—1462no—
706C22—1462no—
707C22—1462no—
708C22#1798913812yes—
709C22#1798939712yes—
710C22#1798940312yes—
711C22C22×D4×D7311yescharacteristic
712C4—22no—
713C4—22no—
714C4—42no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—2922no—
719C4—2922no—
720C4—2922no—
721C4—1462no—
722C4—1462no—
723C4—1462no—
724C4#1798913812yes—
725C4C22×#1192402911yescharacteristic
726C4C22×#1192402911yescharacteristic
727C2—2922no—
728C2—5842no—
729C2#2262060414yesdirect product factor
730C2C2×#1798913811yescharacteristic
731C2C2×#1798939711yescharacteristic
732C2C2×#1798940311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#501×C73C2
socleC23×C73C22×D4
prime radicalC2×#14556566C22
hypercenterC2×#501D73
hypocenterC73C2×#3178
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
2. C2×#17989200C2semidirect
3. #22620604C2direct (N × H)
4. C2×#17988981C2semidirect
5. C2×#17988944C2semidirect
6. C2×#17988939C2semidirect
7. C2×#17988846C2semidirect
9. C2×#17988829C2semidirect
11. C2×#17988693C2semidirect
12. C2×#17988686C2semidirect
13. C2×#17988681C2semidirect
14. C2×#17988674C2semidirect
15. C2×#17988544C2semidirect
16. C2×#501×C73C2semidirect
26. #17989200C22semidirect
46. #17988981C22semidirect
47. #17988944C22semidirect
48. #17988939C22semidirect
49. #17988846C22semidirect
51. #17988829C22semidirect
53. #17988693C22semidirect
54. #17988686C22semidirect
55. #17988681C22semidirect
56. #17988674C22semidirect
65. #17988544C22semidirect
71. #501×C73C22semidirect
361. C2×C73#3178semidirect
370. C2×#501D73semidirect
383. C73C2×#3178semidirect
415. #501C2×D73semidirect
729. C2#22620604direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892112
C2×#179892002
#226206042
C2×#179889812
C2×#179889442
C2×#179889392
C2×#179888462
C2×#179888342
C2×#179888292
C2×#179888172
C2×#179886932
C2×#179886862
C2×#179886812
C2×#179886742
C2×#179885442
C2×#501×C732
C2×#317873