Finite Group Databasebeta

← C2×#22621355 #33958908

Subgroups — C2×#22621355 #33958908

Order 18688.

1818 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×#17989209C211yesmaximal, characteristic
2C2×#17989198C211yesmaximal, characteristic, complemented
3#22621355C2116yesmaximal, direct product factor
4C2×#17988894C211yesmaximal, characteristic, complemented
5C2×#17988880C211yesmaximal, characteristic, complemented
6C2×#17988870C211yesmaximal, characteristic, complemented
7C2×#17988888C211yesmaximal, characteristic, complemented
8C2×#17988842C211yesmaximal, characteristic, complemented
9C2×#17988836C211yesmaximal, characteristic
10C2×#17988825C211yesmaximal, characteristic, complemented
11C2×#17988819C211yesmaximal, characteristic
12C2×#17988811C211yesmaximal, characteristic, complemented
13C2×#17988811C211yesmaximal, characteristic, complemented
14C2×#17988789C211yesmaximal, characteristic, complemented
15C2×#17988612C211yesmaximal, characteristic, complemented
16C2×#462×C73C211yesmaximal, characteristic, complemented
17C22×#11924015C2211yescharacteristic
18C22×#11924015C2211yescharacteristic
19C22×#11924011C2211yescharacteristic
20C22×C8×D73C2211yescharacteristic
21#17989209—24no—
22#17989209C2218yes—
23#17989198—24no—
24#17989198C2218yescomplemented
25C2×#14556590C2211yescharacteristic
26C2×#14556586—21no—
27C2×#14556586—21no—
28C2×#14556585—21no—
29C2×#14556583C2211yescharacteristic
30C2×#14556581—21no—
31C2×#14556581—21no—
32C2×#14556580C2211yescharacteristic
33C2×#14556579—21no—
34C2×#14556576—21no—
35C2×#14556569—21no—
36C2×#14556567C2211yescharacteristic
37C2×#14556567C2211yescharacteristic
38C2×#14556567C2211yescharacteristic
39C2×#14556566C2211yescharacteristic
40C2×Q8×Dic73C2211yescharacteristic
41C2×Q8×Dic73C2211yescharacteristic
42C2×C4×D292C2211yescharacteristic
43C2×#14556548C2211yescharacteristic
44#17988894C2218yescomplemented
45#17988888C2218yescomplemented
46#17988880C2218yescomplemented
47#17988870C2218yescomplemented
48#17988842C2218yescomplemented
49#17988836C2218yes—
50#17988825C2218yescomplemented
51#17988819C2218yes—
52#17988811C2218yescomplemented
53#17988811C2218yescomplemented
54#17988789C2218yescomplemented
55C2×#14556525C2211yescharacteristic
56C2×#14556524C2211yescharacteristic
57C2×#14556523C2211yescharacteristic
58C2×#14556522C2211yescharacteristic
59#17988612C2218yescomplemented
60C2×C4⋊#10596831C2211yescharacteristic
61C2×#14556520C2211yescharacteristic
62C2×#14556520C2211yescharacteristic
63C2×#14556515C2211yescharacteristic
64C2×#14556515C2211yescharacteristic
65C2×#14556515C2211yescharacteristic
66C2×#14556515C2211yescharacteristic
67C2×#14556513C2211yescharacteristic
68C2×#14556513C2211yescharacteristic
69C22×Q16×C73C2211yescharacteristic
70C22×Q16×C73C2211yescharacteristic
71C2×C4⋊Q8×C73C2211yescharacteristic
72C2×C4×Q8×C73C2211yescharacteristic
73#462×C73C2218yescomplemented
74C2×C4⋊C8×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#103×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×D292—21no—
79C22×D292C2311yescharacteristic
80C22×C4×D73—21no—
81C22×C4×D73C2311yescharacteristic
82C2×#11924015—42no—
83C2×#11924015—42no—
84C2×#11924015C2314yes—
85C2×#11924015C2314yes—
86C2×#11924011—42no—
87C2×#11924011C2314yes—
88C22×#10596831C2311yescharacteristic
89C22×#10596831C2311yescharacteristic
90C2×C8×D73—42no—
91C2×C8×D73C2314yes—
92#14556590—22no—
93#14556590C2314yes—
94#14556586—28no—
95#14556586—28no—
96#14556585—28no—
97#14556583—22no—
98#14556583C2314yes—
99#14556581—28no—
100#14556581—28no—
101#14556580—22no—
102#14556580C2314yes—
103#14556579—28no—
104#14556576—28no—
105#14556569—28no—
106#14556567—22no—
107#14556567—22no—
108#14556567—22no—
109#14556567C2314yes—
110#14556567C2314yes—
111#14556567C2314yes—
112#14556566—22no—
113#14556566C2314yes—
114Q8×Dic73—22no—
115Q8×Dic73—22no—
116Q8×Dic73C2314yes—
117Q8×Dic73C2314yes—
118C4×D292—22no—
119C4×D292C2314yes—
120#14556548D414yes—
121#14556548C2314yes—
122C2×C4⋊Dic73—21no—
123C2×C4⋊Dic73—21no—
124C2×C4⋊Dic73C2311yescharacteristic
125C2×C4⋊Dic73C2311yescharacteristic
126C2×C4⋊Dic73C2311yescharacteristic
127C2×#11924007—21no—
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007—21no—
133C2×#11924007D411yescharacteristic
134C2×#11924007D411yescharacteristic
135C2×#11924005—21no—
136C2×#11924005—21no—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×#11924005—21no—
141C2×#11924005—21no—
142C2×#11924005D411yescharacteristic
143C2×#11924005D411yescharacteristic
144C2×C4×Dic73—21no—
145C2×C4×Dic73—21no—
146C2×C4×Dic73C2311yescharacteristic
147#14556525C2314yes—
148#14556524C2314yes—
149#14556523C2314yes—
150#14556522C2314yes—
151C4⋊#10596831C2314yes—
152#14556520C2314yes—
153#14556520C2314yes—
154#14556515C2314yes—
155#14556515C2314yes—
156#14556515C2314yes—
157#14556515C2314yes—
158#14556513C2314yes—
159#14556513C2314yes—
160C22×Q8×C73C2311yescharacteristic
161C22×Q8×C73C2311yescharacteristic
162C22×Q8×C73C2311yescharacteristic
163C2×Q16×C73—42no—
164C2×Q16×C73—42no—
165C2×Q16×C73C2314yes—
166C2×Q16×C73C2314yes—
167C22×C8×C73C2311yescharacteristic
168C22×C8×C73C2311yescharacteristic
169C4⋊Q8×C73—22no—
170C4⋊Q8×C73C2314yes—
171C4×Q8×C73—22no—
172C4×Q8×C73C2314yes—
173C2×C4⋊C4×C73—21no—
174C2×C4⋊C4×C73—21no—
175C2×C4⋊C4×C73—21no—
176C2×C4⋊C4×C73C2311yescharacteristic
177C2×C42×C73—21no—
178C2×C42×C73C2311yescharacteristic
179C4⋊C8×C73C2314yes—
180#103×C73C2314yes—
181#103×C73C2314yes—
182C23×D73—21no—
183C23×D73C2×D411yescharacteristic
184C2×Dic146—24no—
185C2×Dic146—82no—
186C2×D292—22no—
187C2×D292—22no—
188C2×D292—21no—
189C2×D292—24no—
190C2×D292—82no—
191C2×D292C2412yes—
192C22×Dic73—21no—
193C22×Dic73—21no—
194C22×Dic73—21no—
195C22×Dic73C2×D411yescharacteristic
196C22×Dic73C2×D411yescharacteristic
197C22×Dic73C2×D411yescharacteristic
198C2×C4×D73—22no—
199C2×C4×D73—22no—
200C2×C4×D73—24no—
201C2×C4×D73—82no—
202C2×C4×D73C2×D412yes—
203C2×C4×D73C2412yes—
204#11924015—44no—
205#11924015—44no—
206#11924011—44no—
207C2×#10596831—22no—
208C2×#10596831—22no—
209C2×#10596831C2412yes—
210C2×#10596831C2412yes—
211C8×D73—44no—
212C4⋊Dic73—21no—
213C4⋊Dic73—21no—
214C4⋊Dic73—21no—
215C4⋊Dic73—24no—
216C4⋊Dic73—24no—
217C4⋊Dic73C2412yes—
218C4⋊Dic73C2412yes—
219C4⋊Dic73C2412yes—
220#11924007—24no—
221#11924007—24no—
222#11924007—24no—
223#11924007—24no—
224#11924007—24no—
225#11924007—24no—
226#11924007C2×D414yes—
227#11924007C2×D414yes—
228#11924005—24no—
229#11924005—24no—
230#11924005—24no—
231#11924005—24no—
232#11924005—24no—
233#11924005—24no—
234#11924005—24no—
235#11924005C2×D414yes—
236#11924005C2×D414yes—
237C4×Dic73—24no—
238C4×Dic73—24no—
239C4×Dic73C2×D412yes—
240C4×Dic73C2412yes—
241C2×Q8×C73—21no—
242C2×Q8×C73—21no—
243C2×Q8×C73—21no—
244C2×Q8×C73—22no—
245C2×Q8×C73—22no—
246C2×Q8×C73—22no—
247C2×Q8×C73—22no—
248C2×Q8×C73—22no—
249C2×Q8×C73—22no—
250C2×Q8×C73C2412yes—
251C2×Q8×C73C2412yes—
252C2×Q8×C73C2412yes—
253C22×C4×C73—21no—
254C22×C4×C73—21no—
255C22×C4×C73—21no—
256C22×C4×C73—21no—
257C22×C4×C73C2×D411yescharacteristic
258C22×C4×C73C2×D411yescharacteristic
259C22×C4×C73C2411yescharacteristic
260Q16×C73—44no—
261Q16×C73—44no—
262C2×C8×C73—22no—
263C2×C8×C73—22no—
264C2×C8×C73C2412yes—
265C2×C8×C73C2412yes—
266C4⋊C4×C73—24no—
267C4⋊C4×C73—24no—
268C4⋊C4×C73—24no—
269C4⋊C4×C73—21no—
270C4⋊C4×C73C2412yes—
271C42×C73—24no—
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—22no—
284Q8×C73—22no—
285Q8×C73—22no—
286Q8×C73—22no—
287Q8×C73—22no—
288Q8×C73—22no—
289Q8×C73—42no—
290Q8×C73—42no—
291Q8×C73—42no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—42no—
299C2×C4×C73—42no—
300C2×C4×C73—42no—
301C2×C4×C73—42no—
302C2×C4×C73C22×D412yes—
303C2×C4×C73C22×D412yes—
304C2×C4×C73C22×D411yescharacteristic
305C2×C4×C73H(5,𝔽2)12yes—
306C2×C4×C732−1+412yes—
307C2×C4×C73C2511yescharacteristic
308C2×Dic73—22no—
309C2×Dic73—22no—
310C2×Dic73—22no—
311C2×Dic73—22no—
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—42no—
315C2×Dic73—42no—
316C2×Dic73—42no—
317C2×Dic73C22×D412yes—
318C2×Dic73C22×D412yes—
319C2×Dic73C22×D412yes—
320D292—22no—
321D292—22no—
322D292—42no—
323D292—84no—
324C4×D73—24no—
325C4×D73—22no—
326C4×D73—22no—
327C4×D73—84no—
328Dic146—84no—
329C8×C73—22no—
330C8×C73—22no—
331#10596831—22no—
332#10596831—22no—
333C22×C73#53712yes—
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#53712yes—
352C4×C73C2×H(5,𝔽2)11yescharacteristic
353C4×C73C2×2−1+411yescharacteristic
354Dic73—22no—
355Dic73—22no—
356Dic73—22no—
357Dic73—42no—
358Dic73—42no—
359Dic73—42no—
360C2×#3258—731nomaximal, Sylow
361C2×C73#325814yescomplemented
362C2×C73C2×#53711yescharacteristic
363C2×C73C2×#57711yescharacteristic
364C2×C73C2×#57811yescharacteristic
365D73—42no—
366D73—82no—
367C2×#542—731no—
368C2×#541—731no—
369#3258—7316no—
370C2×#479—731no—
371C2×#477—731no—
372C2×#475—731no—
373C2×#478—731no—
374C2×#470—731no—
375C2×#468—731no—
376C2×#467—731no—
377C2×#465—731no—
378C2×#464—731no—
379C2×#464—731no—
380C2×#462D7311yescharacteristic, complemented
381C2×#461—731no—
382C2×#424—731no—
383C73C2×#325811yescharacteristic, complemented, Sylow
384C22×Q16C2×D7311yescharacteristic
385C22×Q16C2×D7311yescharacteristic
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—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×Q8C2×D7311yescharacteristic
413C2×C4×D4—731no—
414C2×#117—731no—
415#479—738no—
416#478—738no—
417#477—738no—
418#475—738no—
419#470—738no—
420#468—738no—
421#467—738no—
422#465—738no—
423#464—738no—
424#464—738no—
425#462C2×D7318yescomplemented
426#461—738no—
427C2×#107—731no—
428C2×#107—731no—
429C2×#106—731no—
430C2×#106—731no—
431#424—738no—
432C2×C4⋊C8—731no—
433C2×C4⋊C8—731no—
434C2×C4⋊C8—731no—
435C2×C4⋊C8C2×D7311yescharacteristic
436C2×#103—731no—
437C2×#103—731no—
438C2×#103—731no—
439C2×#103—731no—
440C2×#103C2×D7311yescharacteristic
441C2×#103C2×D7311yescharacteristic
442C2×#102—731no—
443C2×#102—731no—
444C22×Q8—1461no—
445C22×Q8C22×D7311yescharacteristic
446C22×Q8C22×D7311yescharacteristic
447C22×Q8C22×D7311yescharacteristic
448C22×D4—731no—
449C22×D4—1461no—
450C23×C4—731no—
451C23×C4—1461no—
452C2×Q16—42no—
453C2×Q16—42no—
454C2×Q16C22×D7314yes—
455C2×Q16C22×D7314yes—
456C2×SD16—2922no—
457C2×SD16—2922no—
458C2×SD16—734no—
459C2×SD16—734no—
460C2×M16—2922no—
461C2×M16—734no—
462C22×C8—2922no—
463C22×C8—734no—
464C22×C8—731no—
465C22×C8—731no—
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—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—1468no—
487C22⋊Q8—1462no—
488C22⋊Q8—1462no—
489C22⋊Q8—1462no—
490#121—734no—
491#121—1462no—
492C4×Q8—22no—
493C4×Q8—734no—
494C4×Q8—734no—
495C4×Q8—1462no—
496C4×Q8—1462no—
497C4×Q8C22×D7314yes—
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—731no—
508C2×C4⋊C4—731no—
509C2×C4⋊C4—731no—
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⋊C4—1461no—
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—21no—
529C2×C42—731no—
530C2×C42—1461no—
531C2×C42—1461no—
532C2×C42C22×D7311yescharacteristic
533#107—734no—
534#107—734no—
535#106—734no—
536#106—734no—
537C4⋊C8—734no—
538C4⋊C8—734no—
539C4⋊C8—734no—
540C4⋊C8C22×D7314yes—
541#103—734no—
542#103—734no—
543#103—734no—
544#103—734no—
545#103C22×D7314yes—
546#103C22×D7314yes—
547#102—734no—
548#102—734no—
549C24—731no—
550C24—1461no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—5842no—
561C2×Q8—1464no—
562C2×Q8C23×D7312yes—
563C2×Q8C23×D7312yes—
564C2×Q8C23×D7312yes—
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—1461no—
582C22×C4—1461no—
583C22×C4—1461no—
584C22×C4—1464no—
585C22×C4—1462no—
586C22×C4—1462no—
587C22×C4D4×D7311yescharacteristic
588C22×C4D4×D7311yescharacteristic
589C22×C4C23×D7311yescharacteristic
590Q16—44no—
591Q16—44no—
592SD16—2924no—
593SD16—2924no—
594M16—2924no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—2924no—
598C2×C8—732no—
599C2×C8—732no—
600C2×C8—1462no—
601C2×C8—1462no—
602C2×C8C23×D7312yes—
603C2×C8C23×D7312yes—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—21no—
608C4⋊C4—734no—
609C4⋊C4—734no—
610C4⋊C4—732no—
611C4⋊C4—732no—
612C4⋊C4—732no—
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⋊C4—1461no—
622C4⋊C4—1461no—
623C4⋊C4—1461no—
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—24no—
635C42—732no—
636C42—732no—
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—22no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—42no—
657Q8—42no—
658Q8—42no—
659Q8—5844no—
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—1462no—
688C2×C4—1462no—
689C2×C4—1464no—
690C2×C4C2×D4×D7312yes—
691C2×C4C2×D4×D7312yes—
692C2×C4C2×D4×D7311yescharacteristic
693C2×C4#1455663612yes—
694C2×C4#1455663812yes—
695C2×C4C24×D7311yescharacteristic
696C8—22no—
697C8—22no—
698C8—1462no—
699C8—1462no—
700C22—2924no—
701C22—2922no—
702C22—2922no—
703C22—2922no—
704C22—5844no—
705C22—1462no—
706C22—1462no—
707C22—1462no—
708C22#1798916612yes—
709C22#1798939612yes—
710C22#1798940012yes—
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#1798916612yes—
725C4C2×#1455663611yescharacteristic
726C4C2×#1455663811yescharacteristic
727C2—2922no—
728C2—5842no—
729C2#2262135514yesdirect product factor
730C2C2×#1798916611yescharacteristic
731C2C2×#1798939611yescharacteristic
732C2C2×#1798940011yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#462×C73C2
socleC23×C73C22×D4
prime radicalC2×#14556566C22
hypercenterC2×#462D73
hypocenterC73C2×#3258
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
2. C2×#17989198C2semidirect
3. #22621355C2direct (N × H)
4. C2×#17988894C2semidirect
5. C2×#17988880C2semidirect
6. C2×#17988870C2semidirect
7. C2×#17988888C2semidirect
8. C2×#17988842C2semidirect
10. C2×#17988825C2semidirect
12. C2×#17988811C2semidirect
13. C2×#17988811C2semidirect
14. C2×#17988789C2semidirect
15. C2×#17988612C2semidirect
16. C2×#462×C73C2semidirect
24. #17989198C22semidirect
44. #17988894C22semidirect
45. #17988888C22semidirect
46. #17988880C22semidirect
47. #17988870C22semidirect
48. #17988842C22semidirect
50. #17988825C22semidirect
52. #17988811C22semidirect
53. #17988811C22semidirect
54. #17988789C22semidirect
59. #17988612C22semidirect
73. #462×C73C22semidirect
361. C2×C73#3258semidirect
380. C2×#462D73semidirect
383. C73C2×#3258semidirect
425. #462C2×D73semidirect
729. C2#22621355direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892092
C2×#179891982
#226213552
C2×#179888942
C2×#179888802
C2×#179888702
C2×#179888882
C2×#179888422
C2×#179888362
C2×#179888252
C2×#179888192
C2×#179888112
C2×#179887892
C2×#179886122
C2×#462×C732
C2×#325873