Finite Group Databasebeta

← C2×#22624021 #33994203

Subgroups — C2×#22624021 #33994203

Order 18688.

7022 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624021C2132yesmaximal, direct product factor
2C2×#17989315C213yesmaximal, complemented
3C2×#17989313C211yesmaximal, characteristic, complemented
4C2×#17989305C213yesmaximal, complemented
5C2×#17989278C213yesmaximal, complemented
6C2×#17989276C213yesmaximal, complemented
7C2×Q8×D292C211yesmaximal, characteristic, complemented
8C2×Q8×C22⋊D73C211yesmaximal, characteristic, complemented
9C2×Q8×C22⋊D73C211yesmaximal, characteristic, complemented
10C2×#17989199C213yesmaximal, complemented
11C2×#17989195C213yesmaximal, complemented
12C2×#17989141C213yesmaximal, complemented
13C2×#17989115C213yesmaximal
14C2×#17989063C211yesmaximal, characteristic, complemented
15C2×C4×Q8×D73C211yesmaximal, characteristic, complemented
16C2×#519×C73C211yesmaximal, characteristic, complemented
17C22×Q8×D73C2211yescharacteristic
18C22×Q8×D73C2211yescharacteristic
19#17989315C22148yescomplemented
20#17989313C22116yescomplemented
21#17989305C22148yescomplemented
22#17989278C22148yescomplemented
23#17989276C22148yescomplemented
24Q8×D292C22116yescomplemented
25Q8×C22⋊D73C22116yescomplemented
26Q8×C22⋊D73C22116yescomplemented
27#17989199C22148yescomplemented
28#17989195C22148yescomplemented
29#17989141C22148yescomplemented
30C2×#14556591C2213yes—
31C2×#14556590C2213yes—
32C2×#14556589C2213yes—
33C2×#14556589C2213yes—
34#17989115C22148yes—
35C2×#14556586C2213yes—
36C2×#14556585C2216yes—
37C2×#14556584C2213yes—
38C2×#14556584C2216yes—
39C2×#14556583C2213yes—
40C2×#14556583C2216yes—
41C2×#14556582C2213yes—
42C2×#14556581C2213yes—
43C2×#14556581C2216yes—
44C2×#14556581C2216yes—
45C2×#14556577C2213yes—
46C2×#14556576C2213yes—
47C2×#14556573C2213yes—
48C2×#14556571C2213yes—
49C2×#14556571C2213yes—
50C2×#14556570C2213yes—
51C2×#14556570C2213yes—
52C2×#14556569C2213yes—
53C2×#14556567C2213yes—
54C2×#14556567C2213yes—
55C2×#14556564C2211yescharacteristic
56#17989063C22116yescomplemented
57C2×Q8×Dic73C2211yescharacteristic
58C2×Q8×Dic73C2211yescharacteristic
59C2×C4×Dic146C2213yes—
60C2×C4×Dic146C2216yes—
61C2×C4×Dic146C2213yes—
62C2×C4×Dic146C2213yes—
63C2×#14556556C2213yes—
64C2×#14556556C2213yes—
65C4×Q8×D73C22116yescomplemented
66C2×C4×D292C2213yes—
67C2×C4×C22⋊D73C2213yes—
68C2×C4×C22⋊D73C2213yes—
69C2×#14556549C2213yes—
70C2×#14556548C2213yes—
71C2×#14556548C2216yes—
72C2×C4⋊C4×D73C2213yes—
73C2×C42×D73C2213yes—
74C23×Q8×C73C2211yescharacteristic
75#519×C73C22116yescomplemented
76C2×C4×Q8×C73C2211yescharacteristic
77C2×C4×Q8×C73C2213yes—
78C2×C4×Q8×C73C2213yes—
79C2×C4×Q8×C73C2211yescharacteristic
80C2×#117×C73C2213yes—
81C2×#117×C73C2213yes—
82C22×Dic146C2313yes—
83C22×Dic146C2313yes—
84C22×Dic146C2313yes—
85C2×Q8×D73—28no—
86C2×Q8×D73—28no—
87C2×Q8×D73C2318yes—
88C2×Q8×D73C2318yes—
89C22×D292C2311yescharacteristic
90C22×C22⋊D73C2311yescharacteristic
91C22×C22⋊D73C2311yescharacteristic
92C22×C4×D73C2313yes—
93C22×C4×D73C2313yes—
94C22×C4×D73C2311yescharacteristic
95C22×C4×D73C2313yes—
96#14556591C23124yes—
97#14556590C23124yes—
98#14556589C23124yes—
99#14556589C23124yes—
100#14556586C23124yes—
101#14556585C23148yes—
102#14556584C23124yes—
103#14556584C23148yes—
104#14556583C23148yes—
105#14556583C23124yes—
106#14556582C23124yes—
107#14556581C23148yes—
108#14556581C23148yes—
109#14556581C23124yes—
110#14556577C23124yes—
111#14556576C23124yes—
112#14556573C23124yes—
113#14556571C23124yes—
114#14556571C23124yes—
115#14556570C23124yes—
116#14556570C23124yes—
117#14556569C23124yes—
118#14556567C23124yes—
119#14556567C23124yes—
120#14556564C2318yes—
121Q8×Dic73C2318yes—
122Q8×Dic73C2318yes—
123C4×Dic146C23124yes—
124C4×Dic146C23148yes—
125C4×Dic146C23124yes—
126C4×Dic146C23124yes—
127#14556556C23124yes—
128#14556556C23124yes—
129C4×D292C23124yes—
130C4×C22⋊D73C23124yes—
131C4×C22⋊D73C23124yes—
132#14556549C23124yes—
133#14556548C23148yes—
134#14556548C23124yes—
135C2×C4⋊Dic73C2313yes—
136C2×C4⋊Dic73C2313yes—
137C2×C4⋊Dic73C2316yes—
138C2×C4⋊Dic73C2313yes—
139C2×C4⋊Dic73C2313yes—
140C2×#11924007C2313yes—
141C2×#11924007C2313yes—
142C2×#11924007C2316yes—
143C2×#11924007C2316yes—
144C2×#11924007C2316yes—
145C2×#11924007C2316yes—
146C2×#11924007C2313yes—
147C2×#11924007C2313yes—
148C2×#11924007C2311yescharacteristic
149C2×#11924007C2313yes—
150C4⋊C4×D73C23124yes—
151C2×C22⋊Dic73C2313yes—
152C2×C22⋊Dic73C2313yes—
153C2×#11924005C2311yescharacteristic
154C2×#11924005C2313yes—
155C2×#11924005C2313yes—
156C2×#11924005C2313yes—
157C2×#11924005C2313yes—
158C2×#11924005C2313yes—
159C2×C4×Dic73C2313yes—
160C2×C4×Dic73C2313yes—
161C2×C4×Dic73C2313yes—
162C2×C4×Dic73C2313yes—
163C2×C4×Dic73C2316yes—
164C42×D73C23124yes—
165C22×Q8×C73—28no—
166C22×Q8×C73C2313yes—
167C22×Q8×C73C2318yes—
168C22×Q8×C73C2311yescharacteristic
169C23×C4×C73C2313yes—
170C4×Q8×C73C23124yes—
171C4×Q8×C73C2318yes—
172C4×Q8×C73C23124yes—
173C4×Q8×C73C2318yes—
174#117×C73C23124yes—
175#117×C73C23124yes—
176C2×C4⋊C4×C73C2313yes—
177C2×C4⋊C4×C73C2313yes—
178C2×C4⋊C4×C73C2313yes—
179C2×C4⋊C4×C73C2313yes—
180C2×C22⋊C4×C73C2311yescharacteristic
181C2×C22⋊C4×C73C2313yes—
182C2×C42×C73C2313yes—
183C2×C42×C73C2313yes—
184C2×C42×C73C2316yes—
185C23×D73C2411yescharacteristic
186C23×D73C2411yescharacteristic
187C2×Dic146—212no—
188C2×Dic146—212no—
189C2×Dic146—212no—
190C2×Dic146C24112yes—
191C2×Dic146C24112yes—
192C2×Dic146C24112yes—
193Q8×D73—232no—
194Q8×D73—232no—
195C2×D292—24no—
196C2×D292C2414yes—
197C2×C22⋊D73—24no—
198C2×C22⋊D73—24no—
199C2×C22⋊D73C2414yes—
200C2×C22⋊D73C2414yes—
201C22×Dic73C2413yes—
202C22×Dic73C2411yescharacteristic
203C22×Dic73C2413yes—
204C22×Dic73C2413yes—
205C22×Dic73C2413yes—
206C22×Dic73C2411yescharacteristic
207C2×C4×D73—212no—
208C2×C4×D73—212no—
209C2×C4×D73—212no—
210C2×C4×D73—24no—
211C2×C4×D73C2414yes—
212C2×C4×D73C24112yes—
213C2×C4×D73C24112yes—
214C2×C4×D73C24112yes—
215C4⋊Dic73C24112yes—
216C4⋊Dic73C24112yes—
217C4⋊Dic73C24112yes—
218C4⋊Dic73C24124yes—
219C4⋊Dic73C24112yes—
220#11924007C24124yes—
221#11924007C24112yes—
222#11924007C24112yes—
223#11924007C24124yes—
224#11924007C24124yes—
225#11924007C24112yes—
226#11924007C24112yes—
227#11924007C2414yes—
228#11924007C24124yes—
229#11924007C24112yes—
230C22⋊Dic73C24112yes—
231C22⋊Dic73C24112yes—
232#11924005C2414yes—
233#11924005C24112yes—
234#11924005C24112yes—
235#11924005C24112yes—
236#11924005C24112yes—
237#11924005C24112yes—
238C4×Dic73C24112yes—
239C4×Dic73C24112yes—
240C4×Dic73C24112yes—
241C4×Dic73C24124yes—
242C4×Dic73C24112yes—
243C24×C73C2411yescharacteristic
244C2×Q8×C73—232no—
245C2×Q8×C73—212no—
246C2×Q8×C73#4118yes—
247C2×Q8×C73C24112yes—
248C2×Q8×C73C2414yes—
249C22×C4×C73—212no—
250C22×C4×C73C2411yescharacteristic
251C22×C4×C73C2413yes—
252C22×C4×C73C2413yes—
253C22×C4×C73C2411yescharacteristic
254C22×C4×C73C2413yes—
255C22×C4×C73C24112yes—
256C22×C4×C73C2413yes—
257C4⋊C4×C73C24112yes—
258C4⋊C4×C73C24112yes—
259C4⋊C4×C73C24112yes—
260C4⋊C4×C73C24112yes—
261C22⋊C4×C73C2414yes—
262C22⋊C4×C73C24112yes—
263C42×C73C24112yes—
264C42×C73C24124yes—
265C42×C73C24112yes—
266C23×C73—22no—
267C23×C73—22no—
268C23×C73—22no—
269C23×C73C2512yes—
270C23×C73C2511yescharacteristic
271C22×D73—22no—
272C22×D73—22no—
273C22×D73—22no—
274C22×D73—22no—
275C22×D73—22no—
276C22×D732−1+414yes—
277C22×D73C2512yes—
278C22×D73C2512yes—
279Q8×C73—224no—
280Q8×C73C2×#41116yes—
281C2×C4×C73—26no—
282C2×C4×C73—26no—
283C2×C4×C73—22no—
284C2×C4×C73—22no—
285C2×C4×C73—26no—
286C2×C4×C73—224no—
287C2×C4×C73C2×#41112yes—
288C2×C4×C73C2512yes—
289C2×C4×C73C2516yes—
290C2×C4×C73C2516yes—
291C2×C4×C73C2512yes—
292C2×C4×C73C2516yes—
293C2×C4×C73C2516yes—
294C22⋊D73—28no—
295C22⋊D73—28no—
296C2×Dic73—26no—
297C2×Dic73—26no—
298C2×Dic73—26no—
299C2×Dic73—22no—
300C2×Dic73—26no—
301C2×Dic732−1+414yes—
302C2×Dic73C2516yes—
303C2×Dic73C2512yes—
304C2×Dic73C2516yes—
305C2×Dic73C2516yes—
306C2×Dic73C2516yes—
307C2×Dic73C2512yes—
308D292—28no—
309C4×D73—224no—
310C4×D73—224no—
311C4×D73—224no—
312C4×D73—28no—
313Dic146—224no—
314Dic146—224no—
315Dic146—224no—
316C22×C73—22no—
317C22×C73—22no—
318C22×C73—22no—
319C22×C73—44no—
320C22×C73C22×#4112yes—
321C22×C73C2×2−1+412yes—
322C22×C73C2×2−1+412yes—
323C22×C73C2611yescharacteristic
324C2×D73—22no—
325C2×D73—22no—
326C2×D73—28no—
327C2×D73—22no—
328C2×D73—22no—
329C2×D73—22no—
330C2×D73—44no—
331C2×D73C2×2−1+414yes—
332C4×C73—26no—
333C4×C73—26no—
334C4×C73—26no—
335C4×C73—22no—
336C4×C73—22no—
337C4×C73C22×#41112yes—
338Dic73—26no—
339Dic73—26no—
340Dic73—26no—
341Dic73—26no—
342Dic73—22no—
343Dic73C2×2−1+414yes—
344C2×#3523—731nomaximal, Sylow
345C2×C73—42no—
346C2×C73#352314yescomplemented
347C2×C73C23×#4111yescharacteristic
348C2×C73C22×2−1+411yescharacteristic
349C2×C73C22×2−1+411yescharacteristic
350D73—24no—
351D73—42no—
352#3523—7332no—
353C2×#557—731no—
354C2×#557—733no—
355C2×#556—733no—
356C2×#552—733no—
357C2×#552—733no—
358C2×D4×Q8—731no—
359C2×D4×Q8—731no—
360C2×D4×Q8—731no—
361C2×#541—733no—
362C2×#541—733no—
363C2×#533—733no—
364C2×#529—733no—
365C2×#519—731no—
366C2×#519D7311yescharacteristic, complemented
367C22×C4×Q8—731no—
368C73C2×#352311yescharacteristic, complemented, Sylow
369C23×Q8—731no—
370C23×Q8—731no—
371C23×Q8C2×D7311yescharacteristic
372#557—7316no—
373#557—7348no—
374#556—7348no—
375#552—7348no—
376#552—7348no—
377D4×Q8—7316no—
378D4×Q8—7316no—
379D4×Q8—7316no—
380#541—7348no—
381#541—7348no—
382#533—7348no—
383C2×C4⋊Q8—733no—
384C2×C4⋊Q8—733no—
385C2×C4⋊Q8—733no—
386C2×C4⋊Q8—733no—
387#529—7348no—
388C2×#126—733no—
389C2×#126—733no—
390C2×#126—736no—
391C2×#126—736no—
392C2×#125—733no—
393C2×#125—736no—
394C2×#125—736no—
395C2×#125—733no—
396C2×#125—736no—
397C2×#125—733no—
398C2×#124—733no—
399C2×#123—733no—
400C2×#123—733no—
401C2×C22⋊Q8—733no—
402C2×C22⋊Q8—733no—
403C2×C22⋊Q8—733no—
404C2×C22⋊Q8—733no—
405C2×C22⋊Q8—733no—
406C2×C22⋊Q8—733no—
407C2×C22⋊Q8—733no—
408C2×#121—731no—
409#519—7316no—
410#519C2×D73116yescomplemented
411C2×C4×Q8—731no—
412C2×C4×Q8—731no—
413C2×C4×Q8—7316no—
414C2×C4×Q8—733no—
415C2×C4×Q8—733no—
416C2×C4×Q8—733no—
417C2×C4×Q8—733no—
418C2×C4×Q8—733no—
419C2×C4×Q8—736no—
420C2×C4×Q8C2×D7311yescharacteristic
421C2×C4×Q8C2×D7313yes—
422C2×C4×Q8C2×D7311yescharacteristic
423C2×C4×Q8C2×D7313yes—
424C2×C4×D4—733no—
425C2×C4×D4—733no—
426C2×C4×D4—733no—
427C2×#117—733no—
428C2×#117—733no—
429C2×#117—736no—
430C2×#117C2×D7313yes—
431C2×#117C2×D7313yes—
432C22×C4⋊C4—733no—
433C22×C42—733no—
434C22×Q8—28no—
435C22×Q8—738no—
436C22×Q8—738no—
437C22×Q8—733no—
438C22×Q8—733no—
439C22×Q8—733no—
440C22×Q8—1468no—
441C22×Q8—1468no—
442C22×Q8C22×D7313yes—
443C22×Q8C22×D7318yes—
444C22×Q8C22×D7311yescharacteristic
445C22×D4—731no—
446C22×D4—731no—
447C22×D4—731no—
448C23×C4—733no—
449C23×C4—733no—
450C23×C4—733no—
451C23×C4—731no—
452C23×C4C22×D7313yes—
453C4⋊Q8—7324no—
454C4⋊Q8—7324no—
455C4⋊Q8—7324no—
456C4⋊Q8—7324no—
457#126—7324no—
458#126—7324no—
459#126—7348no—
460#126—7348no—
461#125—7324no—
462#125—7348no—
463#125—7348no—
464#125—7324no—
465#125—7348no—
466#125—7324no—
467#124—7324no—
468#123—7324no—
469#123—7324no—
470C22⋊Q8—7324no—
471C22⋊Q8—7324no—
472C22⋊Q8—7324no—
473C22⋊Q8—7324no—
474C22⋊Q8—7324no—
475C22⋊Q8—7324no—
476C22⋊Q8—7324no—
477#121—738no—
478C4×Q8—738no—
479C4×Q8—738no—
480C4×Q8—7324no—
481C4×Q8—7324no—
482C4×Q8—7324no—
483C4×Q8—7324no—
484C4×Q8—7324no—
485C4×Q8—7348no—
486C4×Q8C22×D7318yes—
487C4×Q8C22×D73124yes—
488C4×Q8C22×D7318yes—
489C4×Q8C22×D73124yes—
490C4×D4—7324no—
491C4×D4—7324no—
492C4×D4—7324no—
493#117—7324no—
494#117—7324no—
495#117—7348no—
496#117C22×D73124yes—
497#117C22×D73124yes—
498C2×C4⋊C4—733no—
499C2×C4⋊C4—736no—
500C2×C4⋊C4—733no—
501C2×C4⋊C4—733no—
502C2×C4⋊C4—733no—
503C2×C4⋊C4—736no—
504C2×C4⋊C4—736no—
505C2×C4⋊C4—733no—
506C2×C4⋊C4—733no—
507C2×C4⋊C4—733no—
508C2×C4⋊C4—731no—
509C2×C4⋊C4—736no—
510C2×C4⋊C4—736no—
511C2×C4⋊C4—733no—
512C2×C4⋊C4—733no—
513C2×C4⋊C4—7324no—
514C2×C4⋊C4C22×D7313yes—
515C2×C4⋊C4C22×D7313yes—
516C2×C4⋊C4C22×D7313yes—
517C2×C4⋊C4C22×D7313yes—
518C2×C22⋊C4—733no—
519C2×C22⋊C4—733no—
520C2×C22⋊C4—731no—
521C2×C22⋊C4—733no—
522C2×C22⋊C4—733no—
523C2×C22⋊C4—733no—
524C2×C22⋊C4—733no—
525C2×C22⋊C4—733no—
526C2×C22⋊C4C22×D7311yescharacteristic
527C2×C22⋊C4C22×D7313yes—
528C2×C42—736no—
529C2×C42—733no—
530C2×C42—733no—
531C2×C42—733no—
532C2×C42—733no—
533C2×C42—7324no—
534C2×C42C22×D7313yes—
535C2×C42C22×D7316yes—
536C2×C42C22×D7313yes—
537C24—731no—
538C24—731no—
539C24C23×D7311yescharacteristic
540C2×Q8—232no—
541C2×Q8—212no—
542C2×Q8—7312no—
543C2×Q8—7312no—
544C2×Q8—7312no—
545C2×Q8—14612no—
546C2×Q8—14632no—
547C2×Q8—14632no—
548C2×Q8—14612no—
549C2×Q8—14612no—
550C2×Q8#1192402818yes—
551C2×Q8C23×D73112yes—
552C2×Q8C23×D7314yes—
553C2×D4—734no—
554C2×D4—734no—
555C2×D4—734no—
556C2×D4—1464no—
557C2×D4—1464no—
558C2×D4—1464no—
559C22×C4—212no—
560C22×C4—731no—
561C22×C4—733no—
562C22×C4—731no—
563C22×C4—733no—
564C22×C4—733no—
565C22×C4—733no—
566C22×C4—734no—
567C22×C4—7312no—
568C22×C4—7312no—
569C22×C4—7312no—
570C22×C4—1464no—
571C22×C4—14612no—
572C22×C4—14612no—
573C22×C4—14612no—
574C22×C4C23×D73112yes—
575C22×C4C23×D7313yes—
576C22×C4C23×D7311yescharacteristic
577C22×C4C23×D7313yes—
578C22×C4C23×D7311yescharacteristic
579C22×C4C23×D7313yes—
580C22×C4C23×D7313yes—
581C4⋊C4—7324no—
582C4⋊C4—7312no—
583C4⋊C4—7312no—
584C4⋊C4—7324no—
585C4⋊C4—7324no—
586C4⋊C4—7312no—
587C4⋊C4—7312no—
588C4⋊C4—734no—
589C4⋊C4—7324no—
590C4⋊C4—7312no—
591C4⋊C4—7312no—
592C4⋊C4—7312no—
593C4⋊C4—7312no—
594C4⋊C4—7324no—
595C4⋊C4—7312no—
596C4⋊C4C23×D73112yes—
597C4⋊C4C23×D73112yes—
598C4⋊C4C23×D73112yes—
599C4⋊C4C23×D73112yes—
600C22⋊C4—7312no—
601C22⋊C4—7312no—
602C22⋊C4—734no—
603C22⋊C4—7312no—
604C22⋊C4—7312no—
605C22⋊C4—7312no—
606C22⋊C4—7312no—
607C22⋊C4—7312no—
608C22⋊C4C23×D7314yes—
609C22⋊C4C23×D73112yes—
610C42—7312no—
611C42—7312no—
612C42—7312no—
613C42—7324no—
614C42—7312no—
615C42C23×D73112yes—
616C42C23×D73124yes—
617C42C23×D73112yes—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—734no—
622C23—732no—
623C23—732no—
624C23—1462no—
625C23—1462no—
626C23—1462no—
627C23—1462no—
628C23—1462no—
629C23C24×D7312yes—
630C23C24×D7311yescharacteristic
631Q8—224no—
632Q8—14624no—
633Q8—14624no—
634Q8—14624no—
635Q8C2×#11924028116yes—
636D4—1468no—
637D4—1468no—
638D4—1468no—
639C2×C4—26no—
640C2×C4—22no—
641C2×C4—26no—
642C2×C4—22no—
643C2×C4—26no—
644C2×C4—224no—
645C2×C4—734no—
646C2×C4—732no—
647C2×C4—736no—
648C2×C4—732no—
649C2×C4—736no—
650C2×C4—736no—
651C2×C4—736no—
652C2×C4—1468no—
653C2×C4—14624no—
654C2×C4—1466no—
655C2×C4—1466no—
656C2×C4—1466no—
657C2×C4—1462no—
658C2×C4—1466no—
659C2×C4—14624no—
660C2×C4—14624no—
661C2×C4C2×#11924028112yes—
662C2×C4C24×D7316yes—
663C2×C4C24×D7312yes—
664C2×C4C24×D7316yes—
665C2×C4C24×D7312yes—
666C2×C4C24×D7316yes—
667C2×C4C24×D7316yes—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—44no—
672C22—2924no—
673C22—734no—
674C22—1462no—
675C22—1462no—
676C22—1462no—
677C22—1468no—
678C22—1462no—
679C22—1462no—
680C22C22×#1192402812yes—
681C222−1+4×D7312yes—
682C222−1+4×D7312yes—
683C22C25×D7311yescharacteristic
684C4—26no—
685C4—22no—
686C4—26no—
687C4—22no—
688C4—26no—
689C4—734no—
690C4—1466no—
691C4—1466no—
692C4—1466no—
693C4—1462no—
694C4—1466no—
695C4C22×#11924028112yes—
696C2—42no—
697C2—2922no—
698C2—1464no—
699C2#2262402114yesdirect product factor
700C2C23×#1192402811yescharacteristic
701C2C2×2−1+4×D7311yescharacteristic
702C2C2×2−1+4×D7311yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#519×C73C2
socleC23×C73C25
prime radicalC2×#14556564C22
hypercenterC2×#519D73
hypocenterC73C2×#3523
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
1. #22624021C2direct (N × H)
2. C2×#17989315C2semidirect
3. C2×#17989313C2semidirect
4. C2×#17989305C2semidirect
5. C2×#17989278C2semidirect
6. C2×#17989276C2semidirect
7. C2×Q8×D292C2semidirect
8. C2×Q8×C22⋊D73C2semidirect
9. C2×Q8×C22⋊D73C2semidirect
10. C2×#17989199C2semidirect
11. C2×#17989195C2semidirect
12. C2×#17989141C2semidirect
14. C2×#17989063C2semidirect
15. C2×C4×Q8×D73C2semidirect
16. C2×#519×C73C2semidirect
19. #17989315C22semidirect
20. #17989313C22semidirect
21. #17989305C22semidirect
22. #17989278C22semidirect
23. #17989276C22semidirect
24. Q8×D292C22semidirect
25. Q8×C22⋊D73C22semidirect
26. Q8×C22⋊D73C22semidirect
27. #17989199C22semidirect
28. #17989195C22semidirect
29. #17989141C22semidirect
56. #17989063C22semidirect
65. C4×Q8×D73C22semidirect
75. #519×C73C22semidirect
346. C2×C73#3523semidirect
366. C2×#519D73semidirect
368. C73C2×#3523semidirect
410. #519C2×D73semidirect
699. C2#22624021direct (N × H)

Maximal subgroups

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

subgroupindex
#226240212
C2×#179893152
C2×#179893132
C2×#179893052
C2×#179892782
C2×#179892762
C2×Q8×D2922
C2×Q8×C22⋊D732
C2×#179891992
C2×#179891952
C2×#179891412
C2×#179891152
C2×#179890632
C2×C4×Q8×D732
C2×#519×C732
C2×#352373