Finite Group Databasebeta

← C2×#22624018 #33994204

Subgroups — C2×#22624018 #33994204

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#22624018C2132yesmaximal, direct product factor
2C2×#17989313C211yesmaximal, characteristic, complemented
3C2×#17989312C213yesmaximal, complemented
4C2×#17989308C213yesmaximal, complemented
5C2×#17989279C213yesmaximal, complemented
6C2×#17989277C213yesmaximal, complemented
7C2×Q8×C22⋊D73C211yesmaximal, characteristic, complemented
8C2×Q8×C22⋊D73C211yesmaximal, characteristic, complemented
9C2×#17989198C213yesmaximal, complemented
10C2×#17989197C213yesmaximal, complemented
11C2×#17989139C213yesmaximal, complemented
12C2×#17989117C213yesmaximal
13C2×#17989065C211yesmaximal, characteristic, complemented
14C2×#17989063C211yesmaximal, characteristic, complemented
15C22×Q8×Dic73C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C73C211yesmaximal, characteristic, complemented
17C22×Q8×D73C2211yescharacteristic
18#17989313C22116yescomplemented
19#17989312C22148yescomplemented
20#17989308C22148yescomplemented
21#17989279C22148yescomplemented
22#17989277C22148yescomplemented
23Q8×C22⋊D73C22116yescomplemented
24Q8×C22⋊D73C22116yescomplemented
25#17989198C22148yescomplemented
26#17989197C22148yescomplemented
27#17989139C22148yescomplemented
28C2×#14556590C2213yes—
29C2×#14556589C2213yes—
30C2×#14556589C2213yes—
31#17989117C22148yes—
32C2×#14556586C2213yes—
33C2×#14556586C2216yes—
34C2×#14556584C2213yes—
35C2×#14556584C2216yes—
36C2×#14556583C2213yes—
37C2×#14556582C2216yes—
38C2×#14556582C2213yes—
39C2×#14556581C2213yes—
40C2×#14556581C2216yes—
41C2×#14556581C2216yes—
42C2×#14556577C2213yes—
43C2×#14556575C2213yes—
44C2×#14556572C2213yes—
45C2×#14556570C2213yes—
46C2×#14556570C2213yes—
47C2×#14556568C2213yes—
48C2×#14556567C2213yes—
49C2×#14556567C2213yes—
50C2×#14556563C2211yescharacteristic
51#17989065C22116yescomplemented
52#17989063C22116yescomplemented
53C2×Q8×Dic73C2213yes—
54C2×Q8×Dic73C2213yes—
55C2×Q8×Dic73C2211yescharacteristic
56C2×Q8×Dic73C2211yescharacteristic
57C2×Q8×Dic73C2213yes—
58C2×Q8×Dic73C2213yes—
59C2×Q8×Dic73C2211yescharacteristic
60C2×Q8×Dic73C22116yescomplemented
61C2×C4×Dic146C2213yes—
62C2×C4×Dic146C2213yes—
63C2×#14556556C2216yes—
64C2×#14556556C2213yes—
65C2×C4×C22⋊D73C2213yes—
66C2×C4×C22⋊D73C2213yes—
67C2×#14556550C2213yes—
68C2×#14556550C2213yes—
69C2×#14556549C2213yes—
70C2×#14556548C2213yes—
71C2×#14556547C2216yes—
72C22×C4⋊Dic73C2213yes—
73C22×C4×Dic73C2213yes—
74C23×Q8×C73C2211yescharacteristic
75C23×Q8×C73C2211yescharacteristic
76D4×Q8×C73C22116yescomplemented
77C2×C4⋊Q8×C73C2213yes—
78C2×C22⋊Q8×C73C2213yes—
79C2×C22⋊Q8×C73C2213yes—
80C2×C4×Q8×C73C2211yescharacteristic
81C2×C4×D4×C73C2213yes—
82C22×Dic146C2313yes—
83C22×Dic146C2313yes—
84C2×Q8×D73—28no—
85C2×Q8×D73C2318yes—
86C22×C22⋊D73C2311yescharacteristic
87C22×C22⋊D73C2311yescharacteristic
88C23×Dic73C2311yescharacteristic
89C23×Dic73C2313yes—
90C22×C4×D73C2313yes—
91#14556590C23124yes—
92#14556589C23124yes—
93#14556589C23124yes—
94#14556586C23124yes—
95#14556586C23148yes—
96#14556584C23124yes—
97#14556584C23148yes—
98#14556583C23124yes—
99#14556582C23148yes—
100#14556582C23124yes—
101#14556581C23148yes—
102#14556581C23148yes—
103#14556581C23124yes—
104#14556577C23124yes—
105#14556575C23124yes—
106#14556572C23124yes—
107#14556570C23124yes—
108#14556570C23124yes—
109#14556568C23124yes—
110#14556567C23124yes—
111#14556567C23124yes—
112#14556563C2318yes—
113Q8×Dic73C23124yes—
114Q8×Dic73C23124yes—
115Q8×Dic73C2318yes—
116Q8×Dic73C2318yes—
117Q8×Dic73C23124yes—
118Q8×Dic73C23124yes—
119Q8×Dic73C2318yes—
120C4×Dic146C23124yes—
121C4×Dic146C23124yes—
122#14556556C23124yes—
123#14556556C23148yes—
124C4×C22⋊D73C23124yes—
125C4×C22⋊D73C23124yes—
126#14556550C23124yes—
127#14556550C23124yes—
128#14556549C23124yes—
129#14556548C23124yes—
130#14556547C23148yes—
131C2×C4⋊Dic73C2313yes—
132C2×C4⋊Dic73C23124yes—
133C2×C4⋊Dic73C2313yes—
134C2×C4⋊Dic73C2313yes—
135C2×C4⋊Dic73C2316yes—
136C2×C4⋊Dic73C2313yes—
137C2×C4⋊Dic73C2313yes—
138C2×C4⋊Dic73C2313yes—
139C2×#11924007C2313yes—
140C2×#11924007C2313yes—
141C2×#11924007C2316yes—
142C2×#11924007C2316yes—
143C2×#11924007C2316yes—
144C2×#11924007C2313yes—
145C2×#11924007C2313yes—
146C2×#11924007C2311yescharacteristic
147C2×#11924007C2313yes—
148C2×C22⋊Dic73C2313yes—
149C2×C22⋊Dic73C2311yescharacteristic
150C2×C22⋊Dic73C2313yes—
151C2×C22⋊Dic73C2313yes—
152C2×#11924005C2311yescharacteristic
153C2×#11924005C2313yes—
154C2×#11924005C2313yes—
155C2×#11924005C2313yes—
156C2×C4×Dic73C2313yes—
157C2×C4×Dic73C2313yes—
158C2×C4×Dic73C23124yes—
159C2×C4×Dic73C2313yes—
160C2×C4×Dic73C2313yes—
161C2×C4×Dic73C2313yes—
162C2×C4×Dic73C2316yes—
163C2×C4×Dic73C2316yes—
164C22×Q8×C73—28no—
165C22×Q8×C73—28no—
166C22×Q8×C73C2313yes—
167C22×Q8×C73C2313yes—
168C22×Q8×C73C2318yes—
169C22×Q8×C73C2318yes—
170C22×Q8×C73C2311yescharacteristic
171C22×D4×C73C2311yescharacteristic
172C23×C4×C73C2313yes—
173C23×C4×C73C2313yes—
174C4⋊Q8×C73C23124yes—
175C22⋊Q8×C73C23124yes—
176C22⋊Q8×C73C23124yes—
177C4×Q8×C73C2318yes—
178C4×D4×C73C23124yes—
179C2×C4⋊C4×C73C2313yes—
180C2×C4⋊C4×C73C2313yes—
181C2×C4⋊C4×C73C2316yes—
182C2×C22⋊C4×C73C2313yes—
183C2×C22⋊C4×C73C2313yes—
184C2×C42×C73C2313yes—
185C23×D73C2411yescharacteristic
186C2×Dic146—212no—
187C2×Dic146—212no—
188C2×Dic146C24112yes—
189C2×Dic146C24112yes—
190Q8×D73—232no—
191C2×C22⋊D73—24no—
192C2×C22⋊D73—24no—
193C2×C22⋊D73C2414yes—
194C2×C22⋊D73C2414yes—
195C22×Dic73—212no—
196C22×Dic73—24no—
197C22×Dic73C2411yescharacteristic
198C22×Dic73C2413yes—
199C22×Dic73C2414yes—
200C22×Dic73C2413yes—
201C22×Dic73C2411yescharacteristic
202C22×Dic73C2413yes—
203C22×Dic73C2413yes—
204C22×Dic73C24112yes—
205C22×Dic73C2411yescharacteristic
206C2×C4×D73—212no—
207C2×C4×D73C24112yes—
208C4⋊Dic73C24112yes—
209C4⋊Dic73C24112yes—
210C4⋊Dic73C24124yes—
211C4⋊Dic73C24112yes—
212C4⋊Dic73C24112yes—
213C4⋊Dic73C24112yes—
214C4⋊Dic73C24112yes—
215#11924007C24124yes—
216#11924007C24124yes—
217#11924007C24112yes—
218#11924007C24112yes—
219#11924007C24112yes—
220#11924007C24112yes—
221#11924007C24124yes—
222#11924007C2414yes—
223#11924007C24112yes—
224C22⋊Dic73C24112yes—
225C22⋊Dic73C2414yes—
226C22⋊Dic73C24112yes—
227C22⋊Dic73C24112yes—
228#11924005C2414yes—
229#11924005C24112yes—
230#11924005C24112yes—
231#11924005C24112yes—
232C4×Dic73C24112yes—
233C4×Dic73C24112yes—
234C4×Dic73C24112yes—
235C4×Dic73C24112yes—
236C4×Dic73C24124yes—
237C4×Dic73C24124yes—
238C4×Dic73C24112yes—
239C24×C73C2411yescharacteristic
240C24×C73C2411yescharacteristic
241C2×Q8×C73—232no—
242C2×Q8×C73—232no—
243C2×Q8×C73—212no—
244C2×Q8×C73—212no—
245C2×Q8×C73#4118yes—
246C2×Q8×C73C24112yes—
247C2×Q8×C73C24112yes—
248C2×Q8×C73C2414yes—
249C2×D4×C73—24no—
250C2×D4×C73C2414yes—
251C22×C4×C73—212no—
252C22×C4×C73—212no—
253C22×C4×C73C2411yescharacteristic
254C22×C4×C73C2413yes—
255C22×C4×C73C2413yes—
256C22×C4×C73C2413yes—
257C22×C4×C73C24112yes—
258C22×C4×C73C24112yes—
259C22×C4×C73C2413yes—
260C4⋊C4×C73C24112yes—
261C4⋊C4×C73C24112yes—
262C4⋊C4×C73C24124yes—
263C22⋊C4×C73C24112yes—
264C22⋊C4×C73C24112yes—
265C42×C73C24112yes—
266C23×C73—22no—
267C23×C73—22no—
268C23×C73—22no—
269C23×C73—22no—
270C23×C73—22no—
271C23×C732−1+414yes—
272C23×C73C2512yes—
273C23×C73C2512yes—
274C23×C73C2511yescharacteristic
275C22×D73—22no—
276C22×D73—22no—
277C22×D73—22no—
278C22×D73C2512yes—
279Q8×C73—224no—
280Q8×C73—224no—
281Q8×C73C2×#41116yes—
282D4×C73—28no—
283C2×C4×C73—26no—
284C2×C4×C73—26no—
285C2×C4×C73—22no—
286C2×C4×C73—26no—
287C2×C4×C73—224no—
288C2×C4×C73—224no—
289C2×C4×C73C2×#41112yes—
290C2×C4×C73C2512yes—
291C2×C4×C73C2516yes—
292C2×C4×C73C2516yes—
293C2×C4×C73C2516yes—
294C2×C4×C73C2516yes—
295C22⋊D73—28no—
296C22⋊D73—28no—
297C2×Dic73—26no—
298C2×Dic73—22no—
299C2×Dic73—224no—
300C2×Dic73—26no—
301C2×Dic73—26no—
302C2×Dic73—22no—
303C2×Dic73—26no—
304C2×Dic73—28no—
305C2×Dic732−1+414yes—
306C2×Dic73C2512yes—
307C2×Dic73C2516yes—
308C2×Dic73C2516yes—
309C2×Dic73C2512yes—
310C2×Dic73C2516yes—
311C2×Dic73C2516yes—
312C2×Dic73C2512yes—
313C4×D73—224no—
314Dic146—224no—
315Dic146—224no—
316C22×C73—22no—
317C22×C73—22no—
318C22×C73—28no—
319C22×C73—22no—
320C22×C73—22no—
321C22×C73—22no—
322C22×C73—44no—
323C22×C73C22×#4112yes—
324C22×C73C2×2−1+412yes—
325C22×C73C2×2−1+414yes—
326C22×C73C2×2−1+412yes—
327C22×C73C2611yescharacteristic
328C2×D73—22no—
329C2×D73—22no—
330C2×D73—22no—
331C2×D73—44no—
332C4×C73—26no—
333C4×C73—26no—
334C4×C73—26no—
335C4×C73—22no—
336C4×C73C22×#41112yes—
337Dic73—26no—
338Dic73—26no—
339Dic73—22no—
340Dic73—26no—
341Dic73—26no—
342Dic73—22no—
343Dic73C2×2−1+414yes—
344C2×#3523—731nomaximal, Sylow
345C2×C73—24no—
346C2×C73—42no—
347C2×C73#352314yescomplemented
348C2×C73C23×#4111yescharacteristic
349C2×C73C22×2−1+411yescharacteristic
350C2×C73C22×2−1+411yescharacteristic
351D73—42no—
352#3523—7332no—
353C2×#557—733no—
354C2×#557—731no—
355C2×#556—733no—
356C2×#552—733no—
357C2×#552—733no—
358C2×D4×Q8—731no—
359C2×D4×Q8—731no—
360C2×D4×Q8D7311yescharacteristic, complemented
361C2×#541—733no—
362C2×#541—733no—
363C2×#533—733no—
364C2×#529—733no—
365C2×#519—731no—
366C2×#519—731no—
367C22×C4×Q8—731no—
368C73C2×#352311yescharacteristic, complemented, Sylow
369C23×Q8—731no—
370C23×Q8C2×D7311yescharacteristic
371C23×Q8C2×D7311yescharacteristic
372#557—7348no—
373#557—7316no—
374#556—7348no—
375#552—7348no—
376#552—7348no—
377D4×Q8—7316no—
378D4×Q8—7316no—
379D4×Q8C2×D73116yescomplemented
380#541—7348no—
381#541—7348no—
382#533—7348no—
383C2×C4⋊Q8—733no—
384C2×C4⋊Q8—733no—
385C2×C4⋊Q8—733no—
386C2×C4⋊Q8C2×D7313yes—
387#529—7348no—
388C2×#126—733no—
389C2×#126—736no—
390C2×#126—733no—
391C2×#126—736no—
392C2×#125—733no—
393C2×#125—736no—
394C2×#125—736no—
395C2×#125—736no—
396C2×#125—733no—
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⋊Q8C2×D7313yes—
407C2×C22⋊Q8C2×D7313yes—
408C2×#121—731no—
409#519—7316no—
410#519—7316no—
411C2×C4×Q8—731no—
412C2×C4×Q8—733no—
413C2×C4×Q8—731no—
414C2×C4×Q8—733no—
415C2×C4×Q8—7316no—
416C2×C4×Q8—733no—
417C2×C4×Q8—731no—
418C2×C4×Q8—733no—
419C2×C4×Q8—733no—
420C2×C4×Q8—736no—
421C2×C4×Q8—733no—
422C2×C4×Q8—733no—
423C2×C4×Q8C2×D7311yescharacteristic
424C2×C4×D4—733no—
425C2×C4×D4—733no—
426C2×C4×D4C2×D7313yes—
427C2×#117—733no—
428C2×#117—733no—
429C2×#117—733no—
430C2×#117—736no—
431C2×#117—733no—
432C22×C4⋊C4—733no—
433C22×C42—733no—
434C22×Q8—28no—
435C22×Q8—28no—
436C22×Q8—738no—
437C22×Q8—733no—
438C22×Q8—733no—
439C22×Q8—1468no—
440C22×Q8C22×D7313yes—
441C22×Q8C22×D7313yes—
442C22×Q8C22×D7318yes—
443C22×Q8C22×D7318yes—
444C22×Q8C22×D7311yescharacteristic
445C22×D4—731no—
446C22×D4—731no—
447C22×D4C22×D7311yescharacteristic
448C23×C4—733no—
449C23×C4—731no—
450C23×C4—733no—
451C23×C4C22×D7313yes—
452C23×C4C22×D7313yes—
453C4⋊Q8—7324no—
454C4⋊Q8—7324no—
455C4⋊Q8—7324no—
456C4⋊Q8C22×D73124yes—
457#126—7324no—
458#126—7348no—
459#126—7324no—
460#126—7348no—
461#125—7324no—
462#125—7348no—
463#125—7348no—
464#125—7348no—
465#125—7324no—
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⋊Q8C22×D73124yes—
476C22⋊Q8C22×D73124yes—
477#121—738no—
478C4×Q8—738no—
479C4×Q8—7324no—
480C4×Q8—738no—
481C4×Q8—7324no—
482C4×Q8—7324no—
483C4×Q8—738no—
484C4×Q8—7324no—
485C4×Q8—7324no—
486C4×Q8—7348no—
487C4×Q8—7324no—
488C4×Q8—7324no—
489C4×Q8C22×D7318yes—
490C4×D4—7324no—
491C4×D4—7324no—
492C4×D4C22×D73124yes—
493#117—7324no—
494#117—7324no—
495#117—7324no—
496#117—7348no—
497#117—7324no—
498C2×C4⋊C4—733no—
499C2×C4⋊C4—733no—
500C2×C4⋊C4—736no—
501C2×C4⋊C4—7324no—
502C2×C4⋊C4—733no—
503C2×C4⋊C4—733no—
504C2×C4⋊C4—733no—
505C2×C4⋊C4—733no—
506C2×C4⋊C4—733no—
507C2×C4⋊C4—736no—
508C2×C4⋊C4—736no—
509C2×C4⋊C4—733no—
510C2×C4⋊C4—733no—
511C2×C4⋊C4—731no—
512C2×C4⋊C4—736no—
513C2×C4⋊C4—733no—
514C2×C4⋊C4—733no—
515C2×C4⋊C4C22×D7313yes—
516C2×C4⋊C4C22×D7313yes—
517C2×C4⋊C4C22×D7316yes—
518C2×C22⋊C4—731no—
519C2×C22⋊C4—733no—
520C2×C22⋊C4—733no—
521C2×C22⋊C4—733no—
522C2×C22⋊C4—731no—
523C2×C22⋊C4—733no—
524C2×C22⋊C4—733no—
525C2×C22⋊C4—733no—
526C2×C22⋊C4C22×D7313yes—
527C2×C22⋊C4C22×D7313yes—
528C2×C42—733no—
529C2×C42—736no—
530C2×C42—736no—
531C2×C42—733no—
532C2×C42—733no—
533C2×C42—733no—
534C2×C42—733no—
535C2×C42—7324no—
536C2×C42C22×D7313yes—
537C24—731no—
538C24C23×D7311yescharacteristic
539C24C23×D7311yescharacteristic
540C2×Q8—232no—
541C2×Q8—232no—
542C2×Q8—212no—
543C2×Q8—212no—
544C2×Q8—7312no—
545C2×Q8—7312no—
546C2×Q8—14612no—
547C2×Q8—14632no—
548C2×Q8—14612no—
549C2×Q8#1192402718yes—
550C2×Q8C23×D73112yes—
551C2×Q8C23×D73112yes—
552C2×Q8C23×D7314yes—
553C2×D4—24no—
554C2×D4—734no—
555C2×D4—734no—
556C2×D4—1464no—
557C2×D4—1464no—
558C2×D4C23×D7314yes—
559C22×C4—212no—
560C22×C4—212no—
561C22×C4—731no—
562C22×C4—734no—
563C22×C4—7312no—
564C22×C4—731no—
565C22×C4—733no—
566C22×C4—733no—
567C22×C4—731no—
568C22×C4—733no—
569C22×C4—733no—
570C22×C4—7312no—
571C22×C4—1464no—
572C22×C4—14612no—
573C22×C4—14612no—
574C22×C4C23×D73112yes—
575C22×C4C23×D73112yes—
576C22×C4C23×D7313yes—
577C22×C4C23×D7313yes—
578C22×C4C23×D7313yes—
579C22×C4C23×D7311yescharacteristic
580C22×C4C23×D7313yes—
581C4⋊C4—7312no—
582C4⋊C4—7312no—
583C4⋊C4—7324no—
584C4⋊C4—7324no—
585C4⋊C4—7312no—
586C4⋊C4—7312no—
587C4⋊C4—734no—
588C4⋊C4—7324no—
589C4⋊C4—7312no—
590C4⋊C4—7312no—
591C4⋊C4—7312no—
592C4⋊C4—7324no—
593C4⋊C4—7312no—
594C4⋊C4—7312no—
595C4⋊C4—7312no—
596C4⋊C4—7312no—
597C4⋊C4C23×D73112yes—
598C4⋊C4C23×D73112yes—
599C4⋊C4C23×D73124yes—
600C22⋊C4—734no—
601C22⋊C4—7312no—
602C22⋊C4—7312no—
603C22⋊C4—7312no—
604C22⋊C4—734no—
605C22⋊C4—7312no—
606C22⋊C4—7312no—
607C22⋊C4—7312no—
608C22⋊C4C23×D73112yes—
609C22⋊C4C23×D73112yes—
610C42—7312no—
611C42—7312no—
612C42—7312no—
613C42—7312no—
614C42—7324no—
615C42—7324no—
616C42—7312no—
617C42C23×D73112yes—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—732no—
624C23—1462no—
625C23—1462no—
626C23—1462no—
627C23#1455663914yes—
628C23C24×D7312yes—
629C23C24×D7312yes—
630C23C24×D7311yescharacteristic
631Q8—224no—
632Q8—224no—
633Q8—14624no—
634Q8—14624no—
635Q8C2×#11924027116yes—
636D4—28no—
637D4—1468no—
638D4—1468no—
639C2×C4—26no—
640C2×C4—26no—
641C2×C4—26no—
642C2×C4—22no—
643C2×C4—224no—
644C2×C4—224no—
645C2×C4—734no—
646C2×C4—732no—
647C2×C4—732no—
648C2×C4—736no—
649C2×C4—736no—
650C2×C4—732no—
651C2×C4—736no—
652C2×C4—736no—
653C2×C4—1468no—
654C2×C4—1466no—
655C2×C4—1462no—
656C2×C4—1466no—
657C2×C4—14624no—
658C2×C4—1466no—
659C2×C4—1466no—
660C2×C4—1462no—
661C2×C4—14624no—
662C2×C4C2×#11924027112yes—
663C2×C4C24×D7316yes—
664C2×C4C24×D7316yes—
665C2×C4C24×D7316yes—
666C2×C4C24×D7312yes—
667C2×C4C24×D7316yes—
668C22—28no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—44no—
675C22—2924no—
676C22—1462no—
677C22—1462no—
678C22—1462no—
679C22C22×#1192402712yes—
680C222−1+4×D7312yes—
681C22C2×#1455663914yes—
682C22C2×#1455663912yes—
683C22C25×D7311yescharacteristic
684C4—26no—
685C4—26no—
686C4—26no—
687C4—22no—
688C4—734no—
689C4—1466no—
690C4—1462no—
691C4—1466no—
692C4—1466no—
693C4—1466no—
694C4—1462no—
695C4C22×#11924027112yes—
696C2—24no—
697C2—42no—
698C2—2922no—
699C2#2262401814yesdirect product factor
700C2C23×#1192402711yescharacteristic
701C2C2×2−1+4×D7311yescharacteristic
702C2C22×#1455663911yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×D4×Q8×C73C2
socleC23×C73C25
prime radicalC2×#14556563C22
hypercenterC2×D4×Q8D73
hypocenterC73C2×#3523
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #22624018C2direct (N × H)
2. C2×#17989313C2semidirect
3. C2×#17989312C2semidirect
4. C2×#17989308C2semidirect
5. C2×#17989279C2semidirect
6. C2×#17989277C2semidirect
7. C2×Q8×C22⋊D73C2semidirect
8. C2×Q8×C22⋊D73C2semidirect
9. C2×#17989198C2semidirect
10. C2×#17989197C2semidirect
11. C2×#17989139C2semidirect
13. C2×#17989065C2semidirect
14. C2×#17989063C2semidirect
15. C22×Q8×Dic73C2semidirect
16. C2×D4×Q8×C73C2semidirect
18. #17989313C22semidirect
19. #17989312C22semidirect
20. #17989308C22semidirect
21. #17989279C22semidirect
22. #17989277C22semidirect
23. Q8×C22⋊D73C22semidirect
24. Q8×C22⋊D73C22semidirect
25. #17989198C22semidirect
26. #17989197C22semidirect
27. #17989139C22semidirect
51. #17989065C22semidirect
52. #17989063C22semidirect
60. C2×Q8×Dic73C22semidirect
76. D4×Q8×C73C22semidirect
347. C2×C73#3523semidirect
360. C2×D4×Q8D73semidirect
368. C73C2×#3523semidirect
379. D4×Q8C2×D73semidirect
699. C2#22624018direct (N × H)

Maximal subgroups

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

subgroupindex
#226240182
C2×#179893132
C2×#179893122
C2×#179893082
C2×#179892792
C2×#179892772
C2×Q8×C22⋊D732
C2×#179891982
C2×#179891972
C2×#179891392
C2×#179891172
C2×#179890652
C2×#179890632
C22×Q8×Dic732
C2×D4×Q8×C732
C2×#352373