Finite Group Databasebeta

← C2×#22623813 #33994425

Subgroups — C2×#22623813 #33994425

Order 18688.

7022 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623813C2132yesmaximal, direct product factor
2C2×#17989314C214yesmaximal, complemented
3C2×#17989304C214yesmaximal, complemented
4C2×#17989273C214yesmaximal, complemented
5C2×#17989269C214yesmaximal, complemented
6C2×#17989200C211yesmaximal, characteristic, complemented
7C2×#17989199C211yesmaximal, characteristic, complemented
8C2×#17989198C211yesmaximal, characteristic, complemented
9C2×#17989160C212yesmaximal
10C2×#17989143C211yesmaximal, characteristic, complemented
11C2×#17989141C212yesmaximal, complemented
12C2×#17989139C212yesmaximal, complemented
13C2×C4⋊Q8×D73C211yesmaximal, characteristic, complemented
14C2×#17989063C212yesmaximal, complemented
15C2×#17989055C211yesmaximal, characteristic
16C2×#541×C73C211yesmaximal, characteristic, complemented
17C22×#11924028C2211yescharacteristic
18C22×Q8×D73C2212yes—
19#17989314C22164yescomplemented
20#17989304C22164yescomplemented
21#17989273C22164yescomplemented
22#17989269C22164yescomplemented
23#17989200C22116yescomplemented
24#17989199C22116yescomplemented
25#17989198C22116yescomplemented
26#17989160C22132yes—
27#17989143C22116yescomplemented
28#17989141C22132yescomplemented
29#17989139C22132yescomplemented
30C2×#14556591C2211yescharacteristic
31C2×#14556590C2214yes—
32C2×#14556590C2214yes—
33C2×#14556590C2212yes—
34C2×#14556589C2212yes—
35C4⋊Q8×D73C22116yescomplemented
36C2×#14556586C2214yes—
37C2×#14556586C2214yes—
38C2×#14556584C2214yes—
39C2×#14556583C2211yescharacteristic
40C2×#14556582C2214yes—
41C2×#14556581C2214yes—
42C2×#14556581C2214yes—
43C2×#14556581C2214yes—
44C2×#14556581C2214yes—
45C2×#14556577C2214yes—
46C2×#14556576C2214yes—
47C2×#14556573C2214yes—
48C2×#14556571C2212yes—
49C2×#14556570C2212yes—
50C2×#14556569C2214yes—
51C2×#14556569C2214yes—
52C2×#14556568C2214yes—
53C2×#14556567C2212yes—
54#17989063C22132yescomplemented
55#17989055C22116yes—
56C2×Q8×Dic73C2212yes—
57C2×C4×Dic146C2214yes—
58C2×C4×Dic146C2214yes—
59C2×C4×Dic146C2212yes—
60C2×#14556556C2212yes—
61C2×#14556556C2214yes—
62C2×#14556556C2214yes—
63C2×#14556556C2214yes—
64C2×#14556556C2212yes—
65C2×#14556553C2212yes—
66C2×#14556551C2212yes—
67C2×#14556551C2212yes—
68C2×#14556549C2212yes—
69C2×#14556549C2214yes—
70C2×#14556548C2211yescharacteristic
71C2×#14556548C2211yescharacteristic
72C2×#14556548C2214yes—
73C2×#14556548C2214yes—
74C2×#14556547C2214yes—
75C2×C4⋊C4×D73C2214yes—
76C22×C4×Dic73C2211yescharacteristic
77C2×C42×D73C2211yescharacteristic
78C2×C42×D73C2211yescharacteristic
79#541×C73C22116yescomplemented
80C2×C4⋊Q8×C73C2211yescharacteristic
81C2×#126×C73C2214yes—
82C2×#125×C73C2214yes—
83C2×#125×C73C2211yescharacteristic
84C2×C22⋊Q8×C73C2212yes—
85C2×C4×Q8×C73C2212yes—
86C2×#117×C73C2211yescharacteristic
87C2×#11924028—28no—
88C2×#11924028C2318yes—
89C22×Dic146C2312yes—
90C22×Dic146C2311yescharacteristic
91C22×Dic146C2314yes—
92C22×Dic146C2314yes—
93C2×Q8×D73—216no—
94C2×Q8×D73C23116yes—
95C22×D292C2311yescharacteristic
96C22×C22⋊D73C2311yescharacteristic
97C22×C22⋊D73C2311yescharacteristic
98C23×Dic73C2312yes—
99C22×C4×D73C2314yes—
100C22×C4×D73C2311yescharacteristic
101C22×C4×D73C2312yes—
102C22×C4×D73C2312yes—
103C22×C4×D73C2311yescharacteristic
104#14556591C2318yes—
105#14556590C23132yes—
106#14556590C23116yes—
107#14556590C23132yes—
108#14556589C23116yes—
109#14556586C23132yes—
110#14556586C23132yes—
111#14556584C23132yes—
112#14556583C2318yes—
113#14556582C23132yes—
114#14556581C23132yes—
115#14556581C23132yes—
116#14556581C23132yes—
117#14556581C23132yes—
118#14556577C23132yes—
119#14556576C23132yes—
120#14556573C23132yes—
121#14556571C23116yes—
122#14556570C23116yes—
123#14556569C23132yes—
124#14556569C23132yes—
125#14556568C23132yes—
126#14556567C23116yes—
127Q8×Dic73C23116yes—
128C4×Dic146C23116yes—
129C4×Dic146C23132yes—
130C4×Dic146C23132yes—
131#14556556C23116yes—
132#14556556C23132yes—
133#14556556C23132yes—
134#14556556C23132yes—
135#14556556C23116yes—
136#14556553C23116yes—
137#14556551C23116yes—
138#14556551C23116yes—
139#14556549C23116yes—
140#14556549C23132yes—
141#14556548C23132yes—
142#14556548C2318yes—
143#14556548C23132yes—
144#14556548C2318yes—
145#14556547C23132yes—
146C2×C4⋊Dic73C2314yes—
147C2×C4⋊Dic73C2312yes—
148C2×C4⋊Dic73C2314yes—
149C2×C4⋊Dic73C2314yes—
150C2×#11924007C2314yes—
151C2×#11924007C2314yes—
152C2×#11924007C2314yes—
153C2×#11924007C2314yes—
154C2×#11924007C2314yes—
155C2×#11924007C2312yes—
156C2×#11924007C2312yes—
157C2×#11924007C2314yes—
158C2×#11924007C2314yes—
159C2×#11924007C2314yes—
160C4⋊C4×D73C23132yes—
161C2×C22⋊Dic73C2314yes—
162C2×#11924005C2312yes—
163C2×#11924005C2314yes—
164C2×#11924005C2312yes—
165C2×#11924005C2314yes—
166C2×#11924005C2314yes—
167C2×C4×Dic73C2311yescharacteristic
168C2×C4×Dic73C2312yes—
169C2×C4×Dic73C2314yes—
170C2×C4×Dic73C2318yes—
171C2×C4×Dic73C2312yes—
172C2×C4×Dic73C2311yescharacteristic
173C2×C4×Dic73C2312yes—
174C2×C4×Dic73C2314yes—
175C2×C4×Dic73C2314yes—
176C2×C4×Dic73C2314yes—
177C42×D73C2318yes—
178C42×D73C2318yes—
179C22×Q8×C73C2312yes—
180C23×C4×C73C2311yescharacteristic
181C4⋊Q8×C73C2318yes—
182#126×C73C23132yes—
183#125×C73C2318yes—
184#125×C73C23132yes—
185C22⋊Q8×C73C23116yes—
186C4×Q8×C73C23116yes—
187#117×C73C2318yes—
188C2×C4⋊C4×C73C2312yes—
189C2×C4⋊C4×C73C2314yes—
190C2×C4⋊C4×C73C2314yes—
191C2×C4⋊C4×C73C2312yes—
192C2×C4⋊C4×C73C2314yes—
193C2×C4⋊C4×C73C2314yes—
194C2×C22⋊C4×C73C2312yes—
195C2×C22⋊C4×C73C2314yes—
196C2×C42×C73C2311yescharacteristic
197C2×C42×C73C2311yescharacteristic
198C2×C42×C73C2314yes—
199C23×D73C2411yescharacteristic
200C23×D73C2411yescharacteristic
201#11924028—232no—
202C2×Dic146—28no—
203C2×Dic146—216no—
204C2×Dic146—24no—
205C2×Dic146—216no—
206C2×Dic146C24116yes—
207C2×Dic146C2414yes—
208C2×Dic146C2418yes—
209C2×Dic146C24116yes—
210Q8×D73—264no—
211C2×D292—24no—
212C2×D292C2414yes—
213C2×C22⋊D73—24no—
214C2×C22⋊D73—24no—
215C2×C22⋊D73C2414yes—
216C2×C22⋊D73C2414yes—
217C22×Dic73—28no—
218C22×Dic73C2412yes—
219C22×Dic73C2414yes—
220C22×Dic73C2414yes—
221C22×Dic73C2411yescharacteristic
222C22×Dic73C2418yes—
223C22×Dic73C2411yescharacteristic
224C22×Dic73C2412yes—
225C2×C4×D73—216no—
226C2×C4×D73—24no—
227C2×C4×D73—28no—
228C2×C4×D73—28no—
229C2×C4×D73#4118yes—
230C2×C4×D73C2418yes—
231C2×C4×D73C2418yes—
232C2×C4×D73C2414yes—
233C2×C4×D73C24116yes—
234C2×C4×D73C2414yes—
235C4⋊Dic73C24116yes—
236C4⋊Dic73C2418yes—
237C4⋊Dic73C24116yes—
238C4⋊Dic73C24116yes—
239#11924007C24116yes—
240#11924007C24116yes—
241#11924007C24116yes—
242#11924007C2418yes—
243#11924007C2418yes—
244#11924007C24116yes—
245#11924007C24116yes—
246#11924007C24116yes—
247#11924007C24116yes—
248#11924007C24116yes—
249C22⋊Dic73C24116yes—
250#11924005C2418yes—
251#11924005C24116yes—
252#11924005C2418yes—
253#11924005C24116yes—
254#11924005C24116yes—
255C4×Dic73C2414yes—
256C4×Dic73C2418yes—
257C4×Dic73C2418yes—
258C4×Dic73C2414yes—
259C4×Dic73C2418yes—
260C4×Dic73C24116yes—
261C4×Dic73C24116yes—
262C4×Dic73C24116yes—
263C4×Dic73C24116yes—
264C24×C73C2411yescharacteristic
265C2×Q8×C73—28no—
266C2×Q8×C73C2418yes—
267C22×C4×C73—24no—
268C22×C4×C73C2412yes—
269C22×C4×C73C2414yes—
270C22×C4×C73C2412yes—
271C22×C4×C73C2414yes—
272C22×C4×C73C2411yescharacteristic
273C22×C4×C73C2414yes—
274C22×C4×C73C2411yescharacteristic
275C4⋊C4×C73C2418yes—
276C4⋊C4×C73C2418yes—
277C4⋊C4×C73C24116yes—
278C4⋊C4×C73C24116yes—
279C4⋊C4×C73C24116yes—
280C4⋊C4×C73C24116yes—
281C22⋊C4×C73C2418yes—
282C22⋊C4×C73C24116yes—
283C42×C73C2414yes—
284C42×C73C2414yes—
285C42×C73C24116yes—
286C23×C73—22no—
287C23×C73—24no—
288C23×C73C2512yes—
289C23×C73C2511yescharacteristic
290C22×D73—24no—
291C22×D73—22no—
292C22×D73—24no—
293C22×D73C2×#4114yes—
294C22×D73C2512yes—
295C22×D73C2512yes—
296Q8×C73—216no—
297C2×C4×C73—22no—
298C2×C4×C73—28no—
299C2×C4×C73—24no—
300C2×C4×C73—24no—
301C2×C4×C73—28no—
302C2×C4×C73—28no—
303C2×C4×C73C2×#4114yes—
304C2×C4×C73C2514yes—
305C2×C4×C73C2518yes—
306C2×C4×C73C2514yes—
307C2×C4×C73C2518yes—
308C2×C4×C73C2512yes—
309C2×C4×C73C2512yes—
310C22⋊D73—28no—
311C22⋊D73—28no—
312C2×Dic73—22no—
313C2×Dic73—28no—
314C2×Dic73—24no—
315C2×Dic73—28no—
316C2×Dic73—216no—
317C2×Dic73C2×#4114yes—
318C2×Dic732−1+418yes—
319C2×Dic73C2514yes—
320C2×Dic73C2518yes—
321C2×Dic73C2518yes—
322C2×Dic73C2512yes—
323C2×Dic73C2512yes—
324C2×Dic73C2514yes—
325D292—28no—
326C4×D73—232no—
327C4×D73—28no—
328C4×D73—216no—
329C4×D73—216no—
330C4×D73C2×#41116yes—
331Dic146—216no—
332Dic146—232no—
333Dic146—28no—
334Dic146—232no—
335C22×C73—22no—
336C22×C73—24no—
337C22×C73—44no—
338C22×C73C22×#4112yes—
339C22×C73C2×2−1+414yes—
340C22×C73C2611yescharacteristic
341C2×D73—24no—
342C2×D73—28no—
343C2×D73—22no—
344C2×D73—24no—
345C2×D73—44no—
346C2×D73C22×#4114yes—
347C4×C73—28no—
348C4×C73—22no—
349C4×C73—28no—
350C4×C73—24no—
351C4×C73—24no—
352C4×C73C22×#4114yes—
353Dic73—28no—
354Dic73—22no—
355Dic73—28no—
356Dic73—24no—
357Dic73C22×#4114yes—
358Dic73C2×2−1+418yes—
359C2×#3509—731nomaximal, Sylow
360C2×C73—42no—
361C2×C73#350914yescomplemented
362C2×C73C23×#4111yescharacteristic
363C2×C73C22×2−1+412yes—
364D73—24no—
365D73—42no—
366#3509—7332no—
367C2×#557—734no—
368C2×#556—734no—
369C2×#552—734no—
370C2×#552—734no—
371C2×#541—731no—
372C2×#541—731no—
373C2×#541—731no—
374C2×#541D7311yescharacteristic, complemented
375C2×#536—732no—
376C2×#533—731no—
377C2×#533—732no—
378C2×#533—732no—
379C22×C4⋊Q8—731no—
380C2×#519—732no—
381C2×C4×#41—731no—
382C73C2×#350911yescharacteristic, complemented, Sylow
383C22×#41—731no—
384C23×Q8—732no—
385#557—7364no—
386#556—7364no—
387#552—7364no—
388#552—7364no—
389#541—7316no—
390#541—7316no—
391#541—7316no—
392#541C2×D73116yescomplemented
393#536—7332no—
394#533—7316no—
395#533—7332no—
396#533—7332no—
397C2×C4⋊Q8—732no—
398C2×C4⋊Q8—7316no—
399C2×C4⋊Q8—734no—
400C2×C4⋊Q8—732no—
401C2×C4⋊Q8—734no—
402C2×C4⋊Q8—731no—
403C2×C4⋊Q8C2×D7311yescharacteristic
404C2×#126—734no—
405C2×#126—734no—
406C2×#126—734no—
407C2×#126C2×D7314yes—
408C2×#125—734no—
409C2×#125—734no—
410C2×#125—734no—
411C2×#125—734no—
412C2×#125—734no—
413C2×#125—731no—
414C2×#125C2×D7311yescharacteristic
415C2×#125C2×D7314yes—
416C2×#124—734no—
417C2×#123—734no—
418C2×#123—734no—
419C2×C22⋊Q8—732no—
420C2×C22⋊Q8—732no—
421C2×C22⋊Q8—732no—
422C2×C22⋊Q8—734no—
423C2×C22⋊Q8—734no—
424C2×C22⋊Q8—734no—
425C2×C22⋊Q8C2×D7312yes—
426#519—7332no—
427C4×#41—7316no—
428C2×C4×Q8—732no—
429C2×C4×Q8—732no—
430C2×C4×Q8—732no—
431C2×C4×Q8—734no—
432C2×C4×Q8—734no—
433C2×C4×Q8—734no—
434C2×C4×Q8—732no—
435C2×C4×Q8—734no—
436C2×C4×Q8—734no—
437C2×C4×Q8C2×D7312yes—
438C2×C4×D4—732no—
439C2×C4×D4—732no—
440C2×C4×D4—732no—
441C2×#117—732no—
442C2×#117—734no—
443C2×#117—734no—
444C2×#117—731no—
445C2×#117—731no—
446C2×#117—734no—
447C2×#117—734no—
448C2×#117C2×D7311yescharacteristic
449C22×C4⋊C4—734no—
450C22×C42—731no—
451C22×C42—731no—
452C22×C42—731no—
453C2×#41—738no—
454C2×#41—1468no—
455C22×Q8—7316no—
456C22×Q8—734no—
457C22×Q8—732no—
458C22×Q8—734no—
459C22×Q8—731no—
460C22×Q8—14616no—
461C22×Q8C22×D7312yes—
462C22×D4—731no—
463C22×D4—731no—
464C22×D4—731no—
465C23×C4—731no—
466C23×C4—732no—
467C23×C4—734no—
468C23×C4—732no—
469C23×C4—732no—
470C23×C4—731no—
471C23×C4C22×D7311yescharacteristic
472C4⋊Q8—7316no—
473C4⋊Q8—7332no—
474C4⋊Q8—7316no—
475C4⋊Q8—7332no—
476C4⋊Q8—738no—
477C4⋊Q8C22×D7318yes—
478#126—7332no—
479#126—7332no—
480#126—7332no—
481#126C22×D73132yes—
482#125—7332no—
483#125—7332no—
484#125—7332no—
485#125—7332no—
486#125—7332no—
487#125—738no—
488#125C22×D7318yes—
489#125C22×D73132yes—
490#124—7332no—
491#123—7332no—
492#123—7332no—
493C22⋊Q8—7316no—
494C22⋊Q8—7316no—
495C22⋊Q8—7316no—
496C22⋊Q8—7332no—
497C22⋊Q8—7332no—
498C22⋊Q8—7332no—
499C22⋊Q8C22×D73116yes—
500C4×Q8—7316no—
501C4×Q8—7316no—
502C4×Q8—7316no—
503C4×Q8—7332no—
504C4×Q8—7332no—
505C4×Q8—7332no—
506C4×Q8—7316no—
507C4×Q8—7332no—
508C4×Q8—7332no—
509C4×Q8C22×D73116yes—
510C4×D4—7316no—
511C4×D4—7316no—
512C4×D4—7316no—
513#117—7316no—
514#117—7332no—
515#117—7332no—
516#117—738no—
517#117—738no—
518#117—7332no—
519#117—7332no—
520#117C22×D7318yes—
521C2×C4⋊C4—734no—
522C2×C4⋊C4—734no—
523C2×C4⋊C4—734no—
524C2×C4⋊C4—734no—
525C2×C4⋊C4—732no—
526C2×C4⋊C4—732no—
527C2×C4⋊C4—732no—
528C2×C4⋊C4—734no—
529C2×C4⋊C4—734no—
530C2×C4⋊C4—734no—
531C2×C4⋊C4—734no—
532C2×C4⋊C4—734no—
533C2×C4⋊C4—734no—
534C2×C4⋊C4—734no—
535C2×C4⋊C4—7332no—
536C2×C4⋊C4C22×D7314yes—
537C2×C4⋊C4C22×D7312yes—
538C2×C4⋊C4C22×D7314yes—
539C2×C4⋊C4C22×D7312yes—
540C2×C4⋊C4C22×D7314yes—
541C2×C4⋊C4C22×D7314yes—
542C2×C22⋊C4—734no—
543C2×C22⋊C4—732no—
544C2×C22⋊C4—734no—
545C2×C22⋊C4—732no—
546C2×C22⋊C4—734no—
547C2×C22⋊C4—734no—
548C2×C22⋊C4C22×D7314yes—
549C2×C22⋊C4C22×D7312yes—
550C2×C42—731no—
551C2×C42—734no—
552C2×C42—734no—
553C2×C42—734no—
554C2×C42—734no—
555C2×C42—732no—
556C2×C42—732no—
557C2×C42—732no—
558C2×C42—738no—
559C2×C42—731no—
560C2×C42—738no—
561C2×C42—738no—
562C2×C42C22×D7314yes—
563C2×C42C22×D7311yescharacteristic
564C2×C42C22×D7311yescharacteristic
565C24—731no—
566C24—731no—
567C24C23×D7311yescharacteristic
568#41—14632no—
569C2×Q8—28no—
570C2×Q8—7316no—
571C2×Q8—738no—
572C2×Q8—7316no—
573C2×Q8—734no—
574C2×Q8—14616no—
575C2×Q8—14616no—
576C2×Q8—1464no—
577C2×Q8—14664no—
578C2×Q8—1468no—
579C2×Q8C23×D7318yes—
580C2×D4—734no—
581C2×D4—734no—
582C2×D4—734no—
583C2×D4—1464no—
584C2×D4—1464no—
585C2×D4—1464no—
586C22×C4—24no—
587C22×C4—731no—
588C22×C4—732no—
589C22×C4—738no—
590C22×C4—734no—
591C22×C4—738no—
592C22×C4—732no—
593C22×C4—734no—
594C22×C4—734no—
595C22×C4—731no—
596C22×C4—738no—
597C22×C4—738no—
598C22×C4—734no—
599C22×C4—7316no—
600C22×C4—1468no—
601C22×C4—1468no—
602C22×C4—14616no—
603C22×C4—1468no—
604C22×C4—1464no—
605C22×C4C23×D7314yes—
606C22×C4C23×D7312yes—
607C22×C4C23×D7314yes—
608C22×C4C23×D7311yescharacteristic
609C22×C4C23×D7312yes—
610C22×C4C23×D7314yes—
611C22×C4C23×D7311yescharacteristic
612C4⋊C4—7316no—
613C4⋊C4—7316no—
614C4⋊C4—7316no—
615C4⋊C4—738no—
616C4⋊C4—738no—
617C4⋊C4—7316no—
618C4⋊C4—7316no—
619C4⋊C4—7316no—
620C4⋊C4—7316no—
621C4⋊C4—7316no—
622C4⋊C4—7316no—
623C4⋊C4—738no—
624C4⋊C4—7316no—
625C4⋊C4—7316no—
626C4⋊C4C23×D73116yes—
627C4⋊C4C23×D7318yes—
628C4⋊C4C23×D73116yes—
629C4⋊C4C23×D7318yes—
630C4⋊C4C23×D73116yes—
631C4⋊C4C23×D73116yes—
632C22⋊C4—7316no—
633C22⋊C4—738no—
634C22⋊C4—7316no—
635C22⋊C4—738no—
636C22⋊C4—7316no—
637C22⋊C4—7316no—
638C22⋊C4C23×D73116yes—
639C22⋊C4C23×D7318yes—
640C42—734no—
641C42—734no—
642C42—738no—
643C42—738no—
644C42—738no—
645C42—7316no—
646C42—7316no—
647C42—7316no—
648C42—7316no—
649C42C23×D7314yes—
650C42C23×D7314yes—
651C42C23×D73116yes—
652C23—22no—
653C23—24no—
654C23—734no—
655C23—732no—
656C23—732no—
657C23—1462no—
658C23—1464no—
659C23—1464no—
660C23C24×D7312yes—
661C23C24×D7311yescharacteristic
662Q8—216no—
663Q8—14632no—
664Q8—1468no—
665Q8—14632no—
666Q8—14616no—
667D4—1468no—
668D4—1468no—
669D4—1468no—
670C2×C4—22no—
671C2×C4—28no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—28no—
675C2×C4—28no—
676C2×C4—734no—
677C2×C4—738no—
678C2×C4—732no—
679C2×C4—734no—
680C2×C4—7316no—
681C2×C4—734no—
682C2×C4—738no—
683C2×C4—738no—
684C2×C4—732no—
685C2×C4—14616no—
686C2×C4—14616no—
687C2×C4—14632no—
688C2×C4—14616no—
689C2×C4—1462no—
690C2×C4—1468no—
691C2×C4—1464no—
692C2×C4—1468no—
693C2×C4—1468no—
694C2×C4#41×D7314yes—
695C2×C4C24×D7314yes—
696C2×C4C24×D7318yes—
697C2×C4C24×D7312yes—
698C2×C4C24×D7314yes—
699C2×C4C24×D7318yes—
700C2×C4C24×D7312yes—
701C22—22no—
702C22—24no—
703C22—44no—
704C22—2924no—
705C22—734no—
706C22—1462no—
707C22—1464no—
708C22—1468no—
709C22—1464no—
710C22C2×#41×D7312yes—
711C222−1+4×D7314yes—
712C22C25×D7311yescharacteristic
713C4—22no—
714C4—28no—
715C4—24no—
716C4—24no—
717C4—28no—
718C4—734no—
719C4—738no—
720C4—1462no—
721C4—1468no—
722C4—1464no—
723C4—1468no—
724C4C2×#41×D7314yes—
725C2—42no—
726C2—2922no—
727C2—1464no—
728C2#2262381314yesdirect product factor
729C2C22×#41×D7311yescharacteristic
730C2C2×2−1+4×D7312yes—
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#541×C73C2
socleC23×C73C25
prime radicalC22×#11924028C22
hypercenterC2×#541D73
hypocenterC73C2×#3509
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. #22623813C2direct (N × H)
2. C2×#17989314C2semidirect
3. C2×#17989304C2semidirect
4. C2×#17989273C2semidirect
5. C2×#17989269C2semidirect
6. C2×#17989200C2semidirect
7. C2×#17989199C2semidirect
8. C2×#17989198C2semidirect
10. C2×#17989143C2semidirect
11. C2×#17989141C2semidirect
12. C2×#17989139C2semidirect
13. C2×C4⋊Q8×D73C2semidirect
14. C2×#17989063C2semidirect
16. C2×#541×C73C2semidirect
19. #17989314C22semidirect
20. #17989304C22semidirect
21. #17989273C22semidirect
22. #17989269C22semidirect
23. #17989200C22semidirect
24. #17989199C22semidirect
25. #17989198C22semidirect
27. #17989143C22semidirect
28. #17989141C22semidirect
29. #17989139C22semidirect
35. C4⋊Q8×D73C22semidirect
54. #17989063C22semidirect
79. #541×C73C22semidirect
361. C2×C73#3509semidirect
374. C2×#541D73semidirect
382. C73C2×#3509semidirect
392. #541C2×D73semidirect
728. C2#22623813direct (N × H)

Maximal subgroups

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

subgroupindex
#226238132
C2×#179893142
C2×#179893042
C2×#179892732
C2×#179892692
C2×#179892002
C2×#179891992
C2×#179891982
C2×#179891602
C2×#179891432
C2×#179891412
C2×#179891392
C2×C4⋊Q8×D732
C2×#179890632
C2×#179890552
C2×#541×C732
C2×#350973