Finite Group Databasebeta

← C2×#22624013 #33994188

Subgroups — C2×#22624013 #33994188

Order 18688.

7758 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624013C2132yesmaximal, direct product factor
2C2×#17989319C212yesmaximal, complemented
3C2×Q8×Dic146C211yesmaximal, characteristic, complemented
4C2×#17989297C211yesmaximal, characteristic, complemented
5C2×#17989296C212yesmaximal, complemented
6C2×#17989257C211yesmaximal, characteristic, complemented
7C2×#17989245C212yesmaximal, complemented
8C2×#17989242C212yesmaximal, complemented
9C2×#17989235C214yesmaximal, complemented
10C2×#17989206C212yesmaximal, complemented
11C2×#17989205C214yesmaximal, complemented
12C2×#17989135C211yesmaximal, characteristic, complemented
13C2×#17989134C212yesmaximal, complemented
14C2×#17989124C211yesmaximal, characteristic, complemented
15C2×#17989116C212yesmaximal, complemented
16C2×#17989066C212yesmaximal, complemented
17C2×C4×Q8×D73C211yesmaximal, characteristic, complemented
18C2×#559×C73C211yesmaximal, characteristic, complemented
19C22×#11924028C2214yes—
20C22×#11924027C2212yes—
21C22×#11924027C2212yes—
22C22×Q8×D73C2211yescharacteristic
23#17989319C22132yescomplemented
24Q8×Dic146C22116yescomplemented
25#17989297C22116yescomplemented
26#17989296C22132yescomplemented
27#17989257C22116yescomplemented
28#17989245C22132yescomplemented
29#17989242C22132yescomplemented
30#17989235C22164yescomplemented
31#17989206C22132yescomplemented
32#17989205C22164yescomplemented
33#17989135C22116yescomplemented
34#17989134C22132yescomplemented
35C2×#14556591C2212yes—
36C2×#14556591C2211yescharacteristic
37C2×#14556590C2214yes—
38C2×#14556590C2212yes—
39C2×#14556587C2212yes—
40#17989124C22116yescomplemented
41#17989116C22132yescomplemented
42C2×#14556586C2212yes—
43C2×#14556584C2214yes—
44C2×#14556583C2212yes—
45C2×#14556582C2211yescharacteristic
46C2×#14556580C2211yescharacteristic
47C2×#14556578C2212yes—
48C2×#14556577C2214yes—
49C2×#14556577C2214yes—
50C2×#14556576C2212yes—
51C2×#14556575C2214yes—
52C2×#14556573C2214yes—
53C2×#14556573C2214yes—
54C2×#14556570C2214yes—
55C2×#14556569C2214yes—
56C2×#14556568C2214yes—
57C2×#14556568C2214yes—
58C2×#14556567C2212yes—
59C2×#14556567C2211yescharacteristic
60C2×#14556566C2211yescharacteristic
61C2×#14556564C2214yes—
62C2×#14556563C2214yes—
63C2×#14556562C2212yes—
64C2×#14556562C2212yes—
65C2×#14556562C2212yes—
66#17989066C22132yescomplemented
67C2×Q8×Dic73C2212yes—
68C2×Q8×Dic73C2211yescharacteristic
69C2×C4×Dic146C2211yescharacteristic
70C2×C4×Dic146C2212yes—
71C2×C4×Dic146C2212yes—
72C2×#14556556C2212yes—
73C2×#14556556C2211yescharacteristic
74C4×Q8×D73C22116yescomplemented
75C2×C4×D292C2212yes—
76C2×C4×D292C2212yes—
77C2×C4×D292C2211yescharacteristic
78C2×D4×Dic73C2212yes—
79C2×D4×Dic73C2212yes—
80C2×D4×Dic73C2212yes—
81C2×C4×C22⋊D73C2214yes—
82C2×#14556551C2214yes—
83C2×#14556551C2214yes—
84C2×#14556548C2212yes—
85C2×#14556547C2214yes—
86C22×#11924007C2214yes—
87C2×C4⋊C4×D73C2212yes—
88C2×C4⋊C4×D73C2211yescharacteristic
89C2×C4⋊C4×D73C2212yes—
90C2×C42×D73C2212yes—
91C2×C42×D73C2211yescharacteristic
92#559×C73C22116yescomplemented
93C2×#127×C73C2211yescharacteristic
94C2×#124×C73C2212yes—
95C2×#124×C73C2212yes—
96C2×#123×C73C2214yes—
97C2×C4×Q8×C73C2211yescharacteristic
98C2×C4×Q8×C73C2211yescharacteristic
99C2×C4×D4×C73C2212yes—
100C2×C4×D4×C73C2212yes—
101C2×#11924028—416no—
102C2×#11924028C23132yes—
103C2×#11924027—216no—
104C2×#11924027—48no—
105C2×#11924027C23116yes—
106C2×#11924027C23116yes—
107C22×Dic146C2312yes—
108C22×Dic146C2312yes—
109C22×Dic146C2314yes—
110C22×Dic146C2311yescharacteristic
111C2×Q8×D73—28no—
112C2×Q8×D73C2318yes—
113C22×D292C2311yescharacteristic
114C22×D292C2312yes—
115C22×C22⋊D73C2314yes—
116C22×C22⋊D73C2314yes—
117C22×C22⋊D73C2314yes—
118C23×Dic73C2314yes—
119C23×Dic73C2314yes—
120C22×C4×D73C2312yes—
121C22×C4×D73C2311yescharacteristic
122C22×C4×D73C2311yescharacteristic
123C22×C4×D73C2312yes—
124C22×C4×D73C2312yes—
125C22×C4×D73C2311yescharacteristic
126C22×C4×D73C2314yes—
127#14556591C2318yes—
128#14556591C23116yes—
129#14556590C23116yes—
130#14556590C23132yes—
131#14556587C23116yes—
132#14556586C23116yes—
133#14556584C23132yes—
134#14556583C23116yes—
135#14556582C2318yes—
136#14556580C2318yes—
137#14556578C23116yes—
138#14556577C23132yes—
139#14556577C23132yes—
140#14556576C23116yes—
141#14556575C23132yes—
142#14556573C23132yes—
143#14556573C23132yes—
144#14556570C23132yes—
145#14556569C23132yes—
146#14556568C23132yes—
147#14556568C23132yes—
148#14556567C2318yes—
149#14556567C23116yes—
150#14556566C2318yes—
151#14556564C23132yes—
152#14556563C23132yes—
153#14556562C23116yes—
154#14556562C23116yes—
155#14556562C23116yes—
156Q8×Dic73C2318yes—
157Q8×Dic73C23116yes—
158C4×Dic146C23116yes—
159C4×Dic146C2318yes—
160C4×Dic146C23116yes—
161#14556556C23116yes—
162#14556556C2318yes—
163C4×D292C23116yes—
164C4×D292C2318yes—
165C4×D292C23116yes—
166D4×Dic73C23116yes—
167D4×Dic73C23116yes—
168D4×Dic73C23116yes—
169C4×C22⋊D73C23132yes—
170#14556551C23132yes—
171#14556551C23132yes—
172#14556548C23116yes—
173#14556547C23132yes—
174C2×C4⋊Dic73C2312yes—
175C2×C4⋊Dic73C2314yes—
176C2×C4⋊Dic73C2312yes—
177C2×C4⋊Dic73C2311yescharacteristic
178C2×C4⋊Dic73C2312yes—
179C2×C4⋊Dic73C2311yescharacteristic
180C2×C4⋊Dic73C2312yes—
181C2×#11924007C2312yes—
182C2×#11924007C2314yes—
183C2×#11924007C23132yes—
184C2×#11924007C2312yes—
185C2×#11924007C2314yes—
186C2×#11924007C2312yes—
187C2×#11924007C2312yes—
188C2×#11924007C2312yes—
189C2×#11924007C2314yes—
190C4⋊C4×D73C23116yes—
191C4⋊C4×D73C2318yes—
192C4⋊C4×D73C23116yes—
193C2×C22⋊Dic73C2314yes—
194C2×C22⋊Dic73C2314yes—
195C2×C22⋊Dic73C2314yes—
196C2×#11924005C2312yes—
197C2×#11924005C2312yes—
198C2×#11924005C2312yes—
199C2×#11924005C2312yes—
200C2×#11924005C2314yes—
201C2×#11924005C2312yes—
202C2×C4×Dic73C2312yes—
203C2×C4×Dic73C2314yes—
204C2×C4×Dic73C2312yes—
205C2×C4×Dic73C2311yescharacteristic
206C2×C4×Dic73C2311yescharacteristic
207C2×C4×Dic73C2311yescharacteristic
208C2×C4×Dic73C2312yes—
209C42×D73C2318yes—
210C42×D73C23116yes—
211C22×Q8×C73C2311yescharacteristic
212C22×Q8×C73C2311yescharacteristic
213C22×D4×C73C2312yes—
214C22×D4×C73C2312yes—
215C22×D4×C73C2312yes—
216C23×C4×C73C2314yes—
217#127×C73C2318yes—
218#124×C73C23116yes—
219#124×C73C23116yes—
220#123×C73C23132yes—
221C4×Q8×C73C2318yes—
222C4×Q8×C73C2318yes—
223C4×D4×C73C23116yes—
224C4×D4×C73C23116yes—
225C2×C4⋊C4×C73C2311yescharacteristic
226C2×C4⋊C4×C73C2312yes—
227C2×C4⋊C4×C73C2311yescharacteristic
228C2×C4⋊C4×C73C2312yes—
229C2×C22⋊C4×C73C2314yes—
230C2×C22⋊C4×C73C2314yes—
231C2×C22⋊C4×C73C2314yes—
232C2×C42×C73C2312yes—
233C2×C42×C73C2311yescharacteristic
234C2×C42×C73C2312yes—
235C23×D73C2412yes—
236C23×D73C2411yescharacteristic
237#11924028—464no—
238#11924027—264no—
239#11924027—432no—
240C2×Dic146—28no—
241C2×Dic146—44no—
242C2×Dic146—48no—
243C2×Dic146#4118yescomplemented
244C2×Dic146C2418yes—
245C2×Dic146C24116yes—
246C2×Dic146C2418yes—
247C2×Dic146C2414yes—
248Q8×D73—232no—
249C2×D292—28no—
250C2×D292—24no—
251C2×D292C2414yes—
252C2×D292C2418yes—
253C2×C22⋊D73—216no—
254C2×C22⋊D73—216no—
255C2×C22⋊D73—48no—
256C2×C22⋊D73C24116yes—
257C2×C22⋊D73C24116yes—
258C2×C22⋊D73C24116yes—
259C22×Dic73—216no—
260C22×Dic73—48no—
261C22×Dic73C2411yescharacteristic
262C22×Dic73C2411yescharacteristic
263C22×Dic73C2411yescharacteristic
264C22×Dic73C2412yes—
265C22×Dic73C2414yes—
266C22×Dic73C2412yes—
267C22×Dic73C24116yes—
268C22×Dic73C24116yes—
269C22×Dic73C2412yes—
270C2×C4×D73—24no—
271C2×C4×D73—28no—
272C2×C4×D73—24no—
273C2×C4×D73—28no—
274C2×C4×D73—24no—
275C2×C4×D73—28no—
276C2×C4×D73—48no—
277C2×C4×D73C2414yes—
278C2×C4×D73C2418yes—
279C2×C4×D73C2414yes—
280C2×C4×D73C2418yes—
281C2×C4×D73C2414yes—
282C2×C4×D73C2418yes—
283C2×C4×D73C24116yes—
284C4⋊Dic73C2418yes—
285C4⋊Dic73C2414yes—
286C4⋊Dic73C2418yes—
287C4⋊Dic73C2414yes—
288C4⋊Dic73C2418yes—
289C4⋊Dic73C2418yes—
290C4⋊Dic73C24116yes—
291#11924007C2418yes—
292#11924007C24116yes—
293#11924007C2418yes—
294#11924007C2418yes—
295#11924007C2418yes—
296#11924007C24116yes—
297#11924007C2418yes—
298#11924007C24116yes—
299C22⋊Dic73C24116yes—
300C22⋊Dic73C24116yes—
301C22⋊Dic73C24116yes—
302#11924005C2418yes—
303#11924005C2418yes—
304#11924005C2418yes—
305#11924005C2418yes—
306#11924005C24116yes—
307#11924005C2418yes—
308C4×Dic73C2418yes—
309C4×Dic73C2414yes—
310C4×Dic73C2414yes—
311C4×Dic73C2418yes—
312C4×Dic73C2414yes—
313C4×Dic73C2418yes—
314C4×Dic73C24116yes—
315C24×C73C2414yes—
316C2×Q8×C73—24no—
317C2×Q8×C73—24no—
318C2×Q8×C73C2414yes—
319C2×Q8×C73C2414yes—
320C2×D4×C73—28no—
321C2×D4×C73—28no—
322C2×D4×C73—44no—
323C2×D4×C73C2418yes—
324C2×D4×C73C2418yes—
325C2×D4×C73C2418yes—
326C22×C4×C73—48no—
327C22×C4×C73C2412yes—
328C22×C4×C73C2412yes—
329C22×C4×C73C2412yes—
330C22×C4×C73C2412yes—
331C22×C4×C73C2411yescharacteristic
332C22×C4×C73C24116yes—
333C22×C4×C73C2411yescharacteristic
334C22×C4×C73C2411yescharacteristic
335C4⋊C4×C73C2414yes—
336C4⋊C4×C73C2414yes—
337C4⋊C4×C73C2418yes—
338C4⋊C4×C73C2418yes—
339C22⋊C4×C73C24116yes—
340C22⋊C4×C73C24116yes—
341C22⋊C4×C73C24116yes—
342C42×C73C2418yes—
343C42×C73C2418yes—
344C42×C73C2414yes—
345C23×C73—28no—
346C23×C73—28no—
347C23×C73—28no—
348C23×C73C2518yes—
349C23×C73C2511yescharacteristic
350C22×D73—22no—
351C22×D73—22no—
352C22×D73—24no—
353C22×D73—24no—
354C22×D73—24no—
355C22×D73H(5,𝔽2)14yes—
356C22×D73C2514yes—
357C22×D73C2512yes—
358Q8×C73—28no—
359Q8×C73—28no—
360D4×C73—216no—
361D4×C73—216no—
362D4×C73—48no—
363C2×C4×C73—24no—
364C2×C4×C73—24no—
365C2×C4×C73—24no—
366C2×C4×C73—22no—
367C2×C4×C73—24no—
368C2×C4×C73—416no—
369C2×C4×C73C2×#4114yes—
370C2×C4×C732−1+414yes—
371C2×C4×C73C2514yes—
372C2×C4×C73C2514yes—
373C2×C4×C73C2514yes—
374C2×C4×C73C2514yes—
375C2×C4×C73C2512yes—
376C2×C4×C73C2512yes—
377C2×C4×C73C2512yes—
378C22⋊D73—232no—
379C22⋊D73—232no—
380C22⋊D73—416no—
381C2×Dic73—24no—
382C2×Dic73—22no—
383C2×Dic73—22no—
384C2×Dic73—24no—
385C2×Dic73—28no—
386C2×Dic73—22no—
387C2×Dic73—232no—
388C2×Dic73—416no—
389C2×Dic73C2×#4118yes—
390C2×Dic73C2512yes—
391C2×Dic73C2512yes—
392C2×Dic73C2512yes—
393C2×Dic73C2514yes—
394C2×Dic73C2518yes—
395C2×Dic73C2514yes—
396C2×Dic73C2514yes—
397D292—216no—
398D292—28no—
399C4×D73—28no—
400C4×D73—216no—
401C4×D73—28no—
402C4×D73—216no—
403C4×D73—28no—
404C4×D73—216no—
405C4×D73—416no—
406Dic146—216no—
407Dic146—48no—
408Dic146—416no—
409Dic146C2×#41116yescomplemented
410C22×C73—28no—
411C22×C73—28no—
412C22×C73—28no—
413C22×C73—416no—
414C22×C73C22×#4112yes—
415C22×C73C2×H(5,𝔽2)12yes—
416C22×C73C2×2−1+412yes—
417C22×C73C2611yescharacteristic
418C2×D73—22no—
419C2×D73—22no—
420C2×D73—28no—
421C2×D73—24no—
422C2×D73—24no—
423C2×D73—24no—
424C2×D73—48no—
425C2×D73C2×H(5,𝔽2)14yes—
426C4×C73—24no—
427C4×C73—22no—
428C4×C73—24no—
429C4×C73—24no—
430C4×C73—24no—
431C4×C73C22×#4114yes—
432C4×C73C2×2−1+414yes—
433Dic73—22no—
434Dic73—24no—
435Dic73—24no—
436Dic73—28no—
437Dic73—22no—
438Dic73—22no—
439Dic73C22×#4118yes—
440C2×#3522—731nomaximal, Sylow
441C2×C73—48no—
442C2×C73#352214yescomplemented
443C2×C73C23×#4111yescharacteristic
444C2×C73C22×H(5,𝔽2)11yescharacteristic
445C2×C73C22×2−1+411yescharacteristic
446D73—24no—
447D73—44no—
448#3522—7332no—
449C2×#559—732no—
450C2×#559D7311yescharacteristic, complemented
451C2×Q82—731no—
452C2×#554—731no—
453C2×#554—732no—
454C2×#550—731no—
455C2×#548—732no—
456C2×#547—734no—
457C2×#547—732no—
458C2×#542—732no—
459C2×#542—734no—
460C2×#532—731no—
461C2×#532—732no—
462C2×#529—732no—
463C2×#529—731no—
464C2×#520—732no—
465C22×C4×Q8—731no—
466C73C2×#352211yescharacteristic, complemented, Sylow
467C22×#41—732no—
468C22×#41—732no—
469C22×#41—734no—
470C23×Q8—731no—
471#559—7332no—
472#559C2×D73116yescomplemented
473Q82—7316no—
474#554—7316no—
475#554—7332no—
476#550—7316no—
477#548—7332no—
478#547—7364no—
479#547—7332no—
480#542—7332no—
481#542—7364no—
482#532—7316no—
483#532—7332no—
484C2×C4⋊Q8—732no—
485C2×C4⋊Q8—734no—
486C2×C4⋊Q8—731no—
487C2×C4⋊Q8—732no—
488C2×#127—732no—
489C2×#127C2×D7311yescharacteristic
490#529—7332no—
491#529—7316no—
492C2×#126—732no—
493C2×#126—734no—
494C2×#125—731no—
495C2×#125—732no—
496C2×#124—731no—
497C2×#124—732no—
498C2×#124—734no—
499C2×#124—734no—
500C2×#124C2×D7312yes—
501C2×#124C2×D7312yes—
502C2×#123—732no—
503C2×#123—734no—
504C2×#123—734no—
505C2×#123—734no—
506C2×#123C2×D7314yes—
507C2×C22⋊Q8—731no—
508C2×C22⋊Q8—732no—
509C2×C22⋊Q8—734no—
510C2×C22⋊Q8—734no—
511C2×C22⋊Q8—734no—
512C2×C22⋊Q8—734no—
513C2×#121—732no—
514C2×#121—732no—
515C2×#121—732no—
516C2×#121—734no—
517C2×#121—731no—
518C2×#121—734no—
519#520—7332no—
520C2×C4×Q8—731no—
521C2×C4×Q8—732no—
522C2×C4×Q8—7316no—
523C2×C4×Q8—731no—
524C2×C4×Q8—732no—
525C2×C4×Q8—731no—
526C2×C4×Q8—732no—
527C2×C4×Q8—732no—
528C2×C4×Q8C2×D7311yescharacteristic
529C2×C4×Q8C2×D7311yescharacteristic
530C2×C4×D4—732no—
531C2×C4×D4—732no—
532C2×C4×D4—732no—
533C2×C4×D4—734no—
534C2×C4×D4—734no—
535C2×C4×D4—734no—
536C2×C4×D4—732no—
537C2×C4×D4—731no—
538C2×C4×D4—732no—
539C2×C4×D4C2×D7312yes—
540C2×C4×D4C2×D7312yes—
541C2×#117—734no—
542C2×#117—732no—
543C22×C4⋊C4—734no—
544C22×C4⋊C4—732no—
545C22×C4⋊C4—731no—
546C22×C4⋊C4—732no—
547C22×C42—731no—
548C22×C42—732no—
549C2×#41—29216no—
550C2×#41—2928no—
551C2×#41—7316no—
552C2×#41—7316no—
553C2×#41—7332no—
554C2×#41—14616no—
555C22×Q8—738no—
556C22×Q8—734no—
557C22×Q8—732no—
558C22×Q8—731no—
559C22×Q8—732no—
560C22×Q8—1468no—
561C22×Q8C22×D7311yescharacteristic
562C22×Q8C22×D7311yescharacteristic
563C22×D4—734no—
564C22×D4—734no—
565C22×D4—734no—
566C22×D4—731no—
567C22×D4—732no—
568C22×D4C22×D7312yes—
569C22×D4C22×D7312yes—
570C22×D4C22×D7312yes—
571C23×C4—734no—
572C23×C4—734no—
573C23×C4—734no—
574C23×C4—731no—
575C23×C4—732no—
576C23×C4—732no—
577C23×C4—732no—
578C23×C4—731no—
579C23×C4—731no—
580C23×C4C22×D7314yes—
581C4⋊Q8—7316no—
582C4⋊Q8—7332no—
583C4⋊Q8—738no—
584C4⋊Q8—7316no—
585#127—7316no—
586#127C22×D7318yes—
587#126—7316no—
588#126—7332no—
589#125—738no—
590#125—7316no—
591#124—738no—
592#124—7316no—
593#124—7332no—
594#124—7332no—
595#124C22×D73116yes—
596#124C22×D73116yes—
597#123—7316no—
598#123—7332no—
599#123—7332no—
600#123—7332no—
601#123C22×D73132yes—
602C22⋊Q8—738no—
603C22⋊Q8—7316no—
604C22⋊Q8—7332no—
605C22⋊Q8—7332no—
606C22⋊Q8—7332no—
607C22⋊Q8—7332no—
608#121—7316no—
609#121—7316no—
610#121—7316no—
611#121—7332no—
612#121—738no—
613#121—7332no—
614C4×Q8—738no—
615C4×Q8—7316no—
616C4×Q8—738no—
617C4×Q8—7316no—
618C4×Q8—738no—
619C4×Q8—7316no—
620C4×Q8—7316no—
621C4×Q8C22×D7318yes—
622C4×Q8C22×D7318yes—
623C4×D4—7316no—
624C4×D4—7316no—
625C4×D4—7316no—
626C4×D4—7332no—
627C4×D4—7332no—
628C4×D4—7332no—
629C4×D4—7316no—
630C4×D4—738no—
631C4×D4—7316no—
632C4×D4C22×D73116yes—
633C4×D4C22×D73116yes—
634#117—7332no—
635#117—7316no—
636C2×C4⋊C4—732no—
637C2×C4⋊C4—732no—
638C2×C4⋊C4—734no—
639C2×C4⋊C4—734no—
640C2×C4⋊C4—732no—
641C2×C4⋊C4—732no—
642C2×C4⋊C4—731no—
643C2×C4⋊C4—732no—
644C2×C4⋊C4—732no—
645C2×C4⋊C4—7332no—
646C2×C4⋊C4—732no—
647C2×C4⋊C4—731no—
648C2×C4⋊C4—732no—
649C2×C4⋊C4—734no—
650C2×C4⋊C4—732no—
651C2×C4⋊C4—734no—
652C2×C4⋊C4—7316no—
653C2×C4⋊C4—738no—
654C2×C4⋊C4—7316no—
655C2×C4⋊C4C22×D7311yescharacteristic
656C2×C4⋊C4C22×D7312yes—
657C2×C4⋊C4C22×D7311yescharacteristic
658C2×C4⋊C4C22×D7312yes—
659C2×C22⋊C4—734no—
660C2×C22⋊C4—734no—
661C2×C22⋊C4—734no—
662C2×C22⋊C4—732no—
663C2×C22⋊C4—732no—
664C2×C22⋊C4—732no—
665C2×C22⋊C4—732no—
666C2×C22⋊C4—734no—
667C2×C22⋊C4—732no—
668C2×C22⋊C4C22×D7314yes—
669C2×C22⋊C4C22×D7314yes—
670C2×C22⋊C4C22×D7314yes—
671C2×C42—732no—
672C2×C42—731no—
673C2×C42—734no—
674C2×C42—731no—
675C2×C42—732no—
676C2×C42—731no—
677C2×C42—732no—
678C2×C42—738no—
679C2×C42—7316no—
680C2×C42C22×D7312yes—
681C2×C42C22×D7312yes—
682C2×C42C22×D7311yescharacteristic
683C24—731no—
684C24—732no—
685C24C23×D7314yes—
686#41—29264no—
687#41—29232no—
688#41—14664no—
689C2×Q8—24no—
690C2×Q8—24no—
691C2×Q8—2928no—
692C2×Q8—2924no—
693C2×Q8—738no—
694C2×Q8—7316no—
695C2×Q8—738no—
696C2×Q8—734no—
697C2×Q8—738no—
698C2×Q8—1468no—
699C2×Q8—14632no—
700C2×Q8C23×D7314yes—
701C2×Q8C23×D7314yes—
702C2×D4—28no—
703C2×D4—28no—
704C2×D4—44no—
705C2×D4—2928no—
706C2×D4—7316no—
707C2×D4—7316no—
708C2×D4—7316no—
709C2×D4—734no—
710C2×D4—738no—
711C2×D4—1468no—
712C2×D4—14616no—
713C2×D4—14616no—
714C2×D4—1464no—
715C2×D4C23×D7318yes—
716C2×D4C23×D7318yes—
717C2×D4C23×D7318yes—
718C22×C4—48no—
719C22×C4—2928no—
720C22×C4—2928no—
721C22×C4—7316no—
722C22×C4—7316no—
723C22×C4—732no—
724C22×C4—7316no—
725C22×C4—731no—
726C22×C4—731no—
727C22×C4—731no—
728C22×C4—732no—
729C22×C4—734no—
730C22×C4—732no—
731C22×C4—734no—
732C22×C4—734no—
733C22×C4—738no—
734C22×C4—738no—
735C22×C4—734no—
736C22×C4—738no—
737C22×C4—1468no—
738C22×C4—1468no—
739C22×C4—1464no—
740C22×C4—14616no—
741C22×C4—1464no—
742C22×C4—1468no—
743C22×C4—1464no—
744C22×C4C23×D7312yes—
745C22×C4C23×D7312yes—
746C22×C4C23×D7311yescharacteristic
747C22×C4C23×D7312yes—
748C22×C4C23×D7312yes—
749C22×C4C23×D73116yes—
750C22×C4C23×D7311yescharacteristic
751C22×C4C23×D7311yescharacteristic
752C4⋊C4—738no—
753C4⋊C4—738no—
754C4⋊C4—7316no—
755C4⋊C4—7316no—
756C4⋊C4—738no—
757C4⋊C4—738no—
758C4⋊C4—738no—
759C4⋊C4—7316no—
760C4⋊C4—738no—
761C4⋊C4—734no—
762C4⋊C4—738no—
763C4⋊C4—734no—
764C4⋊C4—738no—
765C4⋊C4—738no—
766C4⋊C4—7316no—
767C4⋊C4C23×D7314yes—
768C4⋊C4C23×D7318yes—
769C4⋊C4C23×D7314yes—
770C4⋊C4C23×D7318yes—
771C22⋊C4—7316no—
772C22⋊C4—7316no—
773C22⋊C4—7316no—
774C22⋊C4—738no—
775C22⋊C4—738no—
776C22⋊C4—738no—
777C22⋊C4—738no—
778C22⋊C4—7316no—
779C22⋊C4—738no—
780C22⋊C4C23×D73116yes—
781C22⋊C4C23×D73116yes—
782C22⋊C4C23×D73116yes—
783C42—738no—
784C42—734no—
785C42—734no—
786C42—738no—
787C42—734no—
788C42—738no—
789C42—7316no—
790C42C23×D7318yes—
791C42C23×D7314yes—
792C42C23×D7318yes—
793C23—28no—
794C23—28no—
795C23—28no—
796C23—734no—
797C23—732no—
798C23—734no—
799C23—1464no—
800C23—1464no—
801C23—1464no—
802C23—1462no—
803C23—1462no—
804C23C24×D7318yes—
805C23C24×D7311yescharacteristic
806Q8—28no—
807Q8—28no—
808Q8—29216no—
809Q8—2928no—
810Q8—7316no—
811Q8—14616no—
812D4—216no—
813D4—216no—
814D4—48no—
815D4—29216no—
816D4—14616no—
817D4—14632no—
818D4—14632no—
819D4—1468no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—22no—
824C2×C4—24no—
825C2×C4—416no—
826C2×C4—29216no—
827C2×C4—29216no—
828C2×C4—738no—
829C2×C4—734no—
830C2×C4—732no—
831C2×C4—732no—
832C2×C4—732no—
833C2×C4—734no—
834C2×C4—738no—
835C2×C4—734no—
836C2×C4—14616no—
837C2×C4—14616no—
838C2×C4—1468no—
839C2×C4—14632no—
840C2×C4—1464no—
841C2×C4—1462no—
842C2×C4—1462no—
843C2×C4—1468no—
844C2×C4—1464no—
845C2×C4—1462no—
846C2×C4—1468no—
847C2×C4—14616no—
848C2×C4—1468no—
849C2×C4#41×D7314yes—
850C2×C4#1455663814yes—
851C2×C4C24×D7314yes—
852C2×C4C24×D7314yes—
853C2×C4C24×D7312yes—
854C2×C4C24×D7314yes—
855C2×C4C24×D7314yes—
856C2×C4C24×D7312yes—
857C2×C4C24×D7312yes—
858C22—28no—
859C22—28no—
860C22—28no—
861C22—416no—
862C22—2928no—
863C22—734no—
864C22—1464no—
865C22—1464no—
866C22—1464no—
867C22—1468no—
868C22—1462no—
869C22—1462no—
870C22C2×#41×D7312yes—
871C22H(5,𝔽2)×D7312yes—
872C22C2×#1455663812yes—
873C22C25×D7311yescharacteristic
874C4—24no—
875C4—24no—
876C4—24no—
877C4—22no—
878C4—24no—
879C4—738no—
880C4—1464no—
881C4—1462no—
882C4—1462no—
883C4—1468no—
884C4—1464no—
885C4—1462no—
886C4C2×#41×D7314yes—
887C4C2×#1455663814yes—
888C2—48no—
889C2—2924no—
890C2—1464no—
891C2#2262401314yesdirect product factor
892C2C22×#41×D7311yescharacteristic
893C2C2×H(5,𝔽2)×D7311yescharacteristic
894C2C22×#1455663811yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#559×C73C2
socleC23×C73C25
hypercenterC2×#559D73
hypocenterC73C2×#3522
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. #22624013C2direct (N × H)
2. C2×#17989319C2semidirect
3. C2×Q8×Dic146C2semidirect
4. C2×#17989297C2semidirect
5. C2×#17989296C2semidirect
6. C2×#17989257C2semidirect
7. C2×#17989245C2semidirect
8. C2×#17989242C2semidirect
9. C2×#17989235C2semidirect
10. C2×#17989206C2semidirect
11. C2×#17989205C2semidirect
12. C2×#17989135C2semidirect
13. C2×#17989134C2semidirect
14. C2×#17989124C2semidirect
15. C2×#17989116C2semidirect
16. C2×#17989066C2semidirect
17. C2×C4×Q8×D73C2semidirect
18. C2×#559×C73C2semidirect
23. #17989319C22semidirect
24. Q8×Dic146C22semidirect
25. #17989297C22semidirect
26. #17989296C22semidirect
27. #17989257C22semidirect
28. #17989245C22semidirect
29. #17989242C22semidirect
30. #17989235C22semidirect
31. #17989206C22semidirect
32. #17989205C22semidirect
33. #17989135C22semidirect
34. #17989134C22semidirect
40. #17989124C22semidirect
41. #17989116C22semidirect
66. #17989066C22semidirect
74. C4×Q8×D73C22semidirect
92. #559×C73C22semidirect
243. C2×Dic146#41semidirect
409. Dic146C2×#41semidirect
442. C2×C73#3522semidirect
450. C2×#559D73semidirect
466. C73C2×#3522semidirect
472. #559C2×D73semidirect
891. C2#22624013direct (N × H)

Maximal subgroups

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

subgroupindex
#226240132
C2×#179893192
C2×Q8×Dic1462
C2×#179892972
C2×#179892962
C2×#179892572
C2×#179892452
C2×#179892422
C2×#179892352
C2×#179892062
C2×#179892052
C2×#179891352
C2×#179891342
C2×#179891242
C2×#179891162
C2×#179890662
C2×C4×Q8×D732
C2×#559×C732
C2×#352273