Finite Group Databasebeta

← C2×#22602734 #32905242

Subgroups — C2×#22602734 #32905242

Order 18176.

7810 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602734C2132yesmaximal, direct product factor
2C2×#17986746C214yesmaximal, complemented
3C2×#17986708C212yesmaximal, complemented
4C2×#17986705C212yesmaximal, complemented
5C2×#17986670C212yesmaximal, complemented
6C2×#17986669C212yesmaximal, complemented
7C2×#17986647C214yesmaximal, complemented
8C2×#17986604C211yesmaximal, characteristic, complemented
9C2×#17986602C212yesmaximal, complemented
10C2×#17986578C214yesmaximal, complemented
11C2×#17986576C214yesmaximal, complemented
12C2×#17986552C211yesmaximal, characteristic, complemented
13C2×#17986544C212yesmaximal, complemented
14C2×#540×C71C211yesmaximal, characteristic, complemented
15C22×#11765865C2214yes—
16C22×#11765864C2214yes—
17C22×#11765864C2214yes—
18#17986746C22164yescomplemented
19#17986708C22132yescomplemented
20#17986705C22132yescomplemented
21#17986670C22132yescomplemented
22#17986669C22132yescomplemented
23#17986647C22164yescomplemented
24#17986604C22116yescomplemented
25#17986602C22132yescomplemented
26#17986578C22164yescomplemented
27#17986576C22164yescomplemented
28#17986552C22116yescomplemented
29#17986544C22132yescomplemented
30C2×#14556127C2212yes—
31C2×#14556127C2212yes—
32C2×#14556125C2211yescharacteristic
33C2×#14556124C2212yes—
34C2×#14556124C2212yes—
35C2×#14556120C2211yescharacteristic
36C2×#14556119C2212yes—
37C2×#14556119C2212yes—
38C2×#14556114C2214yes—
39C2×#14556113C2214yes—
40C2×#14556112C2214yes—
41C2×#14556110C2214yes—
42C2×#14556108C2214yes—
43C2×#14556107C2214yes—
44C2×#14556106C2214yes—
45C2×#14556106C2214yes—
46C2×#14556105C2214yes—
47C2×#14556105C2214yes—
48C2×#14556105C2212yes—
49C2×#14556105C2212yes—
50C2×#14556102C2214yes—
51C2×#14556102C2212yes—
52C2×#14556101C2214yes—
53C2×#14556101C2214yes—
54C2×#14556101C2214yes—
55C2×#14556100C2214yes—
56C2×#14556100C2214yes—
57C2×#14556100C2214yes—
58C2×#14556100C2214yes—
59C2×#14556099C2214yes—
60C2×#14556099C2214yes—
61C2×C4×Dic142C2212yes—
62C2×C4×Dic142C2212yes—
63C2×C4×D284C2212yes—
64C2×D4×Dic71C2212yes—
65C2×D4×Dic71C2212yes—
66C2×#14556090C2212yes—
67C2×#14556090C2212yes—
68C2×(C22⋊D71)⋊C4C2214yes—
69C2×#14556087C2211yescharacteristic
70C22×Dic71⋊C4C2214yes—
71C2×C4⋊C4×D71C2214yes—
72C22×C4×Dic71C2211yescharacteristic
73#540×C71C22116yescomplemented
74C2×#127×C71C2211yescharacteristic
75C2×#125×C71C2211yescharacteristic
76C2×#123×C71C2214yes—
77C2×#121×C71C2212yes—
78C2×#121×C71C2214yes—
79C2×C4×D4×C71C2212yes—
80C2×#117×C71C2211yescharacteristic
81C2×#11765865—416no—
82C2×#11765865C23132yes—
83C2×#11765864—416no—
84C2×#11765864—416no—
85C2×#11765864C23132yes—
86C2×#11765864C23132yes—
87C22×Dic142C2312yes—
88C22×Dic142C2312yes—
89C22×Dic142C2314yes—
90C22×D284C2312yes—
91C22×D284C2314yes—
92C22×C22⋊D71C2314yes—
93C22×C22⋊D71C2314yes—
94C22×C22⋊D71C2314yes—
95C22×C22⋊D71C2314yes—
96C22×C22⋊D71C2314yes—
97C23×Dic71C2312yes—
98C23×Dic71C2314yes—
99C23×Dic71C2314yes—
100C22×C4×D71C2314yes—
101C22×C4×D71C2314yes—
102C22×C4×D71C2314yes—
103#14556127C23116yes—
104#14556127C23116yes—
105#14556125C2318yes—
106#14556124C23116yes—
107#14556124C23116yes—
108#14556120C2318yes—
109#14556119C23116yes—
110#14556119C23116yes—
111#14556114C23132yes—
112#14556113C23132yes—
113#14556112C23132yes—
114#14556110C23132yes—
115#14556108C23132yes—
116#14556107C23132yes—
117#14556106C23132yes—
118#14556106C23132yes—
119#14556105C23116yes—
120#14556105C23132yes—
121#14556105C23116yes—
122#14556105C23132yes—
123#14556102C23132yes—
124#14556102C23116yes—
125#14556101C23132yes—
126#14556101C23132yes—
127#14556101C23132yes—
128#14556100C23132yes—
129#14556100C23132yes—
130#14556100C23132yes—
131#14556100C23132yes—
132#14556099C23132yes—
133#14556099C23132yes—
134C4×Dic142C23116yes—
135C4×Dic142C23116yes—
136C4×D284C23116yes—
137D4×Dic71C23116yes—
138D4×Dic71C23116yes—
139#14556090C23116yes—
140#14556090C23116yes—
141(C22⋊D71)⋊C4C23132yes—
142#14556087C2318yes—
143C2×C4⋊Dic71C2314yes—
144C2×C4⋊Dic71C2312yes—
145C2×C4⋊Dic71C2312yes—
146C2×C4⋊Dic71C2312yes—
147C2×C4⋊Dic71C2312yes—
148C2×Dic71⋊C4C23132yes—
149C2×Dic71⋊C4C2312yes—
150C2×Dic71⋊C4C2314yes—
151C2×Dic71⋊C4C2312yes—
152C2×Dic71⋊C4C2314yes—
153C2×Dic71⋊C4C2314yes—
154C2×Dic71⋊C4C2312yes—
155C2×Dic71⋊C4C2312yes—
156C4⋊C4×D71C23132yes—
157C2×C22⋊Dic71C2311yescharacteristic
158C2×C22⋊Dic71C2311yescharacteristic
159C2×C22⋊Dic71C2314yes—
160C2×C22⋊Dic71C2314yes—
161C2×(C2×D71)⋊C4C2314yes—
162C2×(C2×D71)⋊C4C2314yes—
163C2×(C2×D71)⋊C4C2314yes—
164C2×(C2×D71)⋊C4C2314yes—
165C2×C4×Dic71C2311yescharacteristic
166C2×C4×Dic71C2312yes—
167C2×C4×Dic71C2311yescharacteristic
168C2×C4×Dic71C2318yes—
169C2×C4×Dic71C2312yes—
170C22×D4×C71C2312yes—
171C22×D4×C71C2314yes—
172C22×D4×C71C2314yes—
173C23×C4×C71C2311yescharacteristic
174C23×C4×C71C2314yes—
175#127×C71C2318yes—
176#125×C71C2318yes—
177#123×C71C23132yes—
178#121×C71C23132yes—
179#121×C71C23116yes—
180C4×D4×C71C23116yes—
181#117×C71C2318yes—
182C2×C4⋊C4×C71C2312yes—
183C2×C4⋊C4×C71C2312yes—
184C2×C4⋊C4×C71C2314yes—
185C2×C22⋊C4×C71C2312yes—
186C2×C22⋊C4×C71C2314yes—
187C2×C22⋊C4×C71C2314yes—
188C2×C42×C71C2311yescharacteristic
189C2×C42×C71C2311yescharacteristic
190C23×D71C2414yes—
191#11765865—464no—
192#11765864—464no—
193#11765864—464no—
194C2×Dic142—28no—
195C2×Dic142—28no—
196C2×Dic142—48no—
197C2×Dic142C2418yes—
198C2×Dic142C2418yes—
199C2×Dic142C24116yes—
200C2×D284—28no—
201C2×D284—48no—
202C2×D284C2418yes—
203C2×D284C24116yes—
204C2×C22⋊D71—216no—
205C2×C22⋊D71—48no—
206C2×C22⋊D71—48no—
207C2×C22⋊D71—48no—
208C2×C22⋊D71—48no—
209C2×C22⋊D71C24116yes—
210C2×C22⋊D71C24116yes—
211C2×C22⋊D71C24116yes—
212C2×C22⋊D71C24116yes—
213C2×C22⋊D71C24116yes—
214C22×Dic71—216no—
215C22×Dic71—28no—
216C22×Dic71—48no—
217C22×Dic71C2412yes—
218C22×Dic71C2414yes—
219C22×Dic71C2412yes—
220C22×Dic71C2412yes—
221C22×Dic71C2418yes—
222C22×Dic71C24116yes—
223C22×Dic71C24116yes—
224C22×Dic71C2412yes—
225C2×C4×D71—216no—
226C2×C4×D71—48no—
227C2×C4×D71—48no—
228C2×C4×D71C24116yes—
229C2×C4×D71C24116yes—
230C2×C4×D71C24116yes—
231C4⋊Dic71C24116yes—
232C4⋊Dic71C2418yes—
233C4⋊Dic71C2418yes—
234C4⋊Dic71C2418yes—
235C4⋊Dic71C2418yes—
236Dic71⋊C4C2418yes—
237Dic71⋊C4C24116yes—
238Dic71⋊C4C2418yes—
239Dic71⋊C4C24116yes—
240Dic71⋊C4C24116yes—
241Dic71⋊C4C2418yes—
242Dic71⋊C4C2418yes—
243C22⋊Dic71C2414yes—
244C22⋊Dic71C2414yes—
245C22⋊Dic71C24116yes—
246C22⋊Dic71C24116yes—
247(C2×D71)⋊C4C24116yes—
248(C2×D71)⋊C4C24116yes—
249(C2×D71)⋊C4C24116yes—
250(C2×D71)⋊C4C24116yes—
251C4×Dic71C2414yes—
252C4×Dic71C2418yes—
253C4×Dic71C2414yes—
254C4×Dic71C2418yes—
255C24×C71C2414yes—
256C24×C71C2411yescharacteristic
257C2×D4×C71—28no—
258C2×D4×C71—48no—
259C2×D4×C71—48no—
260C2×D4×C71C2418yes—
261C2×D4×C71C24116yes—
262C2×D4×C71C24116yes—
263C22×C4×C71—24no—
264C22×C4×C71—48no—
265C22×C4×C71C2412yes—
266C22×C4×C71C2414yes—
267C22×C4×C71C2412yes—
268C22×C4×C71C2411yescharacteristic
269C22×C4×C71C2414yes—
270C22×C4×C71C24116yes—
271C22×C4×C71C2411yescharacteristic
272C4⋊C4×C71C2418yes—
273C4⋊C4×C71C2418yes—
274C4⋊C4×C71C24116yes—
275C22⋊C4×C71C2418yes—
276C22⋊C4×C71C24116yes—
277C22⋊C4×C71C24116yes—
278C42×C71C2414yes—
279C42×C71C2414yes—
280C23×C71—28no—
281C23×C71—28no—
282C23×C71—24no—
283C23×C71—22no—
284C23×C71—28no—
285C23×C71C2512yes—
286C23×C71C2518yes—
287C23×C71C2511yescharacteristic
288C22×D71—28no—
289C22×D71—28no—
290C22×D71—28no—
291C22×D71C2518yes—
292D4×C71—216no—
293D4×C71—416no—
294D4×C71—416no—
295C2×C4×C71—24no—
296C2×C4×C71—28no—
297C2×C4×C71—24no—
298C2×C4×C71—22no—
299C2×C4×C71—28no—
300C2×C4×C71—416no—
301C2×C4×C712−1+414yes—
302C2×C4×C71C2514yes—
303C2×C4×C71C2514yes—
304C2×C4×C71C2512yes—
305C2×C4×C71C2518yes—
306C2×C4×C71C2512yes—
307C22⋊D71—232no—
308C22⋊D71—416no—
309C22⋊D71—416no—
310C22⋊D71—416no—
311C22⋊D71—416no—
312C2×Dic71—24no—
313C2×Dic71—28no—
314C2×Dic71—24no—
315C2×Dic71—24no—
316C2×Dic71—216no—
317C2×Dic71—232no—
318C2×Dic71—416no—
319C2×Dic71H(5,𝔽2)18yes—
320C2×Dic71C2514yes—
321C2×Dic71C2514yes—
322C2×Dic71C2514yes—
323C2×Dic71C2518yes—
324C2×Dic71C2514yes—
325D284—216no—
326D284—416no—
327C4×D71—232no—
328C4×D71—416no—
329C4×D71—416no—
330Dic142—216no—
331Dic142—216no—
332Dic142—416no—
333C22×C71—24no—
334C22×C71—28no—
335C22×C71—28no—
336C22×C71—22no—
337C22×C71—28no—
338C22×C71—416no—
339C22×C71—44no—
340C22×C71C2×H(5,𝔽2)14yes—
341C22×C71C2×2−1+412yes—
342C22×C71C2611yescharacteristic
343C2×D71—28no—
344C2×D71—28no—
345C2×D71—28no—
346C2×D71—416no—
347C4×C71—24no—
348C4×C71—24no—
349C4×C71—28no—
350C4×C71—22no—
351C4×C71C2×2−1+414yes—
352Dic71—24no—
353Dic71—24no—
354Dic71—24no—
355Dic71—28no—
356Dic71C2×H(5,𝔽2)18yes—
357C2×#3548—711nomaximal, Sylow
358C2×C71—42no—
359C2×C71—48no—
360C2×C71#354814yescomplemented
361C2×C71C22×H(5,𝔽2)12yes—
362C2×C71C22×2−1+411yescharacteristic
363D71—48no—
364#3548—7132no—
365C2×#562—714no—
366C2×#554—712no—
367C2×#554—712no—
368C2×#550—712no—
369C2×#550—712no—
370C2×#547—714no—
371C2×#540—712no—
372C2×#540—711no—
373C2×#540D7111yescharacteristic, complemented
374C2×#537—714no—
375C2×#537—714no—
376C2×#533—711no—
377C2×#532—712no—
378C71C2×#354811yescharacteristic, complemented, Sylow
379C22×#41—714no—
380C22×#41—714no—
381C22×#41—714no—
382#562—7164no—
383#554—7132no—
384#554—7132no—
385#550—7132no—
386#550—7132no—
387#547—7164no—
388#540—7132no—
389#540—7116no—
390#540C2×D71116yescomplemented
391#537—7164no—
392#537—7164no—
393#533—7116no—
394#532—7132no—
395C2×C4⋊Q8—712no—
396C2×C4⋊Q8—712no—
397C2×#127—712no—
398C2×#127—712no—
399C2×#127—711no—
400C2×#127C2×D7111yescharacteristic
401C2×#125—712no—
402C2×#125—712no—
403C2×#125—711no—
404C2×#125C2×D7111yescharacteristic
405C2×#124—714no—
406C2×#123—714no—
407C2×#123—714no—
408C2×#123—714no—
409C2×#123C2×D7114yes—
410C2×C22⋊Q8—714no—
411C2×C22⋊Q8—714no—
412C2×C22⋊Q8—714no—
413C2×C22⋊Q8—714no—
414C2×C22⋊Q8—712no—
415C2×C22⋊Q8—712no—
416C2×C22⋊Q8—714no—
417C2×C22⋊Q8—714no—
418C2×#121—714no—
419C2×#121—714no—
420C2×#121—714no—
421C2×#121—714no—
422C2×#121—714no—
423C2×#121—714no—
424C2×#121—712no—
425C2×#121—714no—
426C2×#121—714no—
427C2×#121—714no—
428C2×#121—714no—
429C2×#121C2×D7112yes—
430C2×#121C2×D7114yes—
431C2×C4×Q8—712no—
432C2×C4×Q8—712no—
433C2×C4×D4—712no—
434C2×C4×D4—712no—
435C2×C4×D4—712no—
436C2×C4×D4—712no—
437C2×C4×D4—714no—
438C2×C4×D4—712no—
439C2×C4×D4C2×D7112yes—
440C2×#117—711no—
441C2×#117C2×D7111yescharacteristic
442C22×C4⋊C4—714no—
443C22×C4⋊C4—714no—
444C22×C42—711no—
445C2×#41—28416no—
446C2×#41—28416no—
447C2×#41—28416no—
448C2×#41—7132no—
449C2×#41—7132no—
450C2×#41—7132no—
451C22×Q8—714no—
452C22×Q8—712no—
453C22×Q8—712no—
454C22×D4—714no—
455C22×D4—714no—
456C22×D4—714no—
457C22×D4—714no—
458C22×D4—714no—
459C22×D4—714no—
460C22×D4—712no—
461C22×D4C22×D7112yes—
462C22×D4C22×D7114yes—
463C22×D4C22×D7114yes—
464C23×C4—714no—
465C23×C4—714no—
466C23×C4—714no—
467C23×C4—714no—
468C23×C4—712no—
469C23×C4—714no—
470C23×C4C22×D7111yescharacteristic
471C23×C4C22×D7114yes—
472C4⋊Q8—7116no—
473C4⋊Q8—7116no—
474#127—7116no—
475#127—7116no—
476#127—718no—
477#127C22×D7118yes—
478#125—7116no—
479#125—7116no—
480#125—718no—
481#125C22×D7118yes—
482#124—7132no—
483#123—7132no—
484#123—7132no—
485#123—7132no—
486#123C22×D71132yes—
487C22⋊Q8—7132no—
488C22⋊Q8—7132no—
489C22⋊Q8—7132no—
490C22⋊Q8—7132no—
491C22⋊Q8—7116no—
492C22⋊Q8—7116no—
493C22⋊Q8—7132no—
494C22⋊Q8—7132no—
495#121—7132no—
496#121—7132no—
497#121—7132no—
498#121—7132no—
499#121—7132no—
500#121—7132no—
501#121—7116no—
502#121—7132no—
503#121—7132no—
504#121—7132no—
505#121—7132no—
506#121C22×D71116yes—
507#121C22×D71132yes—
508C4×Q8—7116no—
509C4×Q8—7116no—
510C4×D4—7116no—
511C4×D4—7116no—
512C4×D4—7116no—
513C4×D4—7116no—
514C4×D4—7132no—
515C4×D4—7116no—
516C4×D4C22×D71116yes—
517#117—718no—
518#117C22×D7118yes—
519C2×C4⋊C4—714no—
520C2×C4⋊C4—712no—
521C2×C4⋊C4—712no—
522C2×C4⋊C4—714no—
523C2×C4⋊C4—714no—
524C2×C4⋊C4—714no—
525C2×C4⋊C4—7132no—
526C2×C4⋊C4—712no—
527C2×C4⋊C4—712no—
528C2×C4⋊C4—712no—
529C2×C4⋊C4—712no—
530C2×C4⋊C4—712no—
531C2×C4⋊C4—712no—
532C2×C4⋊C4—7132no—
533C2×C4⋊C4C22×D7114yes—
534C2×C4⋊C4C22×D7112yes—
535C2×C4⋊C4C22×D7112yes—
536C2×C22⋊C4—711no—
537C2×C22⋊C4—711no—
538C2×C22⋊C4—714no—
539C2×C22⋊C4—714no—
540C2×C22⋊C4—714no—
541C2×C22⋊C4—714no—
542C2×C22⋊C4—714no—
543C2×C22⋊C4—714no—
544C2×C22⋊C4C22×D7112yes—
545C2×C22⋊C4C22×D7114yes—
546C2×C22⋊C4C22×D7114yes—
547C2×C42—712no—
548C2×C42—711no—
549C2×C42—712no—
550C2×C42—711no—
551C2×C42—718no—
552C2×C42C22×D7111yescharacteristic
553C2×C42C22×D7111yescharacteristic
554C24—714no—
555C24C23×D7114yes—
556C24C23×D7111yescharacteristic
557#41—28464no—
558#41—28464no—
559#41—28464no—
560C2×Q8—2848no—
561C2×Q8—7116no—
562C2×Q8—718no—
563C2×Q8—718no—
564C2×Q8—1428no—
565C2×Q8—1428no—
566C2×D4—28no—
567C2×D4—48no—
568C2×D4—48no—
569C2×D4—2848no—
570C2×D4—2848no—
571C2×D4—2848no—
572C2×D4—2848no—
573C2×D4—2848no—
574C2×D4—7116no—
575C2×D4—7116no—
576C2×D4—7116no—
577C2×D4—7116no—
578C2×D4—7116no—
579C2×D4—7116no—
580C2×D4—718no—
581C2×D4—14216no—
582C2×D4—1428no—
583C2×D4C23×D7118yes—
584C2×D4C23×D71116yes—
585C2×D4C23×D71116yes—
586C22×C4—24no—
587C22×C4—48no—
588C22×C4—2848no—
589C22×C4—2848no—
590C22×C4—2848no—
591C22×C4—7116no—
592C22×C4—7116no—
593C22×C4—7116no—
594C22×C4—712no—
595C22×C4—718no—
596C22×C4—7116no—
597C22×C4—712no—
598C22×C4—712no—
599C22×C4—712no—
600C22×C4—714no—
601C22×C4—7116no—
602C22×C4—14216no—
603C22×C4—14216no—
604C22×C4—1428no—
605C22×C4C23×D7114yes—
606C22×C4C23×D7111yescharacteristic
607C22×C4C23×D7112yes—
608C22×C4C23×D7112yes—
609C22×C4C23×D7114yes—
610C22×C4C23×D71116yes—
611C22×C4C23×D7111yescharacteristic
612C4⋊C4—7116no—
613C4⋊C4—718no—
614C4⋊C4—718no—
615C4⋊C4—7116no—
616C4⋊C4—7116no—
617C4⋊C4—718no—
618C4⋊C4—718no—
619C4⋊C4—7116no—
620C4⋊C4—718no—
621C4⋊C4—718no—
622C4⋊C4—718no—
623C4⋊C4—718no—
624C4⋊C4C23×D71116yes—
625C4⋊C4C23×D7118yes—
626C4⋊C4C23×D7118yes—
627C22⋊C4—714no—
628C22⋊C4—714no—
629C22⋊C4—7116no—
630C22⋊C4—7116no—
631C22⋊C4—7116no—
632C22⋊C4—7116no—
633C22⋊C4—7116no—
634C22⋊C4—7116no—
635C22⋊C4C23×D7118yes—
636C22⋊C4C23×D71116yes—
637C22⋊C4C23×D71116yes—
638C42—714no—
639C42—718no—
640C42—714no—
641C42—718no—
642C42C23×D7114yes—
643C42C23×D7114yes—
644C23—28no—
645C23—28no—
646C23—24no—
647C23—22no—
648C23—28no—
649C23—718no—
650C23—1428no—
651C23—1428no—
652C23—1428no—
653C23C24×D7118yes—
654C23C24×D7112yes—
655C23C24×D7111yescharacteristic
656Q8—28416no—
657Q8—14216no—
658Q8—14216no—
659D4—216no—
660D4—416no—
661D4—416no—
662D4—28416no—
663D4—28416no—
664D4—28416no—
665D4—28416no—
666D4—28416no—
667D4—14232no—
668D4—14216no—
669C2×C4—24no—
670C2×C4—28no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—28no—
674C2×C4—416no—
675C2×C4—28416no—
676C2×C4—28416no—
677C2×C4—28416no—
678C2×C4—718no—
679C2×C4—714no—
680C2×C4—714no—
681C2×C4—714no—
682C2×C4—714no—
683C2×C4—718no—
684C2×C4—14232no—
685C2×C4—14232no—
686C2×C4—14216no—
687C2×C4—1428no—
688C2×C4—1424no—
689C2×C4—1424no—
690C2×C4—1424no—
691C2×C4#1455617514yes—
692C2×C4C24×D7112yes—
693C2×C4C24×D7114yes—
694C2×C4C24×D7114yes—
695C2×C4C24×D7118yes—
696C2×C4C24×D7112yes—
697C22—28no—
698C22—28no—
699C22—24no—
700C22—22no—
701C22—28no—
702C22—416no—
703C22—44no—
704C22—28416no—
705C22—1428no—
706C22—1428no—
707C22—1428no—
708C22H(5,𝔽2)×D7114yes—
709C22C2×#1455617512yes—
710C22C25×D7111yescharacteristic
711C4—24no—
712C4—28no—
713C4—24no—
714C4—22no—
715C4—718no—
716C4—1428no—
717C4—1424no—
718C4—1424no—
719C4—1424no—
720C4C2×#1455617514yes—
721C2—48no—
722C2—42no—
723C2—2848no—
724C2#2260273414yesdirect product factor
725C2C2×H(5,𝔽2)×D7112yes—
726C2C22×#1455617511yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#540×C71C2
socleC23×C71C25
hypercenterC2×#540D71
hypocenterC71C2×#3548
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. #22602734C2direct (N × H)
2. C2×#17986746C2semidirect
3. C2×#17986708C2semidirect
4. C2×#17986705C2semidirect
5. C2×#17986670C2semidirect
6. C2×#17986669C2semidirect
7. C2×#17986647C2semidirect
8. C2×#17986604C2semidirect
9. C2×#17986602C2semidirect
10. C2×#17986578C2semidirect
11. C2×#17986576C2semidirect
12. C2×#17986552C2semidirect
13. C2×#17986544C2semidirect
14. C2×#540×C71C2semidirect
18. #17986746C22semidirect
19. #17986708C22semidirect
20. #17986705C22semidirect
21. #17986670C22semidirect
22. #17986669C22semidirect
23. #17986647C22semidirect
24. #17986604C22semidirect
25. #17986602C22semidirect
26. #17986578C22semidirect
27. #17986576C22semidirect
28. #17986552C22semidirect
29. #17986544C22semidirect
73. #540×C71C22semidirect
360. C2×C71#3548semidirect
373. C2×#540D71semidirect
378. C71C2×#3548semidirect
390. #540C2×D71semidirect
724. C2#22602734direct (N × H)

Maximal subgroups

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

subgroupindex
#226027342
C2×#179867462
C2×#179867082
C2×#179867052
C2×#179866702
C2×#179866692
C2×#179866472
C2×#179866042
C2×#179866022
C2×#179865782
C2×#179865762
C2×#179865522
C2×#179865442
C2×#540×C712
C2×#354871