Finite Group Databasebeta

← C2×#22602878 #32904814

Subgroups — C2×#22602878 #32904814

Order 18176.

7194 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602878C2132yesmaximal, direct product factor
2C2×#17986749C212yesmaximal, complemented
3C2×#17986743C212yesmaximal, complemented
4C2×#17986708C212yesmaximal, complemented
5C2×#17986701C212yesmaximal, complemented
6C2×#17986699C212yesmaximal, complemented
7C2×#17986649C212yesmaximal, complemented
8C2×#17986648C214yesmaximal, complemented
9C2×#17986626C212yesmaximal, complemented
10C2×#17986603C212yesmaximal, complemented
11C2×#17986594C212yesmaximal, complemented
12C2×#17986591C214yesmaximal, complemented
13C2×#17986576C212yesmaximal, complemented
14C2×#17986533C211yesmaximal, characteristic, complemented
15C22×#14556120C211yesmaximal, characteristic, complemented
16C2×#532×C71C211yesmaximal, characteristic, complemented
17C22×#11765864C2214yes—
18#17986749C22132yescomplemented
19#17986743C22132yescomplemented
20#17986708C22132yescomplemented
21#17986701C22132yescomplemented
22#17986699C22132yescomplemented
23#17986649C22132yescomplemented
24#17986648C22164yescomplemented
25#17986626C22132yescomplemented
26#17986603C22132yescomplemented
27#17986594C22132yescomplemented
28#17986591C22164yescomplemented
29#17986576C22132yescomplemented
30C2×#14556127C2212yes—
31C2×#14556126C2214yes—
32#17986533C22116yescomplemented
33C2×#14556122C2212yes—
34C2×#14556121C2214yes—
35C2×#14556121C2214yes—
36C2×#14556120C2212yes—
37C2×#14556120C2212yes—
38C2×#14556120C2212yes—
39C2×#14556120C2212yes—
40C2×#14556120C2211yescharacteristic
41C2×#14556120C22116yescomplemented
42C2×#14556119C2212yes—
43C2×#14556118C2214yes—
44C2×#14556116C2211yescharacteristic
45C2×#14556112C2214yes—
46C2×#14556111C2212yes—
47C2×#14556111C2214yes—
48C2×#14556110C2214yes—
49C2×#14556109C2214yes—
50C2×#14556109C2214yes—
51C2×#14556109C2214yes—
52C2×#14556107C2214yes—
53C2×#14556107C2211yescharacteristic
54C2×#14556106C2214yes—
55C2×#14556105C2214yes—
56C2×#14556105C2214yes—
57C2×#14556105C2214yes—
58C2×#14556104C2214yes—
59C2×#14556102C2211yescharacteristic
60C2×#14556101C2214yes—
61C2×#14556100C2214yes—
62C2×#14556100C2214yes—
63C2×#14556100C2214yes—
64C2×#14556099C2212yes—
65C2×#14556099C2212yes—
66C2×C4×Dic142C2211yescharacteristic
67C2×C4×D284C2211yescharacteristic
68C2×D4×Dic71C2214yes—
69C2×D4×Dic71C2212yes—
70C2×D4×Dic71C2212yes—
71C2×C4×C22⋊D71C2214yes—
72C2×C4×C22⋊D71C2212yes—
73C2×#14556086C2212yes—
74C2×#14556085C2212yes—
75C22×C4⋊Dic71C2211yescharacteristic
76C22×C4⋊Dic71C2211yescharacteristic
77C22×Dic71⋊C4C2212yes—
78C22×Dic71⋊C4C2214yes—
79C22×Dic71⋊C4C2212yes—
80C2×C4⋊C4×D71C2212yes—
81C22×#41×C71C2212yes—
82#532×C71C22116yescomplemented
83C2×C4⋊Q8×C71C2211yescharacteristic
84C2×#127×C71C2211yescharacteristic
85C2×#124×C71C2212yes—
86C2×#121×C71C2212yes—
87C2×#121×C71C2212yes—
88C2×C4×D4×C71C2212yes—
89C2×C4×D4×C71C2212yes—
90C22×C42×C71C2211yescharacteristic
91C2×#11765864—416no—
92C2×#11765864C23132yes—
93C22×Dic142C2314yes—
94C22×Dic142C2311yescharacteristic
95C22×D284C2311yescharacteristic
96C22×C22⋊D71C2312yes—
97C22×C22⋊D71C2314yes—
98C22×C22⋊D71C2314yes—
99C23×Dic71C2312yes—
100C23×Dic71C2314yes—
101C23×Dic71C2312yes—
102C23×Dic71C2314yes—
103C22×C4×D71C2312yes—
104C22×C4×D71C2314yes—
105#14556127C23116yes—
106#14556126C23132yes—
107#14556122C23116yes—
108#14556121C23132yes—
109#14556121C23132yes—
110#14556120C23116yes—
111#14556120C23116yes—
112#14556120C23116yes—
113#14556120C23116yes—
114#14556120C2318yes—
115#14556119C23116yes—
116#14556118C23132yes—
117#14556116C2318yes—
118#14556112C23132yes—
119#14556111C23132yes—
120#14556111C23116yes—
121#14556110C23132yes—
122#14556109C23132yes—
123#14556109C23132yes—
124#14556109C23132yes—
125#14556107C23132yes—
126#14556107C2318yes—
127#14556106C23132yes—
128#14556105C23132yes—
129#14556105C23132yes—
130#14556105C23132yes—
131#14556104C23132yes—
132#14556102C2318yes—
133#14556101C23132yes—
134#14556100C23132yes—
135#14556100C23132yes—
136#14556100C23132yes—
137#14556099C23116yes—
138#14556099C23116yes—
139C4×Dic142C2318yes—
140C4×D284C2318yes—
141D4×Dic71C23132yes—
142D4×Dic71C23116yes—
143D4×Dic71C23116yes—
144C4×C22⋊D71C23132yes—
145C4×C22⋊D71C23116yes—
146#14556086C23116yes—
147#14556085C23116yes—
148C2×C4⋊Dic71C2318yes—
149C2×C4⋊Dic71C2318yes—
150C2×C4⋊Dic71C2312yes—
151C2×C4⋊Dic71C2312yes—
152C2×C4⋊Dic71C2312yes—
153C2×C4⋊Dic71C2312yes—
154C2×C4⋊Dic71C2314yes—
155C2×C4⋊Dic71C2311yescharacteristic
156C2×C4⋊Dic71C2311yescharacteristic
157C2×Dic71⋊C4C23116yes—
158C2×Dic71⋊C4C23132yes—
159C2×Dic71⋊C4C23116yes—
160C2×Dic71⋊C4C2314yes—
161C2×Dic71⋊C4C2314yes—
162C2×Dic71⋊C4C2312yes—
163C2×Dic71⋊C4C2314yes—
164C2×Dic71⋊C4C2314yes—
165C2×Dic71⋊C4C2314yes—
166C2×Dic71⋊C4C2314yes—
167C2×Dic71⋊C4C2314yes—
168C2×Dic71⋊C4C2312yes—
169C2×Dic71⋊C4C2312yes—
170C2×Dic71⋊C4C2312yes—
171C4⋊C4×D71C23116yes—
172C2×C22⋊Dic71C2312yes—
173C2×C22⋊Dic71C2314yes—
174C2×C22⋊Dic71C2314yes—
175C2×C22⋊Dic71C2314yes—
176C2×C22⋊Dic71C2314yes—
177C2×(C2×D71)⋊C4C2312yes—
178C2×(C2×D71)⋊C4C2312yes—
179C2×(C2×D71)⋊C4C2314yes—
180C2×(C2×D71)⋊C4C2312yes—
181C2×(C2×D71)⋊C4C2312yes—
182C2×C4×Dic71C2312yes—
183C2×C4×Dic71C2314yes—
184C2×#41×C71—48no—
185C2×#41×C71C23116yes—
186C22×Q8×C71C2312yes—
187C22×D4×C71C2314yes—
188C22×D4×C71C2312yes—
189C22×D4×C71C2312yes—
190C22×D4×C71C2312yes—
191C23×C4×C71C2311yescharacteristic
192C23×C4×C71C2311yescharacteristic
193C23×C4×C71C2311yescharacteristic
194C23×C4×C71C2314yes—
195C4⋊Q8×C71C2318yes—
196#127×C71C2318yes—
197#124×C71C23116yes—
198#121×C71C23116yes—
199#121×C71C23116yes—
200C4×D4×C71C23116yes—
201C4×D4×C71C23116yes—
202C2×C4⋊C4×C71C2312yes—
203C2×C4⋊C4×C71C2312yes—
204C2×C22⋊C4×C71C2314yes—
205C2×C22⋊C4×C71C2314yes—
206C2×C42×C71C2311yescharacteristic
207C2×C42×C71C2311yescharacteristic
208C2×C42×C71C2311yescharacteristic
209C2×C42×C71C2311yescharacteristic
210C2×C42×C71C2318yes—
211C23×D71C2412yes—
212#11765864—464no—
213C2×Dic142—42no—
214C2×Dic142—48no—
215C2×Dic142C24116yes—
216C2×Dic142C2414yes—
217C2×D284—42no—
218C2×D284C2414yes—
219C2×C22⋊D71—28no—
220C2×C22⋊D71—48no—
221C2×C22⋊D71—48no—
222C2×C22⋊D71C2418yes—
223C2×C22⋊D71C24116yes—
224C2×C22⋊D71C24116yes—
225C22×Dic71—28no—
226C22×Dic71—44no—
227C22×Dic71—48no—
228C22×Dic71—48no—
229C22×Dic71C2414yes—
230C22×Dic71C2412yes—
231C22×Dic71C2412yes—
232C22×Dic71C2414yes—
233C22×Dic71C2412yes—
234C22×Dic71C2418yes—
235C22×Dic71C24116yes—
236C22×Dic71C2418yes—
237C22×Dic71C24116yes—
238C2×C4×D71—28no—
239C2×C4×D71—48no—
240C2×C4×D71C2418yes—
241C2×C4×D71C24116yes—
242C4⋊Dic71C2418yes—
243C4⋊Dic71C2418yes—
244C4⋊Dic71C2418yes—
245C4⋊Dic71C2418yes—
246C4⋊Dic71C24116yes—
247C4⋊Dic71C2414yes—
248C4⋊Dic71C2414yes—
249Dic71⋊C4C24116yes—
250Dic71⋊C4C24116yes—
251Dic71⋊C4C2418yes—
252Dic71⋊C4C24116yes—
253Dic71⋊C4C24116yes—
254Dic71⋊C4C24116yes—
255Dic71⋊C4C24116yes—
256Dic71⋊C4C24116yes—
257Dic71⋊C4C2418yes—
258Dic71⋊C4C2418yes—
259Dic71⋊C4C2418yes—
260C22⋊Dic71C2418yes—
261C22⋊Dic71C24116yes—
262C22⋊Dic71C24116yes—
263C22⋊Dic71C24116yes—
264C22⋊Dic71C24116yes—
265(C2×D71)⋊C4C2418yes—
266(C2×D71)⋊C4C2418yes—
267(C2×D71)⋊C4C24116yes—
268(C2×D71)⋊C4C2418yes—
269(C2×D71)⋊C4C2418yes—
270C4×Dic71C2418yes—
271C4×Dic71C24116yes—
272C24×C71C2414yes—
273C24×C71C2411yescharacteristic
274#41×C71—432no—
275C2×Q8×C71—44no—
276C2×Q8×C71C2418yes—
277C2×D4×C71—216no—
278C2×D4×C71—28no—
279C2×D4×C71—44no—
280C2×D4×C71—44no—
281C2×D4×C71C24116yes—
282C2×D4×C71C2418yes—
283C2×D4×C71C2418yes—
284C2×D4×C71C2418yes—
285C22×C4×C71—24no—
286C22×C4×C71—24no—
287C22×C4×C71—42no—
288C22×C4×C71—48no—
289C22×C4×C71C2414yes—
290C22×C4×C71C2411yescharacteristic
291C22×C4×C71C2411yescharacteristic
292C22×C4×C71C2411yescharacteristic
293C22×C4×C71C2414yes—
294C22×C4×C71C2411yescharacteristic
295C22×C4×C71C2411yescharacteristic
296C22×C4×C71C2414yes—
297C22×C4×C71C2414yes—
298C22×C4×C71C24116yes—
299C22×C4×C71C2411yescharacteristic
300C4⋊C4×C71C2418yes—
301C4⋊C4×C71C2418yes—
302C22⋊C4×C71C24116yes—
303C22⋊C4×C71C24116yes—
304C42×C71C2414yes—
305C42×C71C2414yes—
306C42×C71C2414yes—
307C42×C71C2414yes—
308C23×C71—22no—
309C23×C71—22no—
310C23×C71—28no—
311C23×C71—28no—
312C23×C71—28no—
313C23×C71H(5,𝔽2)14yes—
314C23×C71C2518yes—
315C23×C71C2512yes—
316C23×C71C2511yescharacteristic
317C22×D71—24no—
318C22×D71—24no—
319C22×D71—24no—
320C22×D71C2514yes—
321Q8×C71—48no—
322D4×C71—232no—
323D4×C71—216no—
324D4×C71—48no—
325D4×C71—48no—
326C2×C4×C71—22no—
327C2×C4×C71—22no—
328C2×C4×C71—28no—
329C2×C4×C71—28no—
330C2×C4×C71—22no—
331C2×C4×C71—22no—
332C2×C4×C71—22no—
333C2×C4×C71—28no—
334C2×C4×C71—44no—
335C2×C4×C71—416no—
336C2×C4×C712−1+414yes—
337C2×C4×C71C2512yes—
338C2×C4×C71C2512yes—
339C2×C4×C71C2512yes—
340C2×C4×C71C2512yes—
341C2×C4×C71C2512yes—
342C2×C4×C71C2518yes—
343C2×C4×C71C2512yes—
344C22⋊D71—216no—
345C22⋊D71—416no—
346C22⋊D71—416no—
347C2×Dic71—28no—
348C2×Dic71—216no—
349C2×Dic71—24no—
350C2×Dic71—24no—
351C2×Dic71—28no—
352C2×Dic71—24no—
353C2×Dic71—416no—
354C2×Dic71—48no—
355C2×Dic71—416no—
356C2×Dic71C2514yes—
357C2×Dic71C2514yes—
358C2×Dic71C2518yes—
359C2×Dic71C2514yes—
360C2×Dic71C2518yes—
361D284—44no—
362C4×D71—216no—
363C4×D71—416no—
364Dic142—44no—
365Dic142—416no—
366C22×C71—22no—
367C22×C71—22no—
368C22×C71—28no—
369C22×C71—28no—
370C22×C71—28no—
371C22×C71—28no—
372C22×C71—416no—
373C22×C71C2×H(5,𝔽2)14yes—
374C22×C71C2×H(5,𝔽2)12yes—
375C22×C71C2×2−1+412yes—
376C22×C71#58512yes—
377C22×C71C2611yescharacteristic
378C2×D71—24no—
379C2×D71—24no—
380C2×D71—24no—
381C2×D71—48no—
382C4×C71—28no—
383C4×C71—22no—
384C4×C71—22no—
385C4×C71—22no—
386C4×C71—22no—
387C4×C71—22no—
388C4×C71C2×2−1+414yes—
389Dic71—24no—
390Dic71—28no—
391Dic71—24no—
392Dic71—24no—
393Dic71—28no—
394C2×#3559—711nomaximal, Sylow
395C2×C71—24no—
396C2×C71—48no—
397C2×C71#355914yescomplemented
398C2×C71C22×H(5,𝔽2)11yescharacteristic
399C2×C71C22×2−1+411yescharacteristic
400C2×C71C2×#58511yescharacteristic
401D71—44no—
402#3559—7132no—
403C2×#563—712no—
404C2×#562—712no—
405C2×#554—712no—
406C2×#553—712no—
407C2×#553—712no—
408C2×#547—714no—
409C2×#547—712no—
410C2×#544—712no—
411C2×#540—712no—
412C2×#539—712no—
413C2×#539—714no—
414C2×#537—712no—
415C2×#532D7111yescharacteristic, complemented
416C2×#529—711no—
417C22×#125—711no—
418C71C2×#355911yescharacteristic, complemented, Sylow
419C22×#41—714no—
420C22×#41C2×D7112yes—
421#563—7132no—
422#562—7132no—
423#554—7132no—
424#553—7132no—
425#553—7132no—
426#547—7164no—
427#547—7132no—
428#544—7132no—
429#540—7132no—
430#539—7132no—
431#539—7164no—
432#537—7132no—
433#532C2×D71116yescomplemented
434C2×C4⋊Q8—714no—
435C2×C4⋊Q8—712no—
436C2×C4⋊Q8C2×D7111yescharacteristic
437C2×#127C2×D7111yescharacteristic
438#529—7116no—
439C2×#126—714no—
440C2×#126—714no—
441C2×#126—712no—
442C2×#125—714no—
443C2×#125—712no—
444C2×#125—712no—
445C2×#125—712no—
446C2×#125—712no—
447C2×#125—712no—
448C2×#125—7116no—
449C2×#125—711no—
450C2×#124—711no—
451C2×#124C2×D7112yes—
452C2×#123—714no—
453C2×#123—714no—
454C2×#123—714no—
455C2×#123—712no—
456C2×#123—714no—
457C2×#123—714no—
458C2×#123—714no—
459C2×C22⋊Q8—714no—
460C2×C22⋊Q8—711no—
461C2×C22⋊Q8—714no—
462C2×C22⋊Q8—714no—
463C2×C22⋊Q8—714no—
464C2×C22⋊Q8—714no—
465C2×C22⋊Q8—714no—
466C2×#121—714no—
467C2×#121—714no—
468C2×#121—712no—
469C2×#121—714no—
470C2×#121—712no—
471C2×#121—711no—
472C2×#121—714no—
473C2×#121C2×D7112yes—
474C2×#121C2×D7112yes—
475C2×C4×Q8—711no—
476C2×C4×D4—714no—
477C2×C4×D4—712no—
478C2×C4×D4—712no—
479C2×C4×D4—712no—
480C2×C4×D4—714no—
481C2×C4×D4—711no—
482C2×C4×D4C2×D7112yes—
483C2×C4×D4C2×D7112yes—
484C2×#117—712no—
485C2×#117—712no—
486C22×C4⋊C4—712no—
487C22×C4⋊C4—712no—
488C22×C4⋊C4—711no—
489C22×C4⋊C4—711no—
490C22×C4⋊C4—714no—
491C22×C4⋊C4—712no—
492C22×C42C2×D7111yescharacteristic
493C2×#41—48no—
494C2×#41—28416no—
495C2×#41—7132no—
496C2×#41C22×D71116yes—
497C22×Q8—711no—
498C22×Q8—714no—
499C22×Q8C22×D7112yes—
500C22×D4—714no—
501C22×D4—714no—
502C22×D4—712no—
503C22×D4—711no—
504C22×D4C22×D7112yes—
505C22×D4C22×D7114yes—
506C22×D4C22×D7112yes—
507C22×D4C22×D7112yes—
508C23×C4—712no—
509C23×C4—714no—
510C23×C4—714no—
511C23×C4—714no—
512C23×C4—712no—
513C23×C4—712no—
514C23×C4C22×D7111yescharacteristic
515C23×C4C22×D7111yescharacteristic
516C23×C4C22×D7111yescharacteristic
517C23×C4C22×D7114yes—
518C4⋊Q8—7132no—
519C4⋊Q8—7116no—
520C4⋊Q8C22×D7118yes—
521#127C22×D7118yes—
522#126—7132no—
523#126—7132no—
524#126—7116no—
525#125—7132no—
526#125—7116no—
527#125—7116no—
528#125—7116no—
529#125—7116no—
530#125—7116no—
531#125—718no—
532#124—718no—
533#124C22×D71116yes—
534#123—7132no—
535#123—7132no—
536#123—7132no—
537#123—7116no—
538#123—7132no—
539#123—7132no—
540#123—7132no—
541C22⋊Q8—7132no—
542C22⋊Q8—718no—
543C22⋊Q8—7132no—
544C22⋊Q8—7132no—
545C22⋊Q8—7132no—
546C22⋊Q8—7132no—
547C22⋊Q8—7132no—
548#121—7132no—
549#121—7132no—
550#121—7116no—
551#121—7132no—
552#121—7116no—
553#121—718no—
554#121—7132no—
555#121C22×D71116yes—
556#121C22×D71116yes—
557C4×Q8—718no—
558C4×D4—7132no—
559C4×D4—7116no—
560C4×D4—7116no—
561C4×D4—7116no—
562C4×D4—7132no—
563C4×D4—718no—
564C4×D4C22×D71116yes—
565C4×D4C22×D71116yes—
566#117—7116no—
567#117—7116no—
568C2×C4⋊C4—712no—
569C2×C4⋊C4—714no—
570C2×C4⋊C4—712no—
571C2×C4⋊C4—712no—
572C2×C4⋊C4—714no—
573C2×C4⋊C4—714no—
574C2×C4⋊C4—714no—
575C2×C4⋊C4—714no—
576C2×C4⋊C4—712no—
577C2×C4⋊C4—714no—
578C2×C4⋊C4—714no—
579C2×C4⋊C4—712no—
580C2×C4⋊C4—7116no—
581C2×C4⋊C4—7116no—
582C2×C4⋊C4—718no—
583C2×C4⋊C4—718no—
584C2×C4⋊C4—7132no—
585C2×C4⋊C4—712no—
586C2×C4⋊C4—712no—
587C2×C4⋊C4—714no—
588C2×C4⋊C4—712no—
589C2×C4⋊C4—711no—
590C2×C4⋊C4—711no—
591C2×C4⋊C4—7116no—
592C2×C4⋊C4C22×D7112yes—
593C2×C4⋊C4C22×D7112yes—
594C2×C22⋊C4—712no—
595C2×C22⋊C4—714no—
596C2×C22⋊C4—714no—
597C2×C22⋊C4—714no—
598C2×C22⋊C4—714no—
599C2×C22⋊C4—712no—
600C2×C22⋊C4—714no—
601C2×C22⋊C4—712no—
602C2×C22⋊C4—712no—
603C2×C22⋊C4—712no—
604C2×C22⋊C4C22×D7114yes—
605C2×C22⋊C4C22×D7114yes—
606C2×C42—712no—
607C2×C42—714no—
608C2×C42C22×D7111yescharacteristic
609C2×C42C22×D7111yescharacteristic
610C2×C42C22×D7111yescharacteristic
611C2×C42C22×D7111yescharacteristic
612C2×C42C22×D7118yes—
613C24—712no—
614C24C23×D7114yes—
615C24C23×D7111yescharacteristic
616#41—432no—
617#41—28464no—
618C2×Q8—44no—
619C2×Q8—2842no—
620C2×Q8—2848no—
621C2×Q8—714no—
622C2×Q8—7116no—
623C2×Q8C23×D7118yes—
624C2×D4—216no—
625C2×D4—28no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4—2842no—
629C2×D4—2848no—
630C2×D4—2848no—
631C2×D4—7116no—
632C2×D4—7116no—
633C2×D4—718no—
634C2×D4—714no—
635C2×D4—1428no—
636C2×D4C23×D7118yes—
637C2×D4C23×D71116yes—
638C2×D4C23×D7118yes—
639C2×D4C23×D7118yes—
640C22×C4—24no—
641C22×C4—24no—
642C22×C4—42no—
643C22×C4—48no—
644C22×C4—2848no—
645C22×C4—2844no—
646C22×C4—2848no—
647C22×C4—2848no—
648C22×C4—718no—
649C22×C4—7116no—
650C22×C4—7116no—
651C22×C4—7116no—
652C22×C4—718no—
653C22×C4—712no—
654C22×C4—712no—
655C22×C4—714no—
656C22×C4—712no—
657C22×C4—714no—
658C22×C4—718no—
659C22×C4—1428no—
660C22×C4—1428no—
661C22×C4C23×D7114yes—
662C22×C4C23×D7114yes—
663C22×C4C23×D7114yes—
664C22×C4C23×D7111yescharacteristic
665C22×C4C23×D7111yescharacteristic
666C22×C4C23×D7111yescharacteristic
667C22×C4C23×D7111yescharacteristic
668C22×C4C23×D7111yescharacteristic
669C22×C4C23×D7114yes—
670C22×C4C23×D71116yes—
671C22×C4C23×D7111yescharacteristic
672C4⋊C4—7116no—
673C4⋊C4—718no—
674C4⋊C4—7116no—
675C4⋊C4—7116no—
676C4⋊C4—7116no—
677C4⋊C4—7116no—
678C4⋊C4—7116no—
679C4⋊C4—7116no—
680C4⋊C4—718no—
681C4⋊C4—718no—
682C4⋊C4—718no—
683C4⋊C4—718no—
684C4⋊C4—718no—
685C4⋊C4—718no—
686C4⋊C4—718no—
687C4⋊C4—7116no—
688C4⋊C4—714no—
689C4⋊C4—714no—
690C4⋊C4C23×D7118yes—
691C4⋊C4C23×D7118yes—
692C22⋊C4—718no—
693C22⋊C4—7116no—
694C22⋊C4—7116no—
695C22⋊C4—7116no—
696C22⋊C4—7116no—
697C22⋊C4—718no—
698C22⋊C4—7116no—
699C22⋊C4—718no—
700C22⋊C4—718no—
701C22⋊C4—718no—
702C22⋊C4C23×D71116yes—
703C22⋊C4C23×D71116yes—
704C42—718no—
705C42—7116no—
706C42C23×D7114yes—
707C42C23×D7114yes—
708C42C23×D7114yes—
709C42C23×D7114yes—
710C23—22no—
711C23—22no—
712C23—28no—
713C23—28no—
714C23—28no—
715C23—714no—
716C23—1424no—
717C23—1424no—
718C23—1424no—
719C23#1455617314yes—
720C23C24×D7118yes—
721C23C24×D7112yes—
722C23C24×D7111yescharacteristic
723Q8—48no—
724Q8—28416no—
725Q8—2844no—
726D4—232no—
727D4—216no—
728D4—48no—
729D4—48no—
730D4—2844no—
731D4—28416no—
732D4—28416no—
733D4—14216no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—28no—
737C2×C4—28no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—28no—
742C2×C4—416no—
743C2×C4—44no—
744C2×C4—28416no—
745C2×C4—28416no—
746C2×C4—2848no—
747C2×C4—28416no—
748C2×C4—714no—
749C2×C4—714no—
750C2×C4—718no—
751C2×C4—714no—
752C2×C4—718no—
753C2×C4—1428no—
754C2×C4—1424no—
755C2×C4—14216no—
756C2×C4—1424no—
757C2×C4—1428no—
758C2×C4—1424no—
759C2×C4—14216no—
760C2×C4#1455617514yes—
761C2×C4C24×D7118yes—
762C2×C4C24×D7112yes—
763C2×C4C24×D7112yes—
764C2×C4C24×D7112yes—
765C2×C4C24×D7112yes—
766C2×C4C24×D7112yes—
767C2×C4C24×D7112yes—
768C22—28no—
769C22—22no—
770C22—22no—
771C22—28no—
772C22—28no—
773C22—28no—
774C22—416no—
775C22—2848no—
776C22—1424no—
777C22—1424no—
778C22—1424no—
779C22C2×#1455617314yes—
780C22C2×#1455617312yes—
781C22C2×#1455617512yes—
782C22#1798683512yes—
783C22C25×D7111yescharacteristic
784C4—22no—
785C4—22no—
786C4—28no—
787C4—22no—
788C4—22no—
789C4—22no—
790C4—1428no—
791C4—1424no—
792C4—1424no—
793C4—1428no—
794C4—1424no—
795C4C2×#1455617514yes—
796C2—24no—
797C2—48no—
798C2—2844no—
799C2#2260287814yesdirect product factor
800C2C22×#1455617311yescharacteristic
801C2C22×#1455617511yescharacteristic
802C2C2×#1798683511yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#532×C71C2
socleC23×C71C25
hypercenterC2×#532D71
hypocenterC71C2×#3559
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #22602878C2direct (N × H)
2. C2×#17986749C2semidirect
3. C2×#17986743C2semidirect
4. C2×#17986708C2semidirect
5. C2×#17986701C2semidirect
6. C2×#17986699C2semidirect
7. C2×#17986649C2semidirect
8. C2×#17986648C2semidirect
9. C2×#17986626C2semidirect
10. C2×#17986603C2semidirect
11. C2×#17986594C2semidirect
12. C2×#17986591C2semidirect
13. C2×#17986576C2semidirect
14. C2×#17986533C2semidirect
15. C22×#14556120C2semidirect
16. C2×#532×C71C2semidirect
18. #17986749C22semidirect
19. #17986743C22semidirect
20. #17986708C22semidirect
21. #17986701C22semidirect
22. #17986699C22semidirect
23. #17986649C22semidirect
24. #17986648C22semidirect
25. #17986626C22semidirect
26. #17986603C22semidirect
27. #17986594C22semidirect
28. #17986591C22semidirect
29. #17986576C22semidirect
32. #17986533C22semidirect
41. C2×#14556120C22semidirect
82. #532×C71C22semidirect
397. C2×C71#3559semidirect
415. C2×#532D71semidirect
418. C71C2×#3559semidirect
433. #532C2×D71semidirect
799. C2#22602878direct (N × H)

Maximal subgroups

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

subgroupindex
#226028782
C2×#179867492
C2×#179867432
C2×#179867082
C2×#179867012
C2×#179866992
C2×#179866492
C2×#179866482
C2×#179866262
C2×#179866032
C2×#179865942
C2×#179865912
C2×#179865762
C2×#179865332
C22×#145561202
C2×#532×C712
C2×#355971