Finite Group Databasebeta

← C2×#11738085 #14226573

Subgroups — C2×#11738085 #14226573

Order 1792.

2178 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90313C211yesmaximal, characteristic, complemented
2C2×#90287C211yesmaximal, characteristic
3C2×C7×#465C211yesmaximal, characteristic, complemented
4C2×#89935C211yesmaximal, characteristic, complemented
5C2×#89934C211yesmaximal, characteristic, complemented
6C2×#89886C211yesmaximal, characteristic, complemented
7C22×Dic7⋊C8C211yesmaximal, characteristic, complemented
8C2×#89820C211yesmaximal, characteristic, complemented
9C2×#89813C211yesmaximal, characteristic, complemented
10#11738085C2116yesmaximal, direct product factor
11C2×#89626C211yesmaximal, characteristic, complemented
12C2×#89642C211yesmaximal, characteristic, complemented
13C2×#89590C211yesmaximal, characteristic, complemented
14C2×#89563C211yesmaximal, characteristic, complemented
15C2×#89534C211yesmaximal, characteristic, complemented
16C2×#89533C211yesmaximal, characteristic, complemented
17C22×#1159—21no—
18C22×C7×SD16C2211yescharacteristic
19C23×C7×C8C2211yescharacteristic
20C2×C7×C22⋊Q8C2211yescharacteristic
21C2×C7×#121C2211yescharacteristic
22C2×Q8×Dic7C2211yescharacteristic
23C2×#6507C2211yescharacteristic
24C22×#1143C2211yescharacteristic
25C2×#6503C2211yescharacteristic
26C2×#6502—21no—
27C2×D4×Dic7C2211yescharacteristic
28C22×#1142C2211yescharacteristic
29C2×#6493C2211yescharacteristic
30C2×#6487C2211yescharacteristic
31C22×C4×Dic7C2211yescharacteristic
32C23×C7⋊C8C2211yescharacteristic
33C22×#1132C2211yescharacteristic
34#90313—24no—
35#90313C2218yescomplemented
36#90287—24no—
37#90287C2218yes—
38C2×#6456C2211yescharacteristic
39C2×#6452—21no—
40C2×#6451C2211yescharacteristic
41C2×#6451C2211yescharacteristic
42C2×#6450—21no—
43C2×#6450C2211yescharacteristic
44C2×#6448—21no—
45C2×(C22⋊D7)⋊C4—21no—
46C2×#6441—21no—
47C2×#6440—21no—
48C7×#465C2218yescomplemented
49C2×C7×#106C2211yescharacteristic
50C2×C7×#103C2211yescharacteristic
51C2×C7×#102C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53C2×#6406C2211yescharacteristic
54#89935C2218yescomplemented
55#89934C2218yescomplemented
56#89886C2218yescomplemented
57C2×#6395C2211yescharacteristic
58C2×#6391C2211yescharacteristic
59C2×#6390C2211yescharacteristic
60C2×Dic7⋊C8C2211yescharacteristic
61C2×Dic7⋊C8C2211yescharacteristic
62C2×Dic7⋊C8C2211yescharacteristic
63C2×Dic7⋊C8C2211yescharacteristic
64C2×Dic7⋊C8C2218yescomplemented
65#89820C2218yescomplemented
66#89813C2218yescomplemented
67C2×#6384C2211yescharacteristic
68C2×#6383C2211yescharacteristic
69C2×#6382C2211yescharacteristic
70C2×#6382C2211yescharacteristic
71#89642C2218yescomplemented
72#89626C2218yescomplemented
73#89590C2218yescomplemented
74#89563C2218yescomplemented
75#89534C2218yescomplemented
76#89533C2218yescomplemented
77C2×#3246—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×D4—21no—
80C22×C7×D4C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C22×C22⋊D7—21no—
83C22×C22⋊D7—21no—
84C22×C22⋊D7—21no—
85C23×Dic7—21no—
86C23×Dic7D411yescharacteristic
87C23×Dic7D411yescharacteristic
88C2×#1159—28no—
89C2×#1159—48no—
90C22×D28C2311yescharacteristic
91C22×C4×D7—21no—
92C22×Dic14—21no—
93C22×Dic14—21no—
94C22×Dic14C2311yescharacteristic
95C2×C7×SD16—42no—
96C2×C7×SD16C2314yes—
97C22×C7×C8—42no—
98C22×C7×C8C2311yescharacteristic
99C22×C7×C8C2311yescharacteristic
100C22×C7×C8C2314yes—
101C7×C22⋊Q8—22no—
102C7×C22⋊Q8C2314yes—
103C7×#121—22no—
104C7×#121C2314yes—
105C2×C7×C4⋊C4—21no—
106C2×C7×C4⋊C4C2311yescharacteristic
107C2×C7×C4⋊C4C2311yescharacteristic
108C2×C7×C22⋊C4—21no—
109C2×C7×C22⋊C4—21no—
110C2×C22⋊Dic7—21no—
111C2×C22⋊Dic7—21no—
112Q8×Dic7—22no—
113Q8×Dic7C2314yes—
114#6507—22no—
115#6507C2314yes—
116C2×#1143—42no—
117C2×#1143C2314yes—
118#6503—22no—
119#6503C2314yes—
120#6502—28no—
121D4×Dic7—22no—
122D4×Dic7C2314yes—
123C2×#1142—42no—
124C2×#1142C2314yes—
125#6493—22no—
126#6493C2314yes—
127C2×(C2×D7)⋊C4—21no—
128C2×(C2×D7)⋊C4—21no—
129C2×C4⋊Dic7—21no—
130C2×C4⋊Dic7C2311yescharacteristic
131C2×C4⋊Dic7C2311yescharacteristic
132#6487—22no—
133#6487C2314yes—
134C2×Dic7⋊C4—21no—
135C2×Dic7⋊C4—21no—
136C2×Dic7⋊C4—21no—
137C2×Dic7⋊C4—21no—
138C2×Dic7⋊C4—21no—
139C2×Dic7⋊C4—21no—
140C2×C4×Dic7—21no—
141C2×C4×Dic7—21no—
142C2×C4×Dic7D411yescharacteristic
143C2×C4×Dic7D411yescharacteristic
144C2×C4×Dic7D414yes—
145C2×C4×Dic7C2311yescharacteristic
146C2×C4×Dic7C2311yescharacteristic
147C2×C4×Dic7C2314yes—
148C22×C7⋊C8—42no—
149C22×C7⋊C8C2311yescharacteristic
150C22×C7⋊C8C2311yescharacteristic
151C22×C7⋊C8C2314yes—
152C2×#1132—42no—
153C2×#1132C2314yes—
154#6456—22no—
155#6456C2314yes—
156#6452—28no—
157#6451—22no—
158#6451—22no—
159#6451C2314yes—
160#6451C2314yes—
161#6450—28no—
162#6450—22no—
163#6450C2314yes—
164#6448—28no—
165(C22⋊D7)⋊C4—28no—
166#6441—28no—
167#6440—28no—
168C7×#106C2314yes—
169C7×#103C2314yes—
170C7×#102C2314yes—
171#6409C2314yes—
172#6406C2314yes—
173#6395C2314yes—
174#6391C2314yes—
175#6390C2314yes—
176Dic7⋊C8C2314yes—
177Dic7⋊C8C2314yes—
178Dic7⋊C8C2314yes—
179Dic7⋊C8C2314yes—
180#6384C2314yes—
181#6383C2314yes—
182#6382C2314yes—
183#6382C2314yes—
184C2×#533—71no—
185C2×#532—71no—
186#3246—716no—
187C2×#475—71no—
188C2×#475—71no—
189C2×#476—71no—
190C2×#476—71no—
191C2×#465—71no—
192C2×#465—71no—
193C2×#465—71no—
194C2×#465D711yescharacteristic, complemented
195C2×#460—71no—
196C2×#460—71no—
197C2×#461—71no—
198C2×#461—71no—
199C22×C4⋊C8—71no—
200C24×C7—21no—
201C24×C7C2×D411yescharacteristic
202C23×D7—21no—
203C2×C7×Q8—21no—
204C2×C7×Q8—22no—
205C2×C7×Q8—22no—
206C2×C7×Q8C2412yes—
207C2×C7×D4—24no—
208C2×C7×D4—21no—
209C2×C7×D4—22no—
210C2×C7×D4—22no—
211C2×C7×D4—44no—
212C2×C7×D4C2412yes—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7C2×D411yescharacteristic
219C22×C4×C7C2×D412yes—
220C22×C4×C7C2412yes—
221C22×C4×C7C2411yescharacteristic
222C2×C22⋊D7—24no—
223C2×C22⋊D7—24no—
224C2×C22⋊D7—24no—
225C2×C22⋊D7—44no—
226C2×C22⋊D7—44no—
227C2×C22⋊D7—44no—
228C22×Dic7—21no—
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—24no—
232C22×Dic7—42no—
233C22×Dic7—44no—
234C22×Dic7SD1618yescomplemented
235C22×Dic7C2×D411yescharacteristic
236C22×Dic7C2×D411yescharacteristic
237C22×Dic7C2×D414yes—
238C22×Dic7C2×D411yescharacteristic
239C22×Dic7C2×D411yescharacteristic
240C22×Dic7C2×D414yes—
241#1159—432no—
242C2×D28—22no—
243C2×D28—22no—
244C2×D28—21no—
245C2×D28C2412yes—
246C2×C4×D7—24no—
247C2×C4×D7—44no—
248C2×Dic14—22no—
249C2×Dic14—22no—
250C2×Dic14—21no—
251C2×Dic14—24no—
252C2×Dic14—24no—
253C2×Dic14—44no—
254C2×Dic14—44no—
255C2×Dic14C2412yes—
256C7×SD16—44no—
257C2×C7×C8—22no—
258C2×C7×C8—22no—
259C2×C7×C8—44no—
260C2×C7×C8C2412yes—
261C2×C7×C8C2412yes—
262C7×C4⋊C4—21no—
263C7×C4⋊C4—24no—
264C7×C4⋊C4—21no—
265C7×C4⋊C4C2412yes—
266C7×C4⋊C4C2412yes—
267C7×C22⋊C4—24no—
268C7×C22⋊C4—24no—
269C22⋊Dic7—24no—
270C22⋊Dic7—24no—
271#1143—44no—
272#1142—44no—
273(C2×D7)⋊C4—24no—
274(C2×D7)⋊C4—24no—
275C4⋊Dic7—21no—
276C4⋊Dic7—21no—
277C4⋊Dic7—24no—
278C4⋊Dic7C2412yes—
279C4⋊Dic7C2412yes—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282Dic7⋊C4—24no—
283Dic7⋊C4—24no—
284Dic7⋊C4—24no—
285Dic7⋊C4—24no—
286C4×Dic7—24no—
287C4×Dic7—24no—
288C4×Dic7C2×D414yes—
289C4×Dic7C2×D414yes—
290C4×Dic7C2×D412yes—
291C4×Dic7C2×D412yes—
292C4×Dic7C2412yes—
293C4×Dic7C2412yes—
294C2×C7⋊C8—22no—
295C2×C7⋊C8—22no—
296C2×C7⋊C8—44no—
297C2×C7⋊C8C2412yes—
298C2×C7⋊C8C2412yes—
299#1132—44no—
300C22×#41—141no—
301C22×SD16—71no—
302C22×SD16—71no—
303C22×SD16—71no—
304C22×SD16C2×D711yescharacteristic
305C23×C8—71no—
306C23×C8C2×D711yescharacteristic
307#533—78no—
308#533—144no—
309#532—78no—
310#532—144no—
311C2×C4⋊Q8—71no—
312C2×C4⋊Q8—71no—
313C2×C4⋊Q8—71no—
314C2×#127—71no—
315C2×#125—141no—
316C2×#124—141no—
317C2×C22⋊Q8—71no—
318C2×C22⋊Q8—141no—
319C2×C22⋊Q8C2×D711yescharacteristic
320C2×#121—71no—
321C2×#121—141no—
322C2×#121C2×D711yescharacteristic
323C2×C4×Q8—71no—
324C2×C4×Q8—71no—
325C2×C4×Q8—141no—
326C2×C4×D4—71no—
327C2×C4×D4—71no—
328C2×C4×D4—141no—
329C2×#117—141no—
330C22×C42—71no—
331#476—78no—
332#476—78no—
333#475—78no—
334#475—78no—
335#465—78no—
336#465—78no—
337#465—78no—
338#465C2×D718yescomplemented
339#461—78no—
340#461—78no—
341#460—78no—
342#460—78no—
343C2×#106—71no—
344C2×#106—71no—
345C2×#106—71no—
346C2×#106C2×D711yescharacteristic
347C2×C4⋊C8—71no—
348C2×C4⋊C8—71no—
349C2×C4⋊C8—71no—
350C2×C4⋊C8—71no—
351C2×C4⋊C8—78no—
352C2×#103—71no—
353C2×#103—71no—
354C2×#103—71no—
355C2×#103C2×D711yescharacteristic
356C2×#102—71no—
357C2×#102—71no—
358C2×#102—71no—
359C2×#102C2×D711yescharacteristic
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—42no—
364C23×C7—42no—
365C23×C7—42no—
366C23×C7C2×SD1614yes—
367C23×C7C22×D412yes—
368C23×C7C22×D411yescharacteristic
369C22×D7—22no—
370C22×D7—42no—
371C22×D7—42no—
372C22×D7—42no—
373C7×Q8—22no—
374C7×Q8—22no—
375C7×Q8—42no—
376C7×D4—22no—
377C7×D4—22no—
378C7×D4—48no—
379C7×D4—42no—
380C2×C4×C7—22no—
381C2×C4×C7—24no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—42no—
388C2×C4×C7—42no—
389C2×C4×C7—42no—
390C2×C4×C7C22×D412yes—
391C2×C4×C7C22×D411yescharacteristic
392C2×C4×C7H(5,𝔽2)12yes—
393C2×C4×C72−1+412yes—
394C2×C4×C7C2511yescharacteristic
395C22⋊D7—48no—
396C22⋊D7—48no—
397C22⋊D7—48no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—44no—
404C2×Dic7—42no—
405C2×Dic7—42no—
406C2×Dic7—42no—
407C2×Dic7—48no—
408C2×Dic7C2×SD1614yes—
409C2×Dic7C2×SD1614yes—
410C2×Dic7C2×SD16116yescomplemented
411C2×Dic7C22×D412yes—
412C2×Dic7C22×D412yes—
413C2×Dic7C22×D412yes—
414C2×Dic7C22×D412yes—
415D28—22no—
416D28—22no—
417D28—42no—
418C4×D7—48no—
419Dic14—22no—
420Dic14—22no—
421Dic14—48no—
422Dic14—42no—
423Dic14—48no—
424C7×C8—22no—
425C7×C8—22no—
426C7⋊C8—22no—
427C7⋊C8—22no—
428C2×#41—148no—
429C2×#41—288no—
430C22×Q8—71no—
431C22×Q8—141no—
432C22×Q8—141no—
433C22×Q8C22×D711yescharacteristic
434C22×D4—21no—
435C22×D4—71no—
436C22×D4—141no—
437C22×D4—141no—
438C22×D4—141no—
439C22×D4C22×D711yescharacteristic
440C23×C4—71no—
441C23×C4—71no—
442C23×C4—141no—
443C23×C4—141no—
444C23×C4C22×D711yescharacteristic
445C2×SD16—42no—
446C2×SD16—74no—
447C2×SD16—74no—
448C2×SD16—74no—
449C2×SD16—282no—
450C2×SD16—282no—
451C2×SD16—282no—
452C2×SD16C22×D714yes—
453C22×C8—42no—
454C22×C8—71no—
455C22×C8—71no—
456C22×C8—74no—
457C22×C8—282no—
458C22×C8C22×D711yescharacteristic
459C22×C8C22×D711yescharacteristic
460C22×C8C22×D714yes—
461C4⋊Q8—74no—
462C4⋊Q8—74no—
463C4⋊Q8—74no—
464C4⋊Q8—142no—
465C4⋊Q8—142no—
466C4⋊Q8—142no—
467#127—74no—
468#127—142no—
469#125—148no—
470#124—148no—
471C22⋊Q8—22no—
472C22⋊Q8—74no—
473C22⋊Q8—148no—
474C22⋊Q8—142no—
475C22⋊Q8C22×D714yes—
476#121—22no—
477#121—74no—
478#121—148no—
479#121—142no—
480#121C22×D714yes—
481C4×Q8—74no—
482C4×Q8—74no—
483C4×Q8—142no—
484C4×Q8—148no—
485C4×Q8—142no—
486C4×D4—74no—
487C4×D4—74no—
488C4×D4—148no—
489C4×D4—142no—
490C4×D4—142no—
491#117—148no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—71no—
494C2×C4⋊C4—71no—
495C2×C4⋊C4—141no—
496C2×C4⋊C4—141no—
497C2×C4⋊C4—141no—
498C2×C4⋊C4—141no—
499C2×C4⋊C4—141no—
500C2×C4⋊C4—141no—
501C2×C4⋊C4—141no—
502C2×C4⋊C4C22×D711yescharacteristic
503C2×C4⋊C4C22×D711yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—141no—
507C2×C22⋊C4—141no—
508C2×C22⋊C4—141no—
509C2×C22⋊C4—141no—
510C2×C42—71no—
511C2×C42—71no—
512C2×C42—74no—
513C2×C42—71no—
514C2×C42—71no—
515C2×C42—74no—
516C2×C42—141no—
517C2×C42—141no—
518#106—74no—
519#106—74no—
520#106—74no—
521#106C22×D714yes—
522C4⋊C8—74no—
523C4⋊C8—74no—
524C4⋊C8—74no—
525C4⋊C8—74no—
526#103—74no—
527#103—74no—
528#103—74no—
529#103C22×D714yes—
530#102—74no—
531#102—74no—
532#102—74no—
533#102C22×D714yes—
534C22×C7—22no—
535C22×C7—28no—
536C22×C7—22no—
537C22×C7—42no—
538C22×C7—42no—
539C22×C7—42no—
540C22×C7—84no—
541C22×C7#53712yes—
542C22×C7C22×SD1614yes—
543C22×C7C22×SD1612yes—
544C22×C7#57512yes—
545C22×C7C23×D411yescharacteristic
546C2×D7—42no—
547C2×D7—42no—
548C2×D7—42no—
549C2×D7—84no—
550C4×C7—22no—
551C4×C7—42no—
552C4×C7—42no—
553C4×C7—42no—
554C4×C7#53712yes—
555C4×C7C2×H(5,𝔽2)11yescharacteristic
556C4×C7C2×2−1+411yescharacteristic
557Dic7—22no—
558Dic7—22no—
559Dic7—42no—
560Dic7—42no—
561Dic7—42no—
562Dic7C22×SD1614yes—
563Dic7C22×SD1614yes—
564C24—21no—
565C24—141no—
566C24D4×D711yescharacteristic
567#41—2832no—
568C2×Q8—21no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—72no—
572C2×Q8—144no—
573C2×Q8—144no—
574C2×Q8—141no—
575C2×Q8—142no—
576C2×Q8—142no—
577C2×Q8—284no—
578C2×Q8—284no—
579C2×Q8C23×D712yes—
580C2×D4—24no—
581C2×D4—21no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—44no—
585C2×D4—72no—
586C2×D4—144no—
587C2×D4—144no—
588C2×D4—144no—
589C2×D4—141no—
590C2×D4—142no—
591C2×D4—142no—
592C2×D4—284no—
593C2×D4—284no—
594C2×D4—284no—
595C2×D4C23×D712yes—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—78no—
602C22×C4—74no—
603C22×C4—71no—
604C22×C4—71no—
605C22×C4—71no—
606C22×C4—71no—
607C22×C4—74no—
608C22×C4—144no—
609C22×C4—144no—
610C22×C4—141no—
611C22×C4—141no—
612C22×C4—141no—
613C22×C4—284no—
614C22×C4—284no—
615C22×C4—282no—
616C22×C4D4×D712yes—
617C22×C4D4×D711yescharacteristic
618C22×C4C23×D712yes—
619C22×C4C23×D711yescharacteristic
620SD16—44no—
621SD16—284no—
622SD16—284no—
623SD16—284no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—44no—
627C2×C8—72no—
628C2×C8—72no—
629C2×C8—142no—
630C2×C8—142no—
631C2×C8—284no—
632C2×C8C23×D712yes—
633C2×C8C23×D712yes—
634C4⋊C4—24no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—72no—
638C4⋊C4—72no—
639C4⋊C4—144no—
640C4⋊C4—144no—
641C4⋊C4—144no—
642C4⋊C4—144no—
643C4⋊C4—144no—
644C4⋊C4—144no—
645C4⋊C4—144no—
646C4⋊C4—141no—
647C4⋊C4—141no—
648C4⋊C4C23×D712yes—
649C4⋊C4C23×D712yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—144no—
653C22⋊C4—144no—
654C22⋊C4—144no—
655C22⋊C4—144no—
656C42—74no—
657C42—72no—
658C42—74no—
659C42—72no—
660C42—72no—
661C42—72no—
662C42—144no—
663C42—144no—
664C2×C7—24no—
665C2×C7—82no—
666C2×C7#324614yescomplemented
667C2×C7C2×#53711yescharacteristic
668C2×C7C23×SD1611yescharacteristic
669C2×C7C2×#57511yescharacteristic
670D7—82no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—142no—
678C23—282no—
679C23—282no—
680C23—282no—
681C23D7×SD1614yes—
682C23C2×D4×D712yes—
683C23C2×D4×D711yescharacteristic
684Q8—22no—
685Q8—22no—
686Q8—42no—
687Q8—142no—
688Q8—142no—
689Q8—288no—
690Q8—288no—
691Q8—282no—
692D4—22no—
693D4—22no—
694D4—48no—
695D4—42no—
696D4—142no—
697D4—142no—
698D4—288no—
699D4—288no—
700D4—288no—
701D4—282no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—74no—
713C2×C4—74no—
714C2×C4—716no—
715C2×C4—72no—
716C2×C4—72no—
717C2×C4—72no—
718C2×C4—72no—
719C2×C4—142no—
720C2×C4—142no—
721C2×C4—142no—
722C2×C4—142no—
723C2×C4—142no—
724C2×C4—288no—
725C2×C4—288no—
726C2×C4—284no—
727C2×C4—282no—
728C2×C4—282no—
729C2×C4—282no—
730C2×C4C2×D4×D712yes—
731C2×C4C2×D4×D711yescharacteristic
732C2×C4#654812yes—
733C2×C4#655412yes—
734C2×C4C24×D711yescharacteristic
735C8—22no—
736C8—22no—
737C8—142no—
738C8—142no—
739C7C2×#324611yescharacteristic, complemented, Sylow
740C22—22no—
741C22—28no—
742C22—22no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—84no—
747C22—282no—
748C22—282no—
749C22—282no—
750C22—564no—
751C22#9028812yes—
752C22C2×D7×SD1614yes—
753C22C2×D7×SD1612yes—
754C22#9045912yes—
755C22C22×D4×D711yescharacteristic
756C4—22no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—74no—
761C4—74no—
762C4—142no—
763C4—142no—
764C4—282no—
765C4—282no—
766C4—282no—
767C4#9028812yes—
768C4C2×#654811yescharacteristic
769C4C2×#655411yescharacteristic
770C2—24no—
771C2—82no—
772C2—562no—
773C2#1173808514yesdirect product factor
774C2C2×#9028811yescharacteristic
775C2C22×D7×SD1611yescharacteristic
776C2C2×#9045911yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#465C2
socleC23×C7C22×D4
prime radicalC2×#90287C2
hypercenterC2×#465D7
hypocenterC7C2×#3246
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#90313C2semidirect
3. C2×C7×#465C2semidirect
4. C2×#89935C2semidirect
5. C2×#89934C2semidirect
6. C2×#89886C2semidirect
7. C22×Dic7⋊C8C2semidirect
8. C2×#89820C2semidirect
9. C2×#89813C2semidirect
10. #11738085C2direct (N × H)
11. C2×#89626C2semidirect
12. C2×#89642C2semidirect
13. C2×#89590C2semidirect
14. C2×#89563C2semidirect
15. C2×#89534C2semidirect
16. C2×#89533C2semidirect
35. #90313C22semidirect
48. C7×#465C22semidirect
54. #89935C22semidirect
55. #89934C22semidirect
56. #89886C22semidirect
64. C2×Dic7⋊C8C22semidirect
65. #89820C22semidirect
66. #89813C22semidirect
71. #89642C22semidirect
72. #89626C22semidirect
73. #89590C22semidirect
74. #89563C22semidirect
75. #89534C22semidirect
76. #89533C22semidirect
194. C2×#465D7semidirect
234. C22×Dic7SD16semidirect
338. #465C2×D7semidirect
410. C2×Dic7C2×SD16semidirect
666. C2×C7#3246semidirect
739. C7C2×#3246semidirect
773. C2#11738085direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903132
C2×#902872
C2×C7×#4652
C2×#899352
C2×#899342
C2×#898862
C22×Dic7⋊C82
C2×#898202
C2×#898132
#117380852
C2×#896262
C2×#896422
C2×#895902
C2×#895632
C2×#895342
C2×#895332
C2×#32467