Finite Group Databasebeta

← C2×#11737694 #14230252

Subgroups — C2×#11737694 #14230252

Order 1792.

2198 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90525C211yesmaximal, characteristic
2C2×#90332C211yesmaximal, characteristic, complemented
3C2×C7×#452C211yesmaximal, characteristic, complemented
4C2×#90005C211yesmaximal, characteristic, complemented
5C2×#89959C211yesmaximal, characteristic, complemented
6C2×Q16×Dic7C211yesmaximal, characteristic, complemented
7C2×#89943C211yesmaximal, characteristic, complemented
8C2×#89935C211yesmaximal, characteristic, complemented
9C2×#89820C211yesmaximal, characteristic, complemented
10#11737694C2116yesmaximal, direct product factor
11C2×#89576C211yesmaximal, characteristic, complemented
12C2×#89563C211yesmaximal, characteristic, complemented
13C2×#89556C211yesmaximal, characteristic, complemented
14C2×#89532C211yesmaximal, characteristic, complemented
15C2×(C22⋊D7)⋊C8C211yesmaximal, characteristic, complemented
16C2×#89509C211yesmaximal, characteristic, complemented
17C22×C7×#41C2211yescharacteristic
18C22×#1161C2211yescharacteristic
19C22×C7×Q16C2211yescharacteristic
20C22×C7×SD16C2211yescharacteristic
21C2×C7×C22⋊Q8C2211yescharacteristic
22#90525—24no—
23#90525C2218yes—
24C2×#6509C2211yescharacteristic
25C2×Q8×Dic7C2211yescharacteristic
26C2×Q8×Dic7C2211yescharacteristic
27C22×#1143C2211yescharacteristic
28C2×#6503—21no—
29C2×#6503C2211yescharacteristic
30C2×#6501—21no—
31C2×#6501C2211yescharacteristic
32C2×#6493—21no—
33C2×#6493C2211yescharacteristic
34C2×C4×C22⋊D7—21no—
35C2×C4×C22⋊D7C2211yescharacteristic
36C2×#6489C2211yescharacteristic
37C23×C7⋊C8C2211yescharacteristic
38C22×C8×D7C2211yescharacteristic
39#90332—24no—
40#90332C2218yescomplemented
41C2×#6461—21no—
42C2×#6455C2211yescharacteristic
43C2×#6451C2211yescharacteristic
44C2×#6450—21no—
45C2×#6448—21no—
46C2×#6442—21no—
47C7×#452C2218yescomplemented
48C2×C7×#103C2211yescharacteristic
49C2×C7×#102C2211yescharacteristic
50C2×C7×C22⋊C8C2211yescharacteristic
51#90005C2218yescomplemented
52C2×#6409C2211yescharacteristic
53C2×#6409C2211yescharacteristic
54C2×#6409C2211yescharacteristic
55C2×#6406C2211yescharacteristic
56C2×#6406C2211yescharacteristic
57#89959C2218yescomplemented
58Q16×Dic7C2218yescomplemented
59#89943C2218yescomplemented
60#89935C2218yescomplemented
61C2×#6395C2211yescharacteristic
62C2×#6395C2211yescharacteristic
63C2×(C2×D7)⋊C8C2211yescharacteristic
64C2×#6392C2211yescharacteristic
65C2×#6391C2211yescharacteristic
66C2×Dic7⋊C8C2211yescharacteristic
67C2×C8×Dic7C2211yescharacteristic
68#89820C2218yescomplemented
69C2×#6383C2211yescharacteristic
70C2×#6382C2211yescharacteristic
71#89576C2218yescomplemented
72#89563C2218yescomplemented
73#89556C2218yescomplemented
74#89532C2218yescomplemented
75#89509C2218yescomplemented
76(C22⋊D7)⋊C8C2218yescomplemented
77C2×#3304—71nomaximal, Sylow
78C2×C7×#41—22no—
79C2×C7×#41—24no—
80C2×C7×#41—42no—
81C2×C7×#41C2314yes—
82C22×C7×Q8C2311yescharacteristic
83C22×C7×Q8C2311yescharacteristic
84C22×C7×D4—21no—
85C22×C7×D4C2311yescharacteristic
86C23×C4×C7—21no—
87C23×C4×C7C2311yescharacteristic
88C22×C22⋊D7—21no—
89C22×C22⋊D7—21no—
90C22×C22⋊D7—21no—
91C22×C22⋊D7—21no—
92C22×C22⋊D7D411yescharacteristic
93C2×#1161—22no—
94C2×#1161—24no—
95C2×#1161—42no—
96C2×#1161C2314yes—
97C22×D28—21no—
98C22×D28C2311yescharacteristic
99C22×C4×D7—21no—
100C22×C4×D7C2311yescharacteristic
101C22×Dic14—21no—
102C2×C7×Q16—24no—
103C2×C7×Q16C2314yes—
104C2×C7×SD16—42no—
105C2×C7×SD16C2314yes—
106C22×C7×C8C2311yescharacteristic
107C22×C7×C8C2311yescharacteristic
108C7×C22⋊Q8—22no—
109C7×C22⋊Q8C2314yes—
110C2×C7×C4⋊C4—21no—
111C2×C7×C4⋊C4C2311yescharacteristic
112C2×C7×C22⋊C4—21no—
113C2×C22⋊Dic7—21no—
114C2×C22⋊Dic7—21no—
115C2×C22⋊Dic7D411yescharacteristic
116#6509—22no—
117#6509C2314yes—
118Q8×Dic7—22no—
119Q8×Dic7—22no—
120Q8×Dic7C2314yes—
121Q8×Dic7C2314yes—
122C2×#1143—42no—
123C2×#1143C2314yes—
124#6503—28no—
125#6503—22no—
126#6503C2314yes—
127#6501—22no—
128#6501—28no—
129#6501C2314yes—
130#6493—22no—
131#6493—28no—
132#6493C2314yes—
133C4×C22⋊D7—28no—
134C4×C22⋊D7D414yes—
135C4×C22⋊D7C2314yes—
136C2×(C2×D7)⋊C4—21no—
137C2×(C2×D7)⋊C4—21no—
138C2×(C2×D7)⋊C4—21no—
139C2×(C2×D7)⋊C4D411yescharacteristic
140#6489—22no—
141#6489C2314yes—
142C2×C4⋊Dic7—21no—
143C2×C4⋊Dic7—21no—
144C2×C4⋊Dic7C2311yescharacteristic
145C2×C4⋊Dic7C2311yescharacteristic
146C2×C4⋊Dic7C2311yescharacteristic
147C2×Dic7⋊C4—21no—
148C2×Dic7⋊C4—21no—
149C2×Dic7⋊C4D411yescharacteristic
150C2×C4×Dic7—21no—
151C2×C4×Dic7—21no—
152C2×C4×Dic7—21no—
153C2×C4×Dic7—21no—
154C2×C4×Dic7C2311yescharacteristic
155C22×C7⋊C8—42no—
156C22×C7⋊C8C2311yescharacteristic
157C22×C7⋊C8C2311yescharacteristic
158C22×C7⋊C8C2314yes—
159C2×C8×D7—42no—
160C2×C8×D7C2314yes—
161#6461—28no—
162#6455—22no—
163#6455C2314yes—
164#6451—22no—
165#6451C2314yes—
166#6450—28no—
167#6448—28no—
168#6442—28no—
169C7×#103C2314yes—
170C7×#102C2314yes—
171C7×C22⋊C8C2314yes—
172#6409C2314yes—
173#6409C2314yes—
174#6409C2314yes—
175#6406C2314yes—
176#6406C2314yes—
177#6395C2314yes—
178#6395C2314yes—
179(C2×D7)⋊C8C2314yes—
180#6392C2314yes—
181#6391C2314yes—
182Dic7⋊C8C2314yes—
183C8×Dic7C2314yes—
184#6383C2314yes—
185#6382C2314yes—
186C2×#556—71no—
187C2×#550—71no—
188#3304—716no—
189C2×#486—71no—
190C2×#482—71no—
191C2×#482—71no—
192C2×#475—71no—
193C2×#465—71no—
194C2×#465—71no—
195C2×#460—71no—
196C2×#452—71no—
197C2×#452D711yescharacteristic, complemented
198C2×C4×Q16—71no—
199C2×C8×D4—71no—
200C2×#416—71no—
201C2×#416—71no—
202C24×C7—21no—
203C24×C7C2×D411yescharacteristic
204C23×D7—21no—
205C23×D7C2×D411yescharacteristic
206C7×#41—28no—
207C7×#41—44no—
208C7×#41—48no—
209C2×C7×Q8—21no—
210C2×C7×Q8—21no—
211C2×C7×Q8—22no—
212C2×C7×Q8—22no—
213C2×C7×Q8—22no—
214C2×C7×Q8#4114yes—
215C2×C7×Q8C2412yes—
216C2×C7×Q8C2412yes—
217C2×C7×D4—24no—
218C2×C7×D4—21no—
219C2×C7×D4—22no—
220C2×C7×D4—22no—
221C2×C7×D4—44no—
222C2×C7×D4C2412yes—
223C22×C4×C7—21no—
224C22×C4×C7—22no—
225C22×C4×C7—22no—
226C22×C4×C7—21no—
227C22×C4×C7—21no—
228C22×C4×C7—24no—
229C22×C4×C7—44no—
230C22×C4×C7C2×D411yescharacteristic
231C22×C4×C7C2×D412yes—
232C22×C4×C7C2412yes—
233C22×C4×C7C2411yescharacteristic
234C2×C22⋊D7—24no—
235C2×C22⋊D7—24no—
236C2×C22⋊D7—24no—
237C2×C22⋊D7—24no—
238C2×C22⋊D7—24no—
239C2×C22⋊D7—44no—
240C2×C22⋊D7—82no—
241C2×C22⋊D7—82no—
242C2×C22⋊D7—82no—
243C2×C22⋊D7C2×D414yes—
244C22×Dic7—21no—
245C22×Dic7—21no—
246C22×Dic7—21no—
247C22×Dic7C2×D411yescharacteristic
248C22×Dic7C2×D411yescharacteristic
249C22×Dic7C2×D411yescharacteristic
250#1161—28no—
251#1161—44no—
252#1161—48no—
253C2×D28—22no—
254C2×D28—22no—
255C2×D28—24no—
256C2×D28—21no—
257C2×D28—44no—
258C2×D28C2412yes—
259C2×C4×D7—22no—
260C2×C4×D7—22no—
261C2×C4×D7—24no—
262C2×C4×D7—44no—
263C2×C4×D7C2×D412yes—
264C2×C4×D7C2412yes—
265C2×Dic14—24no—
266C2×Dic14—44no—
267C7×Q16—28no—
268C7×SD16—44no—
269C2×C7×C8—22no—
270C2×C7×C8—22no—
271C2×C7×C8C2412yes—
272C2×C7×C8C2412yes—
273C7×C4⋊C4—24no—
274C7×C4⋊C4—21no—
275C7×C4⋊C4C2412yes—
276C7×C22⋊C4—24no—
277C22⋊Dic7—24no—
278C22⋊Dic7—24no—
279C22⋊Dic7C2×D414yes—
280#1143—44no—
281(C2×D7)⋊C4—24no—
282(C2×D7)⋊C4—24no—
283(C2×D7)⋊C4—24no—
284(C2×D7)⋊C4C2×D414yes—
285C4⋊Dic7—21no—
286C4⋊Dic7—21no—
287C4⋊Dic7—21no—
288C4⋊Dic7—24no—
289C4⋊Dic7—24no—
290C4⋊Dic7C2412yes—
291C4⋊Dic7C2412yes—
292C4⋊Dic7C2412yes—
293Dic7⋊C4—24no—
294Dic7⋊C4—24no—
295Dic7⋊C4C2×D414yes—
296C4×Dic7—24no—
297C4×Dic7—24no—
298C4×Dic7—24no—
299C4×Dic7—24no—
300C4×Dic7C2×D412yes—
301C4×Dic7C2412yes—
302C2×C7⋊C8—22no—
303C2×C7⋊C8—22no—
304C2×C7⋊C8—44no—
305C2×C7⋊C8C2412yes—
306C2×C7⋊C8C2412yes—
307C8×D7—44no—
308C22×#41—71no—
309C22×#41C2×D711yescharacteristic
310C22×Q16C2×D711yescharacteristic
311C22×SD16—71no—
312C22×SD16C2×D711yescharacteristic
313C23×C8—71no—
314C23×C8—71no—
315#556—78no—
316#556—144no—
317#550—78no—
318#550—144no—
319C2×C4⋊Q8—71no—
320C2×#127—71no—
321C2×#127—141no—
322C2×#126—141no—
323C2×#126—141no—
324C2×#124—141no—
325C2×C22⋊Q8—71no—
326C2×C22⋊Q8C2×D711yescharacteristic
327C2×#121—71no—
328C2×#121—71no—
329C2×#121—141no—
330C2×#121—141no—
331C2×C4×Q8—71no—
332C2×C4×Q8—71no—
333C2×C4×Q8—141no—
334C2×C4×D4—71no—
335C2×C4×D4—141no—
336C2×#117—71no—
337C2×#117—71no—
338#486—78no—
339#482—78no—
340#482—78no—
341#475—78no—
342#465—78no—
343#465—78no—
344#460—78no—
345#452—78no—
346#452C2×D718yescomplemented
347C4×Q16—78no—
348C8×D4—78no—
349C2×#107—71no—
350C2×#106—71no—
351C2×#106—71no—
352C2×C4⋊C8—71no—
353#416—78no—
354#416—78no—
355C2×#103—71no—
356C2×#103—71no—
357C2×#103—71no—
358C2×#103C2×D711yescharacteristic
359C2×#102—71no—
360C2×#102—71no—
361C2×#102—71no—
362C2×#102—71no—
363C2×#102—71no—
364C2×#102C2×D711yescharacteristic
365C2×C22⋊C8—71no—
366C2×C22⋊C8C2×D711yescharacteristic
367C2×C4×C8—71no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—42no—
373C23×C7—42no—
374C23×C7—42no—
375C23×C7C22×D412yes—
376C23×C7C22×D411yescharacteristic
377C22×D7—22no—
378C22×D7—22no—
379C22×D7—22no—
380C22×D7—22no—
381C22×D7—42no—
382C22×D7—42no—
383C22×D7—42no—
384C22×D7C22×D412yes—
385C7×Q8—24no—
386C7×Q8—22no—
387C7×Q8—22no—
388C7×Q8—22no—
389C7×Q8—42no—
390C7×Q8C2×#4114yes—
391C7×D4—22no—
392C7×D4—22no—
393C7×D4—48no—
394C7×D4—42no—
395C2×C4×C7—24no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—24no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—48no—
404C2×C4×C7—42no—
405C2×C4×C7—42no—
406C2×C4×C7C22×D412yes—
407C2×C4×C7C22×D411yescharacteristic
408C2×C4×C7C2×#4112yes—
409C2×C4×C7H(5,𝔽2)12yes—
410C2×C4×C7C2511yescharacteristic
411C22⋊D7—28no—
412C22⋊D7—48no—
413C22⋊D7—84no—
414C22⋊D7—84no—
415C22⋊D7—84no—
416C2×Dic7—22no—
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—42no—
422C2×Dic7—42no—
423C2×Dic7—42no—
424C2×Dic7#13514yes—
425C2×Dic7C22×D412yes—
426C2×Dic7C22×D412yes—
427C2×Dic7C22×D412yes—
428D28—22no—
429D28—22no—
430D28—48no—
431D28—42no—
432C4×D7—24no—
433C4×D7—22no—
434C4×D7—22no—
435C4×D7—48no—
436Dic14—48no—
437C7×C8—22no—
438C7×C8—22no—
439C7⋊C8—22no—
440C7⋊C8—22no—
441C2×#41—22no—
442C2×#41—24no—
443C2×#41—42no—
444C2×#41—74no—
445C2×#41—142no—
446C2×#41—144no—
447C2×#41—282no—
448C2×#41C22×D714yes—
449C22×Q8—141no—
450C22×Q8C22×D711yescharacteristic
451C22×Q8C22×D711yescharacteristic
452C22×D4—21no—
453C22×D4—71no—
454C22×D4—71no—
455C22×D4—141no—
456C22×D4—141no—
457C22×D4—141no—
458C22×D4—141no—
459C22×D4—141no—
460C22×D4C22×D711yescharacteristic
461C23×C4—21no—
462C23×C4—71no—
463C23×C4—141no—
464C23×C4C22×D711yescharacteristic
465C2×Q16—24no—
466C2×Q16C22×D714yes—
467C2×SD16—42no—
468C2×SD16—74no—
469C2×SD16—282no—
470C2×SD16C22×D714yes—
471C22×C8—71no—
472C22×C8—71no—
473C22×C8—74no—
474C22×C8—74no—
475C22×C8—282no—
476C22×C8—282no—
477C22×C8C22×D711yescharacteristic
478C22×C8C22×D711yescharacteristic
479C4⋊Q8—74no—
480C4⋊Q8—142no—
481#127—74no—
482#127—142no—
483#127—148no—
484#126—148no—
485#126—148no—
486#124—148no—
487C22⋊Q8—22no—
488C22⋊Q8—74no—
489C22⋊Q8—142no—
490C22⋊Q8C22×D714yes—
491#121—74no—
492#121—74no—
493#121—148no—
494#121—148no—
495#121—142no—
496#121—142no—
497C4×Q8—74no—
498C4×Q8—74no—
499C4×Q8—142no—
500C4×Q8—142no—
501C4×Q8—148no—
502C4×D4—74no—
503C4×D4—74no—
504C4×D4—148no—
505#117—74no—
506#117—74no—
507#117—142no—
508#117—142no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—71no—
511C2×C4⋊C4—71no—
512C2×C4⋊C4—71no—
513C2×C4⋊C4—71no—
514C2×C4⋊C4—141no—
515C2×C4⋊C4—141no—
516C2×C4⋊C4—141no—
517C2×C4⋊C4—141no—
518C2×C4⋊C4C22×D711yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—71no—
521C2×C22⋊C4—71no—
522C2×C22⋊C4—141no—
523C2×C22⋊C4—141no—
524C2×C22⋊C4—141no—
525C2×C22⋊C4—141no—
526C2×C22⋊C4—141no—
527C2×C42—71no—
528C2×C42—141no—
529C2×C42—141no—
530C2×C42—141no—
531C2×C42—141no—
532#107—74no—
533#106—74no—
534#106—74no—
535C4⋊C8—74no—
536#103—74no—
537#103—74no—
538#103—74no—
539#103C22×D714yes—
540#102—74no—
541#102—74no—
542#102—74no—
543#102—74no—
544#102—74no—
545#102C22×D714yes—
546C22⋊C8—74no—
547C22⋊C8C22×D714yes—
548C4×C8—74no—
549C22×C7—22no—
550C22×C7—22no—
551C22×C7—22no—
552C22×C7—44no—
553C22×C7—42no—
554C22×C7—42no—
555C22×C7—42no—
556C22×C7—84no—
557C22×C7#54612yes—
558C22×C7C2×#13512yes—
559C22×C7#57712yes—
560C22×C7C23×D411yescharacteristic
561C2×D7—22no—
562C2×D7—22no—
563C2×D7—22no—
564C2×D7—44no—
565C2×D7—42no—
566C2×D7—42no—
567C2×D7—42no—
568C2×D7—84no—
569C4×C7—24no—
570C4×C7—22no—
571C4×C7—42no—
572C4×C7—42no—
573C4×C7#54612yes—
574C4×C7C22×#4111yescharacteristic
575C4×C7C2×H(5,𝔽2)11yescharacteristic
576Dic7—22no—
577Dic7—22no—
578Dic7—42no—
579Dic7—42no—
580Dic7—42no—
581Dic7C2×#13514yes—
582C24—21no—
583C24—71no—
584C24—141no—
585C24D4×D711yescharacteristic
586#41—28no—
587#41—44no—
588#41—48no—
589#41—148no—
590#41—284no—
591#41—288no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—22no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8—144no—
598C2×Q8—284no—
599C2×Q8#115914yes—
600C2×Q8C23×D712yes—
601C2×Q8C23×D712yes—
602C2×D4—24no—
603C2×D4—21no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—44no—
607C2×D4—74no—
608C2×D4—72no—
609C2×D4—144no—
610C2×D4—144no—
611C2×D4—144no—
612C2×D4—144no—
613C2×D4—144no—
614C2×D4—144no—
615C2×D4—141no—
616C2×D4—142no—
617C2×D4—142no—
618C2×D4—284no—
619C2×D4—284no—
620C2×D4—562no—
621C2×D4—562no—
622C2×D4—562no—
623C2×D4C23×D712yes—
624C22×C4—21no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—24no—
630C22×C4—44no—
631C22×C4—71no—
632C22×C4—71no—
633C22×C4—71no—
634C22×C4—72no—
635C22×C4—72no—
636C22×C4—144no—
637C22×C4—142no—
638C22×C4—142no—
639C22×C4—141no—
640C22×C4—141no—
641C22×C4—141no—
642C22×C4—284no—
643C22×C4D4×D712yes—
644C22×C4D4×D711yescharacteristic
645C22×C4C23×D712yes—
646C22×C4C23×D711yescharacteristic
647Q16—28no—
648SD16—44no—
649SD16—284no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—72no—
653C2×C8—72no—
654C2×C8—142no—
655C2×C8—142no—
656C2×C8—284no—
657C2×C8—284no—
658C2×C8C23×D712yes—
659C2×C8C23×D712yes—
660C4⋊C4—24no—
661C4⋊C4—21no—
662C4⋊C4—74no—
663C4⋊C4—72no—
664C4⋊C4—72no—
665C4⋊C4—72no—
666C4⋊C4—144no—
667C4⋊C4—144no—
668C4⋊C4—144no—
669C4⋊C4—144no—
670C4⋊C4—141no—
671C4⋊C4—141no—
672C4⋊C4—141no—
673C4⋊C4C23×D712yes—
674C22⋊C4—24no—
675C22⋊C4—74no—
676C22⋊C4—74no—
677C22⋊C4—144no—
678C22⋊C4—144no—
679C22⋊C4—144no—
680C22⋊C4—144no—
681C22⋊C4—144no—
682C42—72no—
683C42—72no—
684C42—144no—
685C42—144no—
686C42—144no—
687C42—144no—
688C2×C7—42no—
689C2×C7—82no—
690C2×C7#330414yescomplemented
691C2×C7C2×#54611yescharacteristic
692C2×C7C22×#13511yescharacteristic
693C2×C7C2×#57711yescharacteristic
694D7—42no—
695D7—82no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—72no—
704C23—142no—
705C23—142no—
706C23—142no—
707C23—142no—
708C23—282no—
709C23—282no—
710C23—282no—
711C23C2×D4×D712yes—
712C23C2×D4×D711yescharacteristic
713Q8—24no—
714Q8—22no—
715Q8—22no—
716Q8—22no—
717Q8—42no—
718Q8—288no—
719Q8C2×#115914yes—
720D4—22no—
721D4—22no—
722D4—48no—
723D4—42no—
724D4—148no—
725D4—142no—
726D4—142no—
727D4—288no—
728D4—288no—
729D4—282no—
730D4—564no—
731D4—564no—
732D4—564no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—48no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—74no—
745C2×C4—72no—
746C2×C4—72no—
747C2×C4—72no—
748C2×C4—142no—
749C2×C4—142no—
750C2×C4—144no—
751C2×C4—142no—
752C2×C4—142no—
753C2×C4—142no—
754C2×C4—142no—
755C2×C4—142no—
756C2×C4—288no—
757C2×C4—282no—
758C2×C4—282no—
759C2×C4—282no—
760C2×C4C2×D4×D712yes—
761C2×C4C2×D4×D711yescharacteristic
762C2×C4C2×#115912yes—
763C2×C4#654812yes—
764C2×C4C24×D711yescharacteristic
765C8—22no—
766C8—22no—
767C8—142no—
768C8—142no—
769C7C2×#330411yescharacteristic, complemented, Sylow
770C22—22no—
771C22—22no—
772C22—22no—
773C22—44no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—84no—
778C22—142no—
779C22—142no—
780C22—142no—
781C22—284no—
782C22—282no—
783C22—282no—
784C22—282no—
785C22—564no—
786C22#9028212yes—
787C22D7×#13512yes—
788C22#9046912yes—
789C22C22×D4×D711yescharacteristic
790C4—22no—
791C4—24no—
792C4—42no—
793C4—42no—
794C4—74no—
795C4—142no—
796C4—142no—
797C4—282no—
798C4—282no—
799C4—282no—
800C4#9028212yes—
801C4C22×#115911yescharacteristic
802C4C2×#654811yescharacteristic
803C2—42no—
804C2—82no—
805C2—282no—
806C2—562no—
807C2#1173769414yesdirect product factor
808C2C2×#9028211yescharacteristic
809C2C2×D7×#13511yescharacteristic
810C2C2×#9046911yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#452C2
socleC23×C7C22×D4
prime radicalC2×#90525C2
hypercenterC2×#452D7
hypocenterC7C2×#3304
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
2. C2×#90332C2semidirect
3. C2×C7×#452C2semidirect
4. C2×#90005C2semidirect
5. C2×#89959C2semidirect
6. C2×Q16×Dic7C2semidirect
7. C2×#89943C2semidirect
8. C2×#89935C2semidirect
9. C2×#89820C2semidirect
10. #11737694C2direct (N × H)
11. C2×#89576C2semidirect
12. C2×#89563C2semidirect
13. C2×#89556C2semidirect
14. C2×#89532C2semidirect
15. C2×(C22⋊D7)⋊C8C2semidirect
16. C2×#89509C2semidirect
40. #90332C22semidirect
47. C7×#452C22semidirect
51. #90005C22semidirect
57. #89959C22semidirect
58. Q16×Dic7C22semidirect
59. #89943C22semidirect
60. #89935C22semidirect
68. #89820C22semidirect
71. #89576C22semidirect
72. #89563C22semidirect
73. #89556C22semidirect
74. #89532C22semidirect
75. #89509C22semidirect
76. (C22⋊D7)⋊C8C22semidirect
197. C2×#452D7semidirect
346. #452C2×D7semidirect
690. C2×C7#3304semidirect
769. C7C2×#3304semidirect
807. C2#11737694direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#905252
C2×#903322
C2×C7×#4522
C2×#900052
C2×#899592
C2×Q16×Dic72
C2×#899432
C2×#899352
C2×#898202
#117376942
C2×#895762
C2×#895632
C2×#895562
C2×#895322
C2×(C22⋊D7)⋊C82
C2×#895092
C2×#33047