Finite Group Databasebeta

← C2×#11736295 #14230243

Subgroups — C2×#11736295 #14230243

Order 1792.

2210 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×#90515C211yesmaximal, characteristic, complemented
2C2×#90223C211yesmaximal, characteristic, complemented
3C2×C7×#416C211yesmaximal, characteristic, complemented
4C2×#90010C211yesmaximal, characteristic, complemented
5C2×#89886C211yesmaximal, characteristic, complemented
6C2×C8×C22⋊D7C211yesmaximal, characteristic, complemented
7C2×#89768C211yesmaximal, characteristic, complemented
8#11736295C2116yesmaximal, direct product factor
9C2×#89590C211yesmaximal, characteristic, complemented
10C2×#89587C211yesmaximal, characteristic, complemented
11C2×#89579C211yesmaximal, characteristic, complemented
12C2×#89564C211yesmaximal, characteristic, complemented
13C2×#89553C211yesmaximal, characteristic, complemented
14C2×#89544C211yesmaximal, characteristic, complemented
15C2×#89533C211yesmaximal, characteristic, complemented
16C2×#89528C211yesmaximal, characteristic, complemented
17C22×C7×#41C2211yescharacteristic
18C22×#1159C2211yescharacteristic
19C23×C7×C8C2211yescharacteristic
20C2×C7×#117C2211yescharacteristic
21#90515—24no—
22#90515C2218yescomplemented
23C2×#6509C2211yescharacteristic
24C2×#6507C2211yescharacteristic
25C22×#1143C2211yescharacteristic
26C2×#6502—21no—
27C2×#6498—21no—
28C2×D4×Dic7C2211yescharacteristic
29C22×#1141C2211yescharacteristic
30C2×#6493C2211yescharacteristic
31C2×#6492—21no—
32C2×C4×C22⋊D7C2211yescharacteristic
33C2×#6487C2211yescharacteristic
34C22×Dic7⋊C4—21no—
35C22×#1132C2211yescharacteristic
36C22×C8×D7C2211yescharacteristic
37#90223—24no—
38#90223C2218yescomplemented
39C2×#6458C2211yescharacteristic
40C2×#6456C2211yescharacteristic
41C2×#6455C2211yescharacteristic
42C2×#6451C2211yescharacteristic
43C2×#6448—21no—
44C2×#6447—21no—
45C2×#6438—21no—
46C2×#6435—21no—
47C7×#416C2218yescomplemented
48C2×C7×#103C2211yescharacteristic
49C2×C7×#103C2211yescharacteristic
50C2×C7×#102C2211yescharacteristic
51C2×C7×#102C2211yescharacteristic
52#90010C2218yescomplemented
53C2×#6409C2211yescharacteristic
54C2×#6406C2211yescharacteristic
55C2×C22⋊(C7⋊C8)C2211yescharacteristic
56#89886C2218yescomplemented
57C2×#6395C2211yescharacteristic
58C8×C22⋊D7C2218yescomplemented
59C2×(C2×D7)⋊C8C2211yescharacteristic
60C2×#6391C2211yescharacteristic
61C2×#6390C2211yescharacteristic
62C2×Dic7⋊C8C2211yescharacteristic
63C2×C8×Dic7C2211yescharacteristic
64#89768C2218yescomplemented
65C2×#6384C2211yescharacteristic
66C2×#6384C2211yescharacteristic
67C2×#6382C2211yescharacteristic
68C2×#6381C2211yescharacteristic
69#89590C2218yescomplemented
70#89587C2218yescomplemented
71#89579C2218yescomplemented
72#89564C2218yescomplemented
73#89553C2218yescomplemented
74#89544C2218yescomplemented
75#89533C2218yescomplemented
76#89528C2218yescomplemented
77C2×#3303—71nomaximal, Sylow
78C2×C7×#41—22no—
79C2×C7×#41—24no—
80C2×C7×#41—42no—
81C2×C7×#41C2314yes—
82C22×C7×Q8C2311yescharacteristic
83C22×C7×D4—21no—
84C22×C7×D4C2311yescharacteristic
85C23×C4×C7—21no—
86C23×C4×C7C2311yescharacteristic
87C22×C22⋊D7—21no—
88C22×C22⋊D7—21no—
89C22×C22⋊D7D411yescharacteristic
90C23×Dic7—21no—
91C23×Dic7—21no—
92C2×#1159—24no—
93C2×#1159—22no—
94C2×#1159—42no—
95C2×#1159C2314yes—
96C22×D28—21no—
97C22×D28C2311yescharacteristic
98C22×C4×D7—21no—
99C22×C4×D7C2311yescharacteristic
100C22×Dic14—21no—
101C22×Dic14C2311yescharacteristic
102C22×C7×C8—42no—
103C22×C7×C8C2311yescharacteristic
104C22×C7×C8C2311yescharacteristic
105C22×C7×C8C2314yes—
106C7×#117—22no—
107C7×#117C2314yes—
108C2×C7×C4⋊C4C2311yescharacteristic
109C2×C7×C4⋊C4C2311yescharacteristic
110C2×C7×C22⋊C4—21no—
111C2×C42×C7—21no—
112C2×C22⋊Dic7—21no—
113C2×C22⋊Dic7—21no—
114C2×C22⋊Dic7D411yescharacteristic
115#6509—22no—
116#6509C2314yes—
117#6507—22no—
118#6507C2314yes—
119C2×#1143—42no—
120C2×#1143C2314yes—
121#6502—28no—
122#6498—28no—
123D4×Dic7—22no—
124D4×Dic7C2314yes—
125C2×#1141—24no—
126C2×#1141C2314yes—
127#6493—22no—
128#6493C2314yes—
129#6492—28no—
130C4×C22⋊D7D414yes—
131C4×C22⋊D7C2314yes—
132C2×(C2×D7)⋊C4—21no—
133C2×(C2×D7)⋊C4—21no—
134C2×(C2×D7)⋊C4—21no—
135C2×(C2×D7)⋊C4—21no—
136C2×(C2×D7)⋊C4—21no—
137C2×(C2×D7)⋊C4D411yescharacteristic
138C2×C4⋊Dic7C2311yescharacteristic
139C2×C4⋊Dic7C2311yescharacteristic
140#6487—22no—
141#6487C2314yes—
142C2×Dic7⋊C4—21no—
143C2×Dic7⋊C4—21no—
144C2×Dic7⋊C4—21no—
145C2×Dic7⋊C4—21no—
146C2×Dic7⋊C4—21no—
147C2×Dic7⋊C4—28no—
148C2×Dic7⋊C4D411yescharacteristic
149C2×C4×Dic7—21no—
150C2×C4×Dic7C2311yescharacteristic
151C22×C7⋊C8C2311yescharacteristic
152C22×C7⋊C8C2311yescharacteristic
153C2×#1132—42no—
154C2×#1132C2314yes—
155C2×C8×D7—42no—
156C2×C8×D7C2314yes—
157#6458—22no—
158#6458C2314yes—
159#6456—22no—
160#6456C2314yes—
161#6455—22no—
162#6455C2314yes—
163#6451—22no—
164#6451C2314yes—
165#6448—28no—
166#6447—28no—
167#6438—28no—
168#6435—28no—
169C7×#103C2314yes—
170C7×#103C2314yes—
171C7×#102C2314yes—
172C7×#102C2314yes—
173#6409C2314yes—
174#6406C2314yes—
175C22⋊(C7⋊C8)C2314yes—
176#6395C2314yes—
177(C2×D7)⋊C8C2314yes—
178#6391C2314yes—
179#6390C2314yes—
180Dic7⋊C8C2314yes—
181C8×Dic7C2314yes—
182#6384C2314yes—
183#6384C2314yes—
184#6382C2314yes—
185#6381C2314yes—
186C2×#555—71no—
187C2×#547—71no—
188#3303—716no—
189C2×#487—71no—
190C2×#485—71no—
191C2×#485—71no—
192C2×#476—71no—
193C2×#465—71no—
194C2×#465—71no—
195C2×#461—71no—
196C2×#449—71no—
197C2×#449—71no—
198C2×C4×D8—71no—
199C2×C8×D4—71no—
200C2×#416—71no—
201C2×#416D711yescharacteristic, complemented
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—22no—
211C2×C7×Q8—22no—
212C2×C7×Q8C2412yes—
213C2×C7×D4—24no—
214C2×C7×D4—21no—
215C2×C7×D4—22no—
216C2×C7×D4—44no—
217C2×C7×D4#4114yes—
218C2×C7×D4C2412yes—
219C22×C4×C7—22no—
220C22×C4×C7—22no—
221C22×C4×C7—21no—
222C22×C4×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7—24no—
225C22×C4×C7—44no—
226C22×C4×C7C2×D411yescharacteristic
227C22×C4×C7C2×D412yes—
228C22×C4×C7C2412yes—
229C22×C4×C7C2411yescharacteristic
230C2×C22⋊D7—24no—
231C2×C22⋊D7—24no—
232C2×C22⋊D7—24no—
233C2×C22⋊D7—44no—
234C2×C22⋊D7—82no—
235C2×C22⋊D7C2×D414yes—
236C22×Dic7—21no—
237C22×Dic7—21no—
238C22×Dic7—21no—
239C22×Dic7—24no—
240C22×Dic7—24no—
241C22×Dic7—44no—
242C22×Dic7—44no—
243C22×Dic7C2×D411yescharacteristic
244C22×Dic7C2×D411yescharacteristic
245C22×Dic7C2×D411yescharacteristic
246#1159—28no—
247#1159—44no—
248#1159—48no—
249C2×D28—22no—
250C2×D28—22no—
251C2×D28—21no—
252C2×D28—24no—
253C2×D28—82no—
254C2×D28C2412yes—
255C2×C4×D7—22no—
256C2×C4×D7—22no—
257C2×C4×D7—24no—
258C2×C4×D7—44no—
259C2×C4×D7C2×D412yes—
260C2×C4×D7C2412yes—
261C2×Dic14—22no—
262C2×Dic14—22no—
263C2×Dic14—21no—
264C2×Dic14—24no—
265C2×Dic14—82no—
266C2×Dic14C2412yes—
267C2×C7×C8—22no—
268C2×C7×C8—22no—
269C2×C7×C8—44no—
270C2×C7×C8C2412yes—
271C2×C7×C8C2412yes—
272C7×C4⋊C4—21no—
273C7×C4⋊C4—21no—
274C7×C4⋊C4C2412yes—
275C7×C4⋊C4C2412yes—
276C7×C22⋊C4—24no—
277C42×C7—24no—
278C22⋊Dic7—24no—
279C22⋊Dic7—24no—
280C22⋊Dic7C2×D414yes—
281#1143—44no—
282#1141—28no—
283(C2×D7)⋊C4—24no—
284(C2×D7)⋊C4—24no—
285(C2×D7)⋊C4—24no—
286(C2×D7)⋊C4—24no—
287(C2×D7)⋊C4—24no—
288(C2×D7)⋊C4C2×D414yes—
289C4⋊Dic7—21no—
290C4⋊Dic7—21no—
291C4⋊Dic7C2412yes—
292C4⋊Dic7C2412yes—
293Dic7⋊C4—24no—
294Dic7⋊C4—24no—
295Dic7⋊C4—24no—
296Dic7⋊C4—24no—
297Dic7⋊C4—24no—
298Dic7⋊C4C2×D414yes—
299C4×Dic7—24no—
300C4×Dic7C2×D412yes—
301C4×Dic7C2412yes—
302C2×C7⋊C8—22no—
303C2×C7⋊C8—22no—
304C2×C7⋊C8C2412yes—
305C2×C7⋊C8C2412yes—
306#1132—44no—
307C8×D7—44no—
308C22×#41—71no—
309C22×#41C2×D711yescharacteristic
310C22×SD16—71no—
311C22×SD16—71no—
312C22×D8—71no—
313C23×C8—71no—
314C23×C8C2×D711yescharacteristic
315#555—78no—
316#555—144no—
317#547—78no—
318#547—144no—
319C2×C4⋊Q8—71no—
320C2×C4⋊Q8—71no—
321C2×#124—141no—
322C2×#124—141no—
323C2×#123—141no—
324C2×#123—141no—
325C2×C22⋊Q8—71no—
326C2×C22⋊Q8—71no—
327C2×#121—71no—
328C2×#121—71no—
329C2×#121—141no—
330C2×#121—141no—
331C2×C4×D4—71no—
332C2×C4×D4—71no—
333C2×C4×D4—71no—
334C2×#117—71no—
335C2×#117—141no—
336C2×#117C2×D711yescharacteristic
337C22×C4⋊C4—141no—
338#487—78no—
339#485—78no—
340#485—78no—
341#476—78no—
342#465—78no—
343#465—78no—
344#461—78no—
345#449—78no—
346#449—78no—
347C4×D8—78no—
348C8×D4—78no—
349C2×#107—71no—
350C2×#106—71no—
351C2×#106—71no—
352C2×C4⋊C8—71no—
353#416—78no—
354#416C2×D718yescomplemented
355C2×#103—71no—
356C2×#103—71no—
357C2×#103—71no—
358C2×#103—71no—
359C2×#103C2×D711yescharacteristic
360C2×#103C2×D711yescharacteristic
361C2×#102—71no—
362C2×#102—71no—
363C2×#102C2×D711yescharacteristic
364C2×#102C2×D711yescharacteristic
365C2×C22⋊C8—71no—
366C2×C22⋊C8—71no—
367C2×C4×C8—71no—
368C23×C7—24no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—22no—
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—22no—
386C7×Q8—22no—
387C7×Q8—42no—
388C7×D4—24no—
389C7×D4—22no—
390C7×D4—48no—
391C7×D4C2×#4114yes—
392C2×C4×C7—22no—
393C2×C4×C7—24no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—48no—
400C2×C4×C7—42no—
401C2×C4×C7—42no—
402C2×C4×C7—42no—
403C2×C4×C7C22×D412yes—
404C2×C4×C7C22×D411yescharacteristic
405C2×C4×C7C2×#4112yes—
406C2×C4×C7H(5,𝔽2)12yes—
407C2×C4×C7C2511yescharacteristic
408C22⋊D7—28no—
409C22⋊D7—48no—
410C22⋊D7—84no—
411C2×Dic7—22no—
412C2×Dic7—22no—
413C2×Dic7—22no—
414C2×Dic7—22no—
415C2×Dic7—22no—
416C2×Dic7—48no—
417C2×Dic7—42no—
418C2×Dic7—42no—
419C2×Dic7—42no—
420C2×Dic7—48no—
421C2×Dic7#13514yes—
422C2×Dic7C22×D412yes—
423C2×Dic7C22×D412yes—
424C2×Dic7C22×D412yes—
425D28—22no—
426D28—22no—
427D28—42no—
428D28—84no—
429C4×D7—24no—
430C4×D7—22no—
431C4×D7—22no—
432C4×D7—48no—
433Dic14—22no—
434Dic14—22no—
435Dic14—42no—
436Dic14—84no—
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—71no—
450C22×Q8—141no—
451C22×Q8C22×D711yescharacteristic
452C22×D4—21no—
453C22×D4—71no—
454C22×D4—71no—
455C22×D4—141no—
456C22×D4—141no—
457C22×D4—141no—
458C22×D4C22×D711yescharacteristic
459C23×C4—21no—
460C23×C4—71no—
461C23×C4—141no—
462C23×C4—141no—
463C23×C4—141no—
464C23×C4C22×D711yescharacteristic
465C2×SD16—74no—
466C2×SD16—74no—
467C2×SD16—282no—
468C2×SD16—282no—
469C2×D8—74no—
470C2×D8—144no—
471C22×C8—42no—
472C22×C8—71no—
473C22×C8—71no—
474C22×C8—74no—
475C22×C8—282no—
476C22×C8C22×D711yescharacteristic
477C22×C8C22×D711yescharacteristic
478C22×C8C22×D714yes—
479C4⋊Q8—74no—
480C4⋊Q8—74no—
481C4⋊Q8—142no—
482C4⋊Q8—142no—
483#124—148no—
484#124—148no—
485#123—148no—
486#123—148no—
487C22⋊Q8—74no—
488C22⋊Q8—74no—
489C22⋊Q8—142no—
490C22⋊Q8—142no—
491#121—74no—
492#121—74no—
493#121—148no—
494#121—142no—
495#121—148no—
496#121—142no—
497C4×D4—74no—
498C4×D4—74no—
499C4×D4—74no—
500C4×D4—74no—
501C4×D4—142no—
502C4×D4—142no—
503#117—22no—
504#117—74no—
505#117—148no—
506#117—142no—
507#117C22×D714yes—
508C2×C4⋊C4—71no—
509C2×C4⋊C4—71no—
510C2×C4⋊C4—71no—
511C2×C4⋊C4—148no—
512C2×C4⋊C4—141no—
513C2×C4⋊C4—141no—
514C2×C4⋊C4—141no—
515C2×C4⋊C4—141no—
516C2×C4⋊C4—141no—
517C2×C4⋊C4C22×D711yescharacteristic
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×C22⋊C4—141no—
528C2×C22⋊C4—141no—
529C2×C42—21no—
530C2×C42—71no—
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#103—74no—
540#103C22×D714yes—
541#103C22×D714yes—
542#102—74no—
543#102—74no—
544#102C22×D714yes—
545#102C22×D714yes—
546C22⋊C8—74no—
547C22⋊C8—74no—
548C4×C8—74no—
549C22×C7—24no—
550C22×C7—22no—
551C22×C7—22no—
552C22×C7—22no—
553C22×C7—44no—
554C22×C7—48no—
555C22×C7—42no—
556C22×C7—42no—
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—22no—
570C4×C7—42no—
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—22no—
594C2×Q8—22no—
595C2×Q8—72no—
596C2×Q8—144no—
597C2×Q8—141no—
598C2×Q8—142no—
599C2×Q8—142no—
600C2×Q8—562no—
601C2×Q8C23×D712yes—
602C2×D4—24no—
603C2×D4—21no—
604C2×D4—22no—
605C2×D4—44no—
606C2×D4—74no—
607C2×D4—72no—
608C2×D4—144no—
609C2×D4—144no—
610C2×D4—144no—
611C2×D4—144no—
612C2×D4—142no—
613C2×D4—141no—
614C2×D4—142no—
615C2×D4—284no—
616C2×D4—562no—
617C2×D4—562no—
618C2×D4#115714yes—
619C2×D4C23×D712yes—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—24no—
626C22×C4—44no—
627C22×C4—71no—
628C22×C4—71no—
629C22×C4—71no—
630C22×C4—72no—
631C22×C4—72no—
632C22×C4—144no—
633C22×C4—144no—
634C22×C4—144no—
635C22×C4—142no—
636C22×C4—142no—
637C22×C4—141no—
638C22×C4—141no—
639C22×C4—141no—
640C22×C4—284no—
641C22×C4—284no—
642C22×C4—284no—
643C22×C4D4×D712yes—
644C22×C4D4×D711yescharacteristic
645C22×C4C23×D712yes—
646C22×C4C23×D711yescharacteristic
647SD16—284no—
648SD16—284no—
649D8—148no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—44no—
653C2×C8—72no—
654C2×C8—72no—
655C2×C8—142no—
656C2×C8—142no—
657C2×C8—284no—
658C2×C8C23×D712yes—
659C2×C8C23×D712yes—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—74no—
663C4⋊C4—72no—
664C4⋊C4—72no—
665C4⋊C4—144no—
666C4⋊C4—144no—
667C4⋊C4—144no—
668C4⋊C4—144no—
669C4⋊C4—144no—
670C4⋊C4—141no—
671C4⋊C4—141no—
672C4⋊C4C23×D712yes—
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—
682C22⋊C4—144no—
683C22⋊C4—144no—
684C42—24no—
685C42—72no—
686C42—72no—
687C42—144no—
688C2×C7—42no—
689C2×C7—44no—
690C2×C7#330314yescomplemented
691C2×C7C2×#54611yescharacteristic
692C2×C7C22×#13511yescharacteristic
693C2×C7C2×#57711yescharacteristic
694D7—42no—
695D7—82no—
696C23—22no—
697C23—24no—
698C23—22no—
699C23—22no—
700C23—22no—
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—22no—
714Q8—22no—
715Q8—42no—
716Q8—142no—
717Q8—142no—
718Q8—282no—
719Q8—564no—
720D4—24no—
721D4—22no—
722D4—48no—
723D4—148no—
724D4—142no—
725D4—142no—
726D4—288no—
727D4—282no—
728D4—564no—
729D4—564no—
730D4C2×#115714yes—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—48no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—74no—
743C2×C4—72no—
744C2×C4—72no—
745C2×C4—72no—
746C2×C4—142no—
747C2×C4—142no—
748C2×C4—144no—
749C2×C4—142no—
750C2×C4—142no—
751C2×C4—142no—
752C2×C4—142no—
753C2×C4—142no—
754C2×C4—288no—
755C2×C4—288no—
756C2×C4—288no—
757C2×C4—282no—
758C2×C4—282no—
759C2×C4—282no—
760C2×C4C2×#115712yes—
761C2×C4C2×D4×D712yes—
762C2×C4C2×D4×D711yescharacteristic
763C2×C4#654812yes—
764C2×C4C24×D711yescharacteristic
765C8—22no—
766C8—22no—
767C8—142no—
768C8—142no—
769C7C2×#330311yescharacteristic, complemented, Sylow
770C22—22no—
771C22—24no—
772C22—22no—
773C22—22no—
774C22—44no—
775C22—48no—
776C22—42no—
777C22—42no—
778C22—142no—
779C22—142no—
780C22—142no—
781C22—284no—
782C22—282no—
783C22—282no—
784C22—282no—
785C22—564no—
786C22#9018112yes—
787C22D7×#13512yes—
788C22#9046112yes—
789C22C22×D4×D711yescharacteristic
790C4—22no—
791C4—42no—
792C4—42no—
793C4—42no—
794C4—74no—
795C4—142no—
796C4—142no—
797C4—282no—
798C4—282no—
799C4—282no—
800C4#9018112yes—
801C4C22×#115711yescharacteristic
802C4C2×#654811yescharacteristic
803C2—42no—
804C2—44no—
805C2—282no—
806C2—562no—
807C2#1173629514yesdirect product factor
808C2C2×#9018111yescharacteristic
809C2C2×D7×#13511yescharacteristic
810C2C2×#9046111yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#416C2
socleC23×C7C22×D4
hypercenterC2×#416D7
hypocenterC7C2×#3303
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#90515C2semidirect
2. C2×#90223C2semidirect
3. C2×C7×#416C2semidirect
4. C2×#90010C2semidirect
5. C2×#89886C2semidirect
6. C2×C8×C22⋊D7C2semidirect
7. C2×#89768C2semidirect
8. #11736295C2direct (N × H)
9. C2×#89590C2semidirect
10. C2×#89587C2semidirect
11. C2×#89579C2semidirect
12. C2×#89564C2semidirect
13. C2×#89553C2semidirect
14. C2×#89544C2semidirect
15. C2×#89533C2semidirect
16. C2×#89528C2semidirect
22. #90515C22semidirect
38. #90223C22semidirect
47. C7×#416C22semidirect
52. #90010C22semidirect
56. #89886C22semidirect
58. C8×C22⋊D7C22semidirect
64. #89768C22semidirect
69. #89590C22semidirect
70. #89587C22semidirect
71. #89579C22semidirect
72. #89564C22semidirect
73. #89553C22semidirect
74. #89544C22semidirect
75. #89533C22semidirect
76. #89528C22semidirect
201. C2×#416D7semidirect
354. #416C2×D7semidirect
690. C2×C7#3303semidirect
769. C7C2×#3303semidirect
807. C2#11736295direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#905152
C2×#902232
C2×C7×#4162
C2×#900102
C2×#898862
C2×C8×C22⋊D72
C2×#897682
#117362952
C2×#895902
C2×#895872
C2×#895792
C2×#895642
C2×#895532
C2×#895442
C2×#895332
C2×#895282
C2×#33037