Finite Group Databasebeta

← C2×#11737693 #14230228

Subgroups — C2×#11737693 #14230228

Order 1792.

2146 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90515C211yesmaximal, characteristic
2C2×#90332C211yesmaximal, characteristic, complemented
3C2×C7×#452C211yesmaximal, characteristic, complemented
4C2×#90005C211yesmaximal, characteristic, complemented
5C2×#89960C211yesmaximal, characteristic, complemented
6C2×#89954C211yesmaximal, characteristic, complemented
7C2×#89945C211yesmaximal, characteristic, complemented
8C2×SD16×Dic7C211yesmaximal, characteristic, complemented
9C2×#89823C211yesmaximal, characteristic, complemented
10#11737693C2116yesmaximal, direct product factor
11C2×#89587C211yesmaximal, characteristic, complemented
12C2×#89564C211yesmaximal, characteristic, complemented
13C2×#89544C211yesmaximal, characteristic, complemented
14C2×#89531C211yesmaximal, characteristic, complemented
15C2×(C22⋊D7)⋊C8C211yesmaximal, characteristic, complemented
16C2×#89495C211yesmaximal, characteristic, complemented
17C22×C7×#41C2211yescharacteristic
18C22×#1159C2211yescharacteristic
19C22×C7×Q16C2211yescharacteristic
20C22×C7×SD16C2211yescharacteristic
21C2×C7×C22⋊Q8C2211yescharacteristic
22#90515—24no—
23#90515C2218yes—
24C2×#6509C2211yescharacteristic
25C2×#6509C2211yescharacteristic
26C2×Q8×Dic7C2211yescharacteristic
27C2×#6507C2211yescharacteristic
28C22×#1144C2211yescharacteristic
29C2×#6502—21no—
30C2×#6498—21no—
31C2×D4×Dic7C2211yescharacteristic
32C2×#6492—21no—
33C2×C4×C22⋊D7C2211yescharacteristic
34C2×#6489C2211yescharacteristic
35C2×#6487C2211yescharacteristic
36C22×Dic7⋊C4—21no—
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#89960C2218yescomplemented
58#89954C2218yescomplemented
59#89945C2218yescomplemented
60SD16×Dic7C2218yescomplemented
61C2×(C2×D7)⋊C8C2211yescharacteristic
62C2×#6392C2211yescharacteristic
63C2×#6391C2211yescharacteristic
64C2×#6390C2211yescharacteristic
65C2×#6390C2211yescharacteristic
66C2×Dic7⋊C8C2211yescharacteristic
67C2×C8×Dic7C2211yescharacteristic
68#89823C2218yescomplemented
69C2×#6384C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71#89587C2218yescomplemented
72#89564C2218yescomplemented
73#89544C2218yescomplemented
74#89531C2218yescomplemented
75(C22⋊D7)⋊C8C2218yescomplemented
76#89495C2218yescomplemented
77C2×#3302—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⋊D7D411yescharacteristic
90C23×Dic7—21no—
91C23×Dic7—21no—
92C2×#1159—24no—
93C2×#1159—22no—
94C2×#1159—42no—
95C2×#1159C2314yes—
96C22×C4×D7C2311yescharacteristic
97C22×Dic14—21no—
98C22×Dic14C2311yescharacteristic
99C2×C7×Q16—42no—
100C2×C7×Q16C2314yes—
101C2×C7×SD16—24no—
102C2×C7×SD16C2314yes—
103C22×C7×C8C2311yescharacteristic
104C22×C7×C8C2311yescharacteristic
105C7×C22⋊Q8—22no—
106C7×C22⋊Q8C2314yes—
107C2×C7×C4⋊C4—21no—
108C2×C7×C4⋊C4C2311yescharacteristic
109C2×C7×C22⋊C4—21no—
110C2×C22⋊Dic7—21no—
111C2×C22⋊Dic7—21no—
112C2×C22⋊Dic7—21no—
113C2×C22⋊Dic7D411yescharacteristic
114#6509—22no—
115#6509—22no—
116#6509C2314yes—
117#6509C2314yes—
118Q8×Dic7—22no—
119Q8×Dic7C2314yes—
120#6507—22no—
121#6507C2314yes—
122C2×#1144—42no—
123C2×#1144C2314yes—
124#6502—28no—
125#6498—28no—
126D4×Dic7—22no—
127D4×Dic7C2314yes—
128#6492—28no—
129C4×C22⋊D7D414yes—
130C4×C22⋊D7C2314yes—
131C2×(C2×D7)⋊C4—21no—
132C2×(C2×D7)⋊C4—21no—
133C2×(C2×D7)⋊C4—21no—
134C2×(C2×D7)⋊C4D411yescharacteristic
135#6489—22no—
136#6489C2314yes—
137C2×C4⋊Dic7—21no—
138C2×C4⋊Dic7C2311yescharacteristic
139C2×C4⋊Dic7C2311yescharacteristic
140C2×C4⋊Dic7C2311yescharacteristic
141#6487—22no—
142#6487C2314yes—
143C2×Dic7⋊C4—21no—
144C2×Dic7⋊C4—21no—
145C2×Dic7⋊C4—21no—
146C2×Dic7⋊C4—21no—
147C2×Dic7⋊C4—21no—
148C2×Dic7⋊C4—21no—
149C2×Dic7⋊C4—28no—
150C2×Dic7⋊C4D411yescharacteristic
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(C2×D7)⋊C8C2314yes—
178#6392C2314yes—
179#6391C2314yes—
180#6390C2314yes—
181#6390C2314yes—
182Dic7⋊C8C2314yes—
183C8×Dic7C2314yes—
184#6384C2314yes—
185#6381C2314yes—
186C2×#556—71no—
187C2×#547—71no—
188#3302—716no—
189C2×#487—71no—
190C2×#485—71no—
191C2×#485—71no—
192C2×#474—71no—
193C2×#467—71no—
194C2×#467—71no—
195C2×#462—71no—
196C2×#452—71no—
197C2×#452D711yescharacteristic, complemented
198C2×C4×SD16—71no—
199C2×C8×D4—71no—
200C2×#416—71no—
201C2×#416—71no—
202C24×C7—21no—
203C24×C7C2×D411yescharacteristic
204C23×D7C2×D411yescharacteristic
205C7×#41—28no—
206C7×#41—44no—
207C7×#41—48no—
208C2×C7×Q8—21no—
209C2×C7×Q8—21no—
210C2×C7×Q8—22no—
211C2×C7×Q8—22no—
212C2×C7×Q8—22no—
213C2×C7×Q8—22no—
214C2×C7×Q8C2412yes—
215C2×C7×Q8C2412yes—
216C2×C7×D4—24no—
217C2×C7×D4—21no—
218C2×C7×D4—22no—
219C2×C7×D4—44no—
220C2×C7×D4#4114yes—
221C2×C7×D4C2412yes—
222C22×C4×C7—22no—
223C22×C4×C7—22no—
224C22×C4×C7—21no—
225C22×C4×C7—21no—
226C22×C4×C7—21no—
227C22×C4×C7—24no—
228C22×C4×C7—44no—
229C22×C4×C7C2×D411yescharacteristic
230C22×C4×C7C2×D412yes—
231C22×C4×C7C2412yes—
232C22×C4×C7C2411yescharacteristic
233C2×C22⋊D7—24no—
234C2×C22⋊D7—24no—
235C2×C22⋊D7—44no—
236C2×C22⋊D7C2×D414yes—
237C22×Dic7—21no—
238C22×Dic7—21no—
239C22×Dic7—21no—
240C22×Dic7—21no—
241C22×Dic7—24no—
242C22×Dic7—24no—
243C22×Dic7—44no—
244C22×Dic7—44no—
245C22×Dic7C2×D411yescharacteristic
246C22×Dic7C2×D411yescharacteristic
247C22×Dic7C2×D411yescharacteristic
248#1159—28no—
249#1159—44no—
250#1159—48no—
251C2×C4×D7—22no—
252C2×C4×D7—22no—
253C2×C4×D7C2×D412yes—
254C2×C4×D7C2412yes—
255C2×Dic14—22no—
256C2×Dic14—22no—
257C2×Dic14—21no—
258C2×Dic14—24no—
259C2×Dic14—44no—
260C2×Dic14C2412yes—
261C7×Q16—44no—
262C7×SD16—28no—
263C2×C7×C8—22no—
264C2×C7×C8—22no—
265C2×C7×C8C2412yes—
266C2×C7×C8C2412yes—
267C7×C4⋊C4—24no—
268C7×C4⋊C4—21no—
269C7×C4⋊C4C2412yes—
270C7×C22⋊C4—24no—
271C22⋊Dic7—24no—
272C22⋊Dic7—24no—
273C22⋊Dic7—24no—
274C22⋊Dic7C2×D414yes—
275#1144—44no—
276(C2×D7)⋊C4—24no—
277(C2×D7)⋊C4—24no—
278(C2×D7)⋊C4—24no—
279(C2×D7)⋊C4C2×D414yes—
280C4⋊Dic7—21no—
281C4⋊Dic7—21no—
282C4⋊Dic7—21no—
283C4⋊Dic7—24no—
284C4⋊Dic7C2412yes—
285C4⋊Dic7C2412yes—
286C4⋊Dic7C2412yes—
287Dic7⋊C4—24no—
288Dic7⋊C4—24no—
289Dic7⋊C4—24no—
290Dic7⋊C4—24no—
291Dic7⋊C4—24no—
292Dic7⋊C4—24no—
293Dic7⋊C4C2×D414yes—
294C4×Dic7—24no—
295C4×Dic7—24no—
296C4×Dic7—24no—
297C4×Dic7C2×D412yes—
298C4×Dic7C2412yes—
299C2×C7⋊C8—22no—
300C2×C7⋊C8—22no—
301C2×C7⋊C8—44no—
302C2×C7⋊C8C2412yes—
303C2×C7⋊C8C2412yes—
304C8×D7—44no—
305C22×#41—71no—
306C22×#41C2×D711yescharacteristic
307C22×Q16—71no—
308C22×Q16C2×D711yescharacteristic
309C22×SD16C2×D711yescharacteristic
310C23×C8—71no—
311C23×C8—71no—
312#556—78no—
313#556—144no—
314#547—78no—
315#547—144no—
316C2×C4⋊Q8—71no—
317C2×C4⋊Q8—71no—
318C2×#126—141no—
319C2×#126—141no—
320C2×#124—141no—
321C2×#123—141no—
322C2×#123—141no—
323C2×C22⋊Q8—71no—
324C2×C22⋊Q8—71no—
325C2×C22⋊Q8—71no—
326C2×C22⋊Q8C2×D711yescharacteristic
327C2×#121—141no—
328C2×C4×Q8—71no—
329C2×C4×Q8—141no—
330C2×C4×D4—71no—
331C2×C4×D4—71no—
332C2×#117—71no—
333C2×#117—71no—
334C22×C4⋊C4—141no—
335#487—78no—
336#485—78no—
337#485—78no—
338#474—78no—
339#467—78no—
340#467—78no—
341#462—78no—
342#452—78no—
343#452C2×D718yescomplemented
344C4×SD16—78no—
345C8×D4—78no—
346C2×#107—71no—
347C2×#107—71no—
348C2×#106—71no—
349C2×C4⋊C8—71no—
350#416—78no—
351#416—78no—
352C2×#103—71no—
353C2×#103—71no—
354C2×#103—71no—
355C2×#103—71no—
356C2×#103—71no—
357C2×#103—71no—
358C2×#103C2×D711yescharacteristic
359C2×#102—71no—
360C2×#102—71no—
361C2×#102C2×D711yescharacteristic
362C2×C22⋊C8—71no—
363C2×C22⋊C8C2×D711yescharacteristic
364C2×C4×C8—71no—
365C23×C7—24no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—42no—
371C23×C7—42no—
372C23×C7C22×D412yes—
373C23×C7C22×D411yescharacteristic
374C22×D7—22no—
375C22×D7—22no—
376C22×D7—22no—
377C22×D7C22×D412yes—
378C7×Q8—22no—
379C7×Q8—22no—
380C7×Q8—22no—
381C7×Q8—22no—
382C7×Q8—42no—
383C7×Q8—42no—
384C7×D4—24no—
385C7×D4—22no—
386C7×D4—48no—
387C7×D4C2×#4114yes—
388C2×C4×C7—22no—
389C2×C4×C7—24no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—48no—
396C2×C4×C7—42no—
397C2×C4×C7—42no—
398C2×C4×C7—42no—
399C2×C4×C7C22×D412yes—
400C2×C4×C7C22×D411yescharacteristic
401C2×C4×C7C2×#4112yes—
402C2×C4×C7H(5,𝔽2)12yes—
403C2×C4×C7C2511yescharacteristic
404C22⋊D7—28no—
405C22⋊D7—48no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—22no—
410C2×Dic7—22no—
411C2×Dic7—22no—
412C2×Dic7—48no—
413C2×Dic7—42no—
414C2×Dic7—42no—
415C2×Dic7—42no—
416C2×Dic7—42no—
417C2×Dic7—48no—
418C2×Dic7#13514yes—
419C2×Dic7C22×D412yes—
420C2×Dic7C22×D412yes—
421C2×Dic7C22×D412yes—
422C4×D7—24no—
423C4×D7—22no—
424C4×D7—22no—
425Dic14—22no—
426Dic14—22no—
427Dic14—42no—
428Dic14—48no—
429C7×C8—22no—
430C7×C8—22no—
431C7⋊C8—22no—
432C7⋊C8—22no—
433C2×#41—22no—
434C2×#41—24no—
435C2×#41—42no—
436C2×#41—74no—
437C2×#41—142no—
438C2×#41—144no—
439C2×#41—282no—
440C2×#41C22×D714yes—
441C22×Q8—71no—
442C22×Q8—141no—
443C22×Q8C22×D711yescharacteristic
444C22×Q8C22×D711yescharacteristic
445C22×D4—21no—
446C22×D4—71no—
447C22×D4—141no—
448C22×D4C22×D711yescharacteristic
449C23×C4—21no—
450C23×C4—71no—
451C23×C4—141no—
452C23×C4—141no—
453C23×C4C22×D711yescharacteristic
454C2×Q16—42no—
455C2×Q16—74no—
456C2×Q16—282no—
457C2×Q16C22×D714yes—
458C2×SD16—24no—
459C2×SD16C22×D714yes—
460C22×C8—71no—
461C22×C8—71no—
462C22×C8—74no—
463C22×C8—74no—
464C22×C8—282no—
465C22×C8—282no—
466C22×C8C22×D711yescharacteristic
467C22×C8C22×D711yescharacteristic
468C4⋊Q8—74no—
469C4⋊Q8—74no—
470C4⋊Q8—142no—
471C4⋊Q8—142no—
472#126—148no—
473#126—148no—
474#124—148no—
475#123—148no—
476#123—148no—
477C22⋊Q8—22no—
478C22⋊Q8—74no—
479C22⋊Q8—74no—
480C22⋊Q8—74no—
481C22⋊Q8—142no—
482C22⋊Q8—142no—
483C22⋊Q8—142no—
484C22⋊Q8C22×D714yes—
485#121—148no—
486C4×Q8—74no—
487C4×Q8—142no—
488C4×Q8—148no—
489C4×D4—74no—
490C4×D4—74no—
491C4×D4—74no—
492C4×D4—142no—
493#117—74no—
494#117—74no—
495#117—142no—
496#117—142no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—71no—
499C2×C4⋊C4—71no—
500C2×C4⋊C4—71no—
501C2×C4⋊C4—71no—
502C2×C4⋊C4—148no—
503C2×C4⋊C4—141no—
504C2×C4⋊C4—141no—
505C2×C4⋊C4—141no—
506C2×C4⋊C4—141no—
507C2×C4⋊C4—141no—
508C2×C4⋊C4—141no—
509C2×C4⋊C4—141no—
510C2×C4⋊C4C22×D711yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—71no—
513C2×C22⋊C4—71no—
514C2×C22⋊C4—141no—
515C2×C22⋊C4—141no—
516C2×C22⋊C4—141no—
517C2×C22⋊C4—141no—
518C2×C22⋊C4—141no—
519C2×C22⋊C4—141no—
520C2×C42—71no—
521C2×C42—141no—
522C2×C42—141no—
523C2×C42—141no—
524#107—74no—
525#107—74no—
526#106—74no—
527C4⋊C8—74no—
528#103—74no—
529#103—74no—
530#103—74no—
531#103—74no—
532#103—74no—
533#103—74no—
534#103C22×D714yes—
535#102—74no—
536#102—74no—
537#102C22×D714yes—
538C22⋊C8—74no—
539C22⋊C8C22×D714yes—
540C4×C8—74no—
541C22×C7—24no—
542C22×C7—22no—
543C22×C7—22no—
544C22×C7—22no—
545C22×C7—44no—
546C22×C7—48no—
547C22×C7—42no—
548C22×C7—42no—
549C22×C7#54612yes—
550C22×C7C2×#13512yes—
551C22×C7#57812yes—
552C22×C7C23×D411yescharacteristic
553C2×D7—22no—
554C2×D7—22no—
555C2×D7—22no—
556C2×D7—44no—
557C4×C7—22no—
558C4×C7—42no—
559C4×C7—42no—
560C4×C7—42no—
561C4×C7#54612yes—
562C4×C7C22×#4111yescharacteristic
563C4×C7C2×H(5,𝔽2)11yescharacteristic
564Dic7—22no—
565Dic7—22no—
566Dic7—42no—
567Dic7—42no—
568Dic7—42no—
569Dic7—42no—
570Dic7C2×#13514yes—
571C24—21no—
572C24—71no—
573C24D4×D711yescharacteristic
574#41—28no—
575#41—44no—
576#41—48no—
577#41—148no—
578#41—284no—
579#41—288no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—22no—
586C2×Q8—72no—
587C2×Q8—144no—
588C2×Q8—141no—
589C2×Q8—142no—
590C2×Q8—142no—
591C2×Q8—284no—
592C2×Q8C23×D712yes—
593C2×Q8C23×D712yes—
594C2×D4—24no—
595C2×D4—21no—
596C2×D4—22no—
597C2×D4—44no—
598C2×D4—74no—
599C2×D4—144no—
600C2×D4—144no—
601C2×D4—284no—
602C2×D4#115914yes—
603C2×D4C23×D712yes—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—24no—
610C22×C4—44no—
611C22×C4—71no—
612C22×C4—71no—
613C22×C4—71no—
614C22×C4—72no—
615C22×C4—72no—
616C22×C4—144no—
617C22×C4—144no—
618C22×C4—142no—
619C22×C4—142no—
620C22×C4—141no—
621C22×C4—141no—
622C22×C4—141no—
623C22×C4—141no—
624C22×C4—284no—
625C22×C4—284no—
626C22×C4D4×D712yes—
627C22×C4D4×D711yescharacteristic
628C22×C4C23×D712yes—
629C22×C4C23×D711yescharacteristic
630Q16—44no—
631Q16—284no—
632SD16—28no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—72no—
636C2×C8—72no—
637C2×C8—142no—
638C2×C8—142no—
639C2×C8—284no—
640C2×C8—284no—
641C2×C8C23×D712yes—
642C2×C8C23×D712yes—
643C4⋊C4—24no—
644C4⋊C4—21no—
645C4⋊C4—74no—
646C4⋊C4—72no—
647C4⋊C4—72no—
648C4⋊C4—72no—
649C4⋊C4—144no—
650C4⋊C4—144no—
651C4⋊C4—144no—
652C4⋊C4—144no—
653C4⋊C4—144no—
654C4⋊C4—144no—
655C4⋊C4—144no—
656C4⋊C4—141no—
657C4⋊C4—141no—
658C4⋊C4—141no—
659C4⋊C4C23×D712yes—
660C22⋊C4—24no—
661C22⋊C4—74no—
662C22⋊C4—74no—
663C22⋊C4—144no—
664C22⋊C4—144no—
665C22⋊C4—144no—
666C22⋊C4—144no—
667C22⋊C4—144no—
668C22⋊C4—144no—
669C42—72no—
670C42—72no—
671C42—144no—
672C42—144no—
673C42—144no—
674C2×C7—42no—
675C2×C7—44no—
676C2×C7#330214yescomplemented
677C2×C7C2×#54611yescharacteristic
678C2×C7C22×#13511yescharacteristic
679C2×C7C2×#57811yescharacteristic
680D7—42no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—24no—
685C23—22no—
686C23—42no—
687C23—42no—
688C23—72no—
689C23—142no—
690C23—142no—
691C23—142no—
692C23C2×D4×D712yes—
693C23C2×D4×D711yescharacteristic
694Q8—22no—
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—42no—
699Q8—42no—
700Q8—142no—
701Q8—142no—
702Q8—288no—
703Q8—282no—
704D4—24no—
705D4—22no—
706D4—48no—
707D4—148no—
708D4—288no—
709D4C2×#115914yes—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—48no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—74no—
722C2×C4—72no—
723C2×C4—72no—
724C2×C4—72no—
725C2×C4—142no—
726C2×C4—142no—
727C2×C4—144no—
728C2×C4—142no—
729C2×C4—142no—
730C2×C4—142no—
731C2×C4—142no—
732C2×C4—142no—
733C2×C4—142no—
734C2×C4—288no—
735C2×C4—288no—
736C2×C4—282no—
737C2×C4—282no—
738C2×C4—282no—
739C2×C4—282no—
740C2×C4C2×D4×D712yes—
741C2×C4C2×D4×D711yescharacteristic
742C2×C4C2×#115912yes—
743C2×C4#654812yes—
744C2×C4C24×D711yescharacteristic
745C8—22no—
746C8—22no—
747C8—142no—
748C8—142no—
749C7C2×#330211yescharacteristic, complemented, Sylow
750C22—22no—
751C22—22no—
752C22—24no—
753C22—22no—
754C22—42no—
755C22—44no—
756C22—48no—
757C22—42no—
758C22—142no—
759C22—142no—
760C22—142no—
761C22—284no—
762C22#9028212yes—
763C22D7×#13512yes—
764C22#9047012yes—
765C22C22×D4×D711yescharacteristic
766C4—22no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—74no—
771C4—142no—
772C4—142no—
773C4—282no—
774C4—282no—
775C4—282no—
776C4—282no—
777C4#9028212yes—
778C4C22×#115911yescharacteristic
779C4C2×#654811yescharacteristic
780C2—42no—
781C2—44no—
782C2—282no—
783C2#1173769314yesdirect product factor
784C2C2×#9028211yescharacteristic
785C2C2×D7×#13511yescharacteristic
786C2C2×#9047011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#452C2
socleC23×C7C22×D4
prime radicalC2×#90515C2
hypercenterC2×#452D7
hypocenterC7C2×#3302
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×#89960C2semidirect
6. C2×#89954C2semidirect
7. C2×#89945C2semidirect
8. C2×SD16×Dic7C2semidirect
9. C2×#89823C2semidirect
10. #11737693C2direct (N × H)
11. C2×#89587C2semidirect
12. C2×#89564C2semidirect
13. C2×#89544C2semidirect
14. C2×#89531C2semidirect
15. C2×(C22⋊D7)⋊C8C2semidirect
16. C2×#89495C2semidirect
40. #90332C22semidirect
47. C7×#452C22semidirect
51. #90005C22semidirect
57. #89960C22semidirect
58. #89954C22semidirect
59. #89945C22semidirect
60. SD16×Dic7C22semidirect
68. #89823C22semidirect
71. #89587C22semidirect
72. #89564C22semidirect
73. #89544C22semidirect
74. #89531C22semidirect
75. (C22⋊D7)⋊C8C22semidirect
76. #89495C22semidirect
197. C2×#452D7semidirect
343. #452C2×D7semidirect
676. C2×C7#3302semidirect
749. C7C2×#3302semidirect
783. C2#11737693direct (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×#903322
C2×C7×#4522
C2×#900052
C2×#899602
C2×#899542
C2×#899452
C2×SD16×Dic72
C2×#898232
#117376932
C2×#895872
C2×#895642
C2×#895442
C2×#895312
C2×(C22⋊D7)⋊C82
C2×#894952
C2×#33027