Finite Group Databasebeta

← C2×#11740982 #14230530

Subgroups — C2×#11740982 #14230530

Order 1792.

2114 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×C7×#548C211yesmaximal, characteristic
2C2×#90233C211yesmaximal, characteristic, complemented
3C2×#90011C211yesmaximal, characteristic, complemented
4C2×#90005C211yesmaximal, characteristic, complemented
5C2×#90000C211yesmaximal, characteristic, complemented
6C2×#89997C211yesmaximal, characteristic, complemented
7#11740982C2116yesmaximal, direct product factor
8C2×#89826C211yesmaximal, characteristic, complemented
9C2×#89827C211yesmaximal, characteristic, complemented
10C2×#89823C211yesmaximal, characteristic, complemented
11C2×#89817C211yesmaximal, characteristic, complemented
12C2×#89814C211yesmaximal, characteristic, complemented
13C2×#89807C211yesmaximal, characteristic, complemented
14C2×#89793C211yesmaximal, characteristic, complemented
15C2×#89802C211yesmaximal, characteristic, complemented
16C2×#89783C211yesmaximal, characteristic, complemented
17C22×C7×#41C2211yescharacteristic
18C23×C7×Q8C2211yescharacteristic
19C7×#548—24no—
20C7×#548C2218yes—
21C2×C7×#124—21no—
22C2×C7×#124C2211yescharacteristic
23C2×C7×C22⋊Q8—21no—
24C2×C7×C22⋊Q8C2211yescharacteristic
25C2×C7×#121—21no—
26C2×C7×#121C2211yescharacteristic
27C2×C4×C7×Q8C2211yescharacteristic
28C2×C4×C7×D4—21no—
29C2×C4×C7×D4C2211yescharacteristic
30C22×#1144C2211yescharacteristic
31C22×#1144C2211yescharacteristic
32C2×#6499—21no—
33C22×#1142C2211yescharacteristic
34C2×#6489C2211yescharacteristic
35C2×#6489C2211yescharacteristic
36C2×#6487C2211yescharacteristic
37C2×#6487C2211yescharacteristic
38C22×#1136C2211yescharacteristic
39C23×C7⋊C8C2211yescharacteristic
40#90233—24no—
41#90233C2218yescomplemented
42C2×#6450—21no—
43C2×#6442—21no—
44C2×#6442—21no—
45C2×#6432C2211yescharacteristic
46C2×C4×Dic14C2211yescharacteristic
47#90011C2218yescomplemented
48#90005C2218yescomplemented
49#90000C2218yescomplemented
50#89997C2218yescomplemented
51C2×#6409C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53C2×#6409C2211yescharacteristic
54C2×#6409C2211yescharacteristic
55C2×#6409C2211yescharacteristic
56C2×#6409C2211yescharacteristic
57C2×#6406C2211yescharacteristic
58C2×#6406C2211yescharacteristic
59C2×#6406C2211yescharacteristic
60C2×C22⋊(C7⋊C8)C2211yescharacteristic
61C2×C22⋊(C7⋊C8)C2211yescharacteristic
62#89827C2218yescomplemented
63#89826C2218yescomplemented
64#89823C2218yescomplemented
65#89817C2218yescomplemented
66#89814C2218yescomplemented
67#89807C2218yescomplemented
68#89802C2218yescomplemented
69#89793C2218yescomplemented
70#89783C2218yescomplemented
71C2×#6384C2211yescharacteristic
72C2×#6382C2211yescharacteristic
73C2×#6381C2211yescharacteristic
74C2×#6381C2211yescharacteristic
75C2×C4⋊(C7⋊C8)C2211yescharacteristic
76C2×#6377C2211yescharacteristic
77C2×#3313—71nomaximal, Sylow
78C2×C7×#41—22no—
79C2×C7×#41—24no—
80C2×C7×#41—42no—
81C2×C7×#41C2314yes—
82C22×C7×Q8—21no—
83C22×C7×Q8—22no—
84C22×C7×Q8—24no—
85C22×C7×Q8—42no—
86C22×C7×Q8C2311yescharacteristic
87C22×C7×Q8C2314yes—
88C22×C7×Q8C2311yescharacteristic
89C22×C7×D4—21no—
90C22×C7×D4—21no—
91C22×C7×D4D411yescharacteristic
92C22×C7×D4C2311yescharacteristic
93C23×C4×C7—21no—
94C23×C4×C7—21no—
95C23×C4×C7C2311yescharacteristic
96C23×C4×C7C2311yescharacteristic
97C22×Dic14—21no—
98C22×Dic14C2311yescharacteristic
99C7×#124—28no—
100C7×#124—22no—
101C7×#124C2314yes—
102C7×C22⋊Q8—22no—
103C7×C22⋊Q8—28no—
104C7×C22⋊Q8C2314yes—
105C7×#121—28no—
106C7×#121—22no—
107C7×#121C2314yes—
108C4×C7×Q8—22no—
109C4×C7×Q8C2314yes—
110C4×C7×D4—28no—
111C4×C7×D4D414yes—
112C4×C7×D4C2314yes—
113C2×C7×C4⋊C4—21no—
114C2×C7×C4⋊C4—21no—
115C2×C7×C4⋊C4D411yescharacteristic
116C2×C7×C4⋊C4C2311yescharacteristic
117C2×C7×C22⋊C4—21no—
118C2×C7×C22⋊C4—21no—
119C2×C7×C22⋊C4—21no—
120C2×C7×C22⋊C4—21no—
121C2×C7×C22⋊C4D411yescharacteristic
122C2×C7×C22⋊C4D411yescharacteristic
123C2×C42×C7—21no—
124C2×C42×C7C2311yescharacteristic
125C2×C22⋊Dic7—21no—
126C2×C22⋊Dic7—21no—
127C2×C22⋊Dic7—21no—
128C2×C22⋊Dic7—21no—
129C2×#1144—24no—
130C2×#1144—42no—
131C2×#1144C2314yes—
132C2×#1144C2314yes—
133#6499—28no—
134C2×#1142—42no—
135C2×#1142C2314yes—
136#6489—22no—
137#6489—22no—
138#6489C2314yes—
139#6489C2314yes—
140C2×C4⋊Dic7—21no—
141C2×C4⋊Dic7C2311yescharacteristic
142C2×C4⋊Dic7C2311yescharacteristic
143C2×C4⋊Dic7C2311yescharacteristic
144#6487—22no—
145#6487—22no—
146#6487C2314yes—
147#6487C2314yes—
148C2×Dic7⋊C4—21no—
149C2×Dic7⋊C4—21no—
150C2×Dic7⋊C4—21no—
151C2×C4×Dic7—21no—
152C2×C4×Dic7—21no—
153C2×C4×Dic7—21no—
154C2×#1136—42no—
155C2×#1136C2314yes—
156C22×C7⋊C8—42no—
157C22×C7⋊C8C2311yescharacteristic
158C22×C7⋊C8C2311yescharacteristic
159C22×C7⋊C8C2311yescharacteristic
160C22×C7⋊C8C2311yescharacteristic
161C22×C7⋊C8C2314yes—
162#6450—28no—
163#6442—28no—
164#6442—28no—
165#6432—22no—
166#6432C2314yes—
167C4×Dic14—22no—
168C4×Dic14C2314yes—
169#6409C2314yes—
170#6409C2314yes—
171#6409C2314yes—
172#6409C2314yes—
173#6409C2314yes—
174#6409C2314yes—
175#6406C2314yes—
176#6406C2314yes—
177#6406C2314yes—
178C22⋊(C7⋊C8)C2314yes—
179C22⋊(C7⋊C8)C2314yes—
180#6384C2314yes—
181#6382C2314yes—
182#6381C2314yes—
183#6381C2314yes—
184C4⋊(C7⋊C8)C2314yes—
185#6377C2314yes—
186C2×#556—71no—
187C2×#548D711yescharacteristic
188#3313—716no—
189C2×#489—71no—
190C2×#485—71no—
191C2×#482—71no—
192C2×#477—71no—
193C2×#468—71no—
194C2×#467—71no—
195C2×#464—71no—
196C2×#452—71no—
197C2×#451—71no—
198C2×#441—71no—
199C2×#435—71no—
200C2×#419—71no—
201C2×#416—71no—
202C24×C7—21no—
203C24×C7C2×D411yescharacteristic
204C24×C7C2×D411yescharacteristic
205C7×#41—28no—
206C7×#41—44no—
207C7×#41—48no—
208C2×C7×Q8—21no—
209C2×C7×Q8—24no—
210C2×C7×Q8—21no—
211C2×C7×Q8—22no—
212C2×C7×Q8—28no—
213C2×C7×Q8—22no—
214C2×C7×Q8—22no—
215C2×C7×Q8—44no—
216C2×C7×Q8—44no—
217C2×C7×Q8—48no—
218C2×C7×Q8#4114yes—
219C2×C7×Q8C2412yes—
220C2×C7×Q8C2412yes—
221C2×C7×D4—24no—
222C2×C7×D4—24no—
223C2×C7×D4—21no—
224C2×C7×D4—22no—
225C2×C7×D4—22no—
226C2×C7×D4—42no—
227C2×C7×D4—44no—
228C2×C7×D4—44no—
229C2×C7×D4C2×D414yes—
230C2×C7×D4C2412yes—
231C22×C4×C7—21no—
232C22×C4×C7—22no—
233C22×C4×C7—22no—
234C22×C4×C7—22no—
235C22×C4×C7—22no—
236C22×C4×C7—21no—
237C22×C4×C7—21no—
238C22×C4×C7—24no—
239C22×C4×C7—24no—
240C22×C4×C7—44no—
241C22×C4×C7—44no—
242C22×C4×C7C2×D411yescharacteristic
243C22×C4×C7C2×D411yescharacteristic
244C22×C4×C7C2×D411yescharacteristic
245C22×C4×C7C2×D411yescharacteristic
246C22×C4×C7C2×D412yes—
247C22×C4×C7C2×D412yes—
248C22×C4×C7C2412yes—
249C22×C4×C7C2412yes—
250C22×C4×C7C2411yescharacteristic
251C22×Dic7—21no—
252C22×Dic7—21no—
253C22×Dic7—21no—
254C22×Dic7—21no—
255C2×Dic14—22no—
256C2×Dic14—22no—
257C2×Dic14—21no—
258C2×Dic14—24no—
259C2×Dic14—44no—
260C2×Dic14C2412yes—
261C7×C4⋊C4—24no—
262C7×C4⋊C4—24no—
263C7×C4⋊C4—21no—
264C7×C4⋊C4C2×D414yes—
265C7×C4⋊C4C2412yes—
266C7×C22⋊C4—24no—
267C7×C22⋊C4—24no—
268C7×C22⋊C4—24no—
269C7×C22⋊C4—24no—
270C7×C22⋊C4C2×D414yes—
271C7×C22⋊C4C2×D414yes—
272C42×C7—24no—
273C42×C7C2×D412yes—
274C42×C7C2412yes—
275C22⋊Dic7—24no—
276C22⋊Dic7—24no—
277C22⋊Dic7—24no—
278C22⋊Dic7—24no—
279#1144—28no—
280#1144—44no—
281#1142—44no—
282C4⋊Dic7—21no—
283C4⋊Dic7—21no—
284C4⋊Dic7—21no—
285C4⋊Dic7—24no—
286C4⋊Dic7C2412yes—
287C4⋊Dic7C2412yes—
288C4⋊Dic7C2412yes—
289Dic7⋊C4—24no—
290Dic7⋊C4—24no—
291Dic7⋊C4—24no—
292C4×Dic7—24no—
293C4×Dic7—24no—
294C4×Dic7—24no—
295#1136—44no—
296C2×C7⋊C8—22no—
297C2×C7⋊C8—22no—
298C2×C7⋊C8—22no—
299C2×C7⋊C8—22no—
300C2×C7⋊C8—44no—
301C2×C7⋊C8C2412yes—
302C2×C7⋊C8C2412yes—
303C2×C7⋊C8C2412yes—
304C2×C7⋊C8C2412yes—
305C22×#41C2×D711yescharacteristic
306C23×Q8C2×D711yescharacteristic
307C22×Q16—71no—
308C22×Q16—71no—
309C22×SD16—71no—
310C22×M16—71no—
311C23×C8—71no—
312#556—78no—
313#556—144no—
314#548—24no—
315#548C2×D718yes—
316C2×C4⋊Q8—71no—
317C2×#126—141no—
318C2×#126—141no—
319C2×#124—21no—
320C2×#124—141no—
321C2×#124C2×D711yescharacteristic
322C2×C22⋊Q8—21no—
323C2×C22⋊Q8—71no—
324C2×C22⋊Q8—71no—
325C2×C22⋊Q8C2×D711yescharacteristic
326C2×#121—21no—
327C2×#121C2×D711yescharacteristic
328C2×C4×Q8—71no—
329C2×C4×Q8—141no—
330C2×C4×Q8C2×D711yescharacteristic
331C2×C4×D4—21no—
332C2×C4×D4C2×D711yescharacteristic
333C2×#117—71no—
334C2×#117—71no—
335#489—78no—
336#485—78no—
337#482—78no—
338#477—78no—
339#468—78no—
340#467—78no—
341#464—78no—
342#452—78no—
343#451—78no—
344#441—78no—
345#435—78no—
346C2×#107—71no—
347C2×#107—71no—
348C2×#106—71no—
349C2×C4⋊C8—71no—
350#419—78no—
351#416—78no—
352C2×#103—71no—
353C2×#103—71no—
354C2×#103—71no—
355C2×#103—71no—
356C2×#103—71no—
357C2×#103—71no—
358C2×#103—71no—
359C2×#102—71no—
360C2×#102—71no—
361C2×#102—71no—
362C2×C22⋊C8—71no—
363C2×C22⋊C8—71no—
364C2×#97—71no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
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×D412yes—
377C23×C7C22×D411yescharacteristic
378C7×Q8—24no—
379C7×Q8—22no—
380C7×Q8—22no—
381C7×Q8—22no—
382C7×Q8—48no—
383C7×Q8—42no—
384C7×Q8C2×#4114yes—
385C7×D4—22no—
386C7×D4—22no—
387C7×D4—44no—
388C7×D4—48no—
389C7×D4—48no—
390C7×D4—42no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—24no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—24no—
398C2×C4×C7—24no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—48no—
406C2×C4×C7—48no—
407C2×C4×C7—42no—
408C2×C4×C7—42no—
409C2×C4×C7C22×D412yes—
410C2×C4×C7C22×D412yes—
411C2×C4×C7C22×D412yes—
412C2×C4×C7C22×D412yes—
413C2×C4×C7C22×D411yescharacteristic
414C2×C4×C7C2×#4112yes—
415C2×C4×C7H(5,𝔽2)12yes—
416C2×C4×C7C2511yescharacteristic
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—42no—
422C2×Dic7—42no—
423C2×Dic7—42no—
424C2×Dic7—42no—
425Dic14—22no—
426Dic14—22no—
427Dic14—48no—
428Dic14—42no—
429C7⋊C8—22no—
430C7⋊C8—22no—
431C7⋊C8—22no—
432C7⋊C8—22no—
433C2×#41—22no—
434C2×#41—24no—
435C2×#41—42no—
436C2×#41C22×D714yes—
437C22×Q8—21no—
438C22×Q8—22no—
439C22×Q8—24no—
440C22×Q8—42no—
441C22×Q8—71no—
442C22×Q8—141no—
443C22×Q8C22×D711yescharacteristic
444C22×Q8C22×D714yes—
445C22×Q8C22×D711yescharacteristic
446C22×D4—21no—
447C22×D4—21no—
448C22×D4C22⋊D711yescharacteristic
449C22×D4C22×D711yescharacteristic
450C23×C4—21no—
451C23×C4—21no—
452C23×C4C22×D711yescharacteristic
453C23×C4C22×D711yescharacteristic
454C2×Q16—74no—
455C2×Q16—74no—
456C2×Q16—144no—
457C2×Q16—282no—
458C2×SD16—74no—
459C2×SD16—282no—
460C2×M16—74no—
461C2×M16—282no—
462C22×C8—71no—
463C22×C8—71no—
464C22×C8—71no—
465C22×C8—71no—
466C22×C8—74no—
467C22×C8—282no—
468C4⋊Q8—74no—
469C4⋊Q8—142no—
470#126—148no—
471#126—148no—
472#124—28no—
473#124—22no—
474#124—148no—
475#124C22×D714yes—
476C22⋊Q8—22no—
477C22⋊Q8—28no—
478C22⋊Q8—74no—
479C22⋊Q8—74no—
480C22⋊Q8—142no—
481C22⋊Q8—142no—
482C22⋊Q8C22×D714yes—
483#121—28no—
484#121—22no—
485#121C22×D714yes—
486C4×Q8—22no—
487C4×Q8—74no—
488C4×Q8—148no—
489C4×Q8—142no—
490C4×Q8C22×D714yes—
491C4×D4—28no—
492C4×D4C22⋊D714yes—
493C4×D4C22×D714yes—
494#117—74no—
495#117—74no—
496#117—142no—
497#117—142no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—71no—
501C2×C4⋊C4—71no—
502C2×C4⋊C4—71no—
503C2×C4⋊C4—141no—
504C2×C4⋊C4—141no—
505C2×C4⋊C4—141no—
506C2×C4⋊C4—141no—
507C2×C4⋊C4C22⋊D711yescharacteristic
508C2×C4⋊C4C22×D711yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—141no—
514C2×C22⋊C4—141no—
515C2×C22⋊C4—141no—
516C2×C22⋊C4—141no—
517C2×C22⋊C4C22⋊D711yescharacteristic
518C2×C22⋊C4C22⋊D711yescharacteristic
519C2×C42—21no—
520C2×C42—141no—
521C2×C42—141no—
522C2×C42—141no—
523C2×C42C22×D711yescharacteristic
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#103—74no—
535#102—74no—
536#102—74no—
537#102—74no—
538C22⋊C8—74no—
539C22⋊C8—74no—
540#97—74no—
541C22×C7—22no—
542C22×C7—22no—
543C22×C7—22no—
544C22×C7—22no—
545C22×C7—22no—
546C22×C7—22no—
547C22×C7—44no—
548C22×C7—44no—
549C22×C7—42no—
550C22×C7—42no—
551C22×C7—42no—
552C22×C7—84no—
553C22×C7#54612yes—
554C22×C7#57512yes—
555C22×C7#57812yes—
556C22×C7C23×D411yescharacteristic
557C4×C7—22no—
558C4×C7—22no—
559C4×C7—24no—
560C4×C7—22no—
561C4×C7—22no—
562C4×C7—42no—
563C4×C7—42no—
564C4×C7#54612yes—
565C4×C7C22×#4111yescharacteristic
566C4×C7C2×H(5,𝔽2)11yescharacteristic
567Dic7—42no—
568Dic7—42no—
569Dic7—42no—
570Dic7—42no—
571C24—21no—
572C24C2×C22⋊D711yescharacteristic
573C24C2×C22⋊D711yescharacteristic
574#41—28no—
575#41—44no—
576#41—48no—
577C2×Q8—22no—
578C2×Q8—21no—
579C2×Q8—24no—
580C2×Q8—21no—
581C2×Q8—28no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—44no—
585C2×Q8—44no—
586C2×Q8—48no—
587C2×Q8—72no—
588C2×Q8—141no—
589C2×Q8—144no—
590C2×Q8—142no—
591C2×Q8—142no—
592C2×Q8—284no—
593C2×Q8#115914yes—
594C2×Q8C23×D712yes—
595C2×Q8C23×D712yes—
596C2×D4—24no—
597C2×D4—24no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—21no—
601C2×D4—42no—
602C2×D4—44no—
603C2×D4—44no—
604C2×D4C2×C22⋊D714yes—
605C2×D4C23×D712yes—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—24no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—24no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—141no—
618C22×C4—141no—
619C22×C4—141no—
620C22×C4—141no—
621C22×C4C2×C22⋊D712yes—
622C22×C4C2×C22⋊D712yes—
623C22×C4C2×C22⋊D711yescharacteristic
624C22×C4C2×C22⋊D711yescharacteristic
625C22×C4C2×C22⋊D711yescharacteristic
626C22×C4C2×C22⋊D711yescharacteristic
627C22×C4C23×D712yes—
628C22×C4C23×D712yes—
629C22×C4C23×D711yescharacteristic
630Q16—148no—
631Q16—284no—
632SD16—284no—
633M16—284no—
634C2×C8—72no—
635C2×C8—72no—
636C2×C8—72no—
637C2×C8—72no—
638C2×C8—142no—
639C2×C8—142no—
640C2×C8—142no—
641C2×C8—142no—
642C2×C8—284no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—21no—
646C4⋊C4—72no—
647C4⋊C4—72no—
648C4⋊C4—72no—
649C4⋊C4—144no—
650C4⋊C4—144no—
651C4⋊C4—144no—
652C4⋊C4—141no—
653C4⋊C4—141no—
654C4⋊C4—141no—
655C4⋊C4—144no—
656C4⋊C4C2×C22⋊D714yes—
657C4⋊C4C23×D712yes—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—24no—
661C22⋊C4—24no—
662C22⋊C4—144no—
663C22⋊C4—144no—
664C22⋊C4—144no—
665C22⋊C4—144no—
666C22⋊C4C2×C22⋊D714yes—
667C22⋊C4C2×C22⋊D714yes—
668C42—24no—
669C42—144no—
670C42—144no—
671C42—144no—
672C42C2×C22⋊D712yes—
673C42C23×D712yes—
674C2×C7—42no—
675C2×C7—42no—
676C2×C7—82no—
677C2×C7#331314yescomplemented
678C2×C7C2×#54611yescharacteristic
679C2×C7C2×#57511yescharacteristic
680C2×C7C2×#57811yescharacteristic
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23C22×C22⋊D712yes—
692C23C22×C22⋊D712yes—
693C23C22×C22⋊D711yescharacteristic
694Q8—24no—
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—48no—
699Q8—42no—
700Q8—142no—
701Q8—142no—
702Q8—288no—
703Q8—282no—
704Q8C2×#115914yes—
705D4—22no—
706D4—22no—
707D4—44no—
708D4—48no—
709D4—48no—
710D4—42no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—48no—
726C2×C4—48no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—142no—
730C2×C4—142no—
731C2×C4—142no—
732C2×C4—142no—
733C2×C4—282no—
734C2×C4—282no—
735C2×C4—282no—
736C2×C4—282no—
737C2×C4C2×#115912yes—
738C2×C4#654812yes—
739C2×C4C22×C22⋊D712yes—
740C2×C4C22×C22⋊D712yes—
741C2×C4C22×C22⋊D712yes—
742C2×C4C22×C22⋊D712yes—
743C2×C4C22×C22⋊D711yescharacteristic
744C2×C4C24×D711yescharacteristic
745C8—142no—
746C8—142no—
747C8—142no—
748C8—142no—
749C7C2×#331311yescharacteristic, complemented, Sylow
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—44no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—84no—
762C22#9049712yes—
763C22#9051312yes—
764C22#9052912yes—
765C22C23×C22⋊D711yescharacteristic
766C4—22no—
767C4—22no—
768C4—24no—
769C4—22no—
770C4—22no—
771C4—42no—
772C4—42no—
773C4—282no—
774C4—282no—
775C4—282no—
776C4—282no—
777C4#9049712yes—
778C4C22×#115911yescharacteristic
779C4C2×#654811yescharacteristic
780C2—42no—
781C2—42no—
782C2—82no—
783C2#1174098214yesdirect product factor
784C2C2×#9049711yescharacteristic
785C2C2×#9051311yescharacteristic
786C2C2×#9052911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
Fitting, prime radicalC2×C7×#548C2
socleC23×C7C22×D4
hypercenterC2×#548D7
hypocenterC7C2×#3313
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
2. C2×#90233C2semidirect
3. C2×#90011C2semidirect
4. C2×#90005C2semidirect
5. C2×#90000C2semidirect
6. C2×#89997C2semidirect
7. #11740982C2direct (N × H)
8. C2×#89826C2semidirect
9. C2×#89827C2semidirect
10. C2×#89823C2semidirect
11. C2×#89817C2semidirect
12. C2×#89814C2semidirect
13. C2×#89807C2semidirect
14. C2×#89793C2semidirect
15. C2×#89802C2semidirect
16. C2×#89783C2semidirect
41. #90233C22semidirect
47. #90011C22semidirect
48. #90005C22semidirect
49. #90000C22semidirect
50. #89997C22semidirect
62. #89827C22semidirect
63. #89826C22semidirect
64. #89823C22semidirect
65. #89817C22semidirect
66. #89814C22semidirect
67. #89807C22semidirect
68. #89802C22semidirect
69. #89793C22semidirect
70. #89783C22semidirect
677. C2×C7#3313semidirect
749. C7C2×#3313semidirect
783. C2#11740982direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5482
C2×#902332
C2×#900112
C2×#900052
C2×#900002
C2×#899972
#117409822
C2×#898262
C2×#898272
C2×#898232
C2×#898172
C2×#898142
C2×#898072
C2×#897932
C2×#898022
C2×#897832
C2×#33137