Finite Group Databasebeta

← C2×#11741117 #14234802

Subgroups — C2×#11741117 #14234802

Order 1792.

2002 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#556C211yesmaximal, characteristic, complemented
2C2×#90276C211yesmaximal, characteristic, complemented
3#11741117C2116yesmaximal, direct product factor
4C2×#89855C211yesmaximal, characteristic, complemented
5C2×#89858C211yesmaximal, characteristic, complemented
6C2×#89826C211yesmaximal, characteristic, complemented
7C2×#89829C211yesmaximal, characteristic, complemented
8C2×#89830C211yesmaximal, characteristic
9C2×#89831C211yesmaximal, characteristic, complemented
10C2×#89800C211yesmaximal, characteristic, complemented
11C2×#89799C211yesmaximal, characteristic, complemented
12C2×#89796C211yesmaximal, characteristic, complemented
13C2×#89802C211yesmaximal, characteristic, complemented
14C2×C4×#1143C211yesmaximal, characteristic, complemented
15C2×#89788C211yesmaximal, characteristic, complemented
16C2×#89786C211yesmaximal, characteristic, complemented
17C7×#556—24no—
18C7×#556C2218yescomplemented
19C2×C7×C4⋊Q8C2211yescharacteristic
20C2×C7×#126—21no—
21C2×C7×#126—21no—
22C2×C7×#124C2211yescharacteristic
23C2×C7×#124C2211yescharacteristic
24C2×C7×C22⋊Q8—21no—
25C2×C4×C7×Q8C2211yescharacteristic
26C2×C4×C7×Q8C2211yescharacteristic
27C2×C4×C7×Q8C2211yescharacteristic
28C2×C4×C7×D4C2211yescharacteristic
29C2×C7×#117—21no—
30C2×#6510—21no—
31C22×#1144C2211yescharacteristic
32C22×#1144C2211yescharacteristic
33C22×#1143C2211yescharacteristic
34C22×#1143C2211yescharacteristic
35C22×#1143C2211yescharacteristic
36C22×#1143C2211yescharacteristic
37C22×#1142C2211yescharacteristic
38C22×#1141C2211yescharacteristic
39C22×#1141C2211yescharacteristic
40#90276—24no—
41#90276C2218yescomplemented
42C2×#6457—21no—
43C2×#6457—21no—
44C2×#6456—21no—
45C2×#6438C2211yescharacteristic
46C2×#6438C2211yescharacteristic
47C2×#6437C2211yescharacteristic
48C2×C4×D28C2211yescharacteristic
49C2×C4×D28C2211yescharacteristic
50C2×C4×Dic14C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53C2×#6406C2211yescharacteristic
54#89858C2218yescomplemented
55#89855C2218yescomplemented
56#89831C2218yescomplemented
57#89830C2218yes—
58#89829C2218yescomplemented
59#89826C2218yescomplemented
60#89802C2218yescomplemented
61#89800C2218yescomplemented
62#89799C2218yescomplemented
63C4×#1143C2218yescomplemented
64#89796C2218yescomplemented
65#89788C2218yescomplemented
66#89786C2218yescomplemented
67C2×#6384C2211yescharacteristic
68C2×#6383C2211yescharacteristic
69C2×#6383C2211yescharacteristic
70C2×#6382C2211yescharacteristic
71C2×C4⋊(C7⋊C8)C2211yescharacteristic
72C2×C4⋊(C7⋊C8)C2211yescharacteristic
73C2×C4⋊(C7⋊C8)C2211yescharacteristic
74C2×#6377C2211yescharacteristic
75C2×#6377C2211yescharacteristic
76C2×C4×C7⋊C8C2211yescharacteristic
77C2×#3401—71nomaximal, Sylow
78C22×C7×Q8D411yescharacteristic
79C22×C7×Q8C2311yescharacteristic
80C22×C7×Q8C2311yescharacteristic
81C22×C7×D4C2311yescharacteristic
82C23×C4×C7—21no—
83C22×D28—21no—
84C22×D28—21no—
85C22×D28C2311yescharacteristic
86C22×D28C2311yescharacteristic
87C22×C4×D7—21no—
88C22×C4×D7—21no—
89C22×Dic14C2311yescharacteristic
90C7×C4⋊Q8—22no—
91C7×C4⋊Q8C2314yes—
92C7×#126—28no—
93C7×#126—28no—
94C7×#124—22no—
95C7×#124—22no—
96C7×#124C2314yes—
97C7×#124C2314yes—
98C7×C22⋊Q8—28no—
99C4×C7×Q8—22no—
100C4×C7×Q8—22no—
101C4×C7×Q8D414yes—
102C4×C7×Q8C2314yes—
103C4×C7×Q8C2314yes—
104C4×C7×Q8C2314yes—
105C4×C7×D4—22no—
106C4×C7×D4C2314yes—
107C7×#117—28no—
108C2×C7×C4⋊C4—21no—
109C2×C7×C4⋊C4—21no—
110C2×C7×C4⋊C4—21no—
111C2×C7×C4⋊C4—21no—
112C2×C7×C4⋊C4D411yescharacteristic
113C2×C7×C4⋊C4D411yescharacteristic
114C2×C7×C4⋊C4D411yescharacteristic
115C2×C7×C4⋊C4C2311yescharacteristic
116C2×C7×C22⋊C4—21no—
117C2×C7×C22⋊C4—21no—
118C2×C7×C22⋊C4—21no—
119C2×C7×C22⋊C4—21no—
120C2×C7×C22⋊C4—21no—
121C2×C42×C7—21no—
122C2×C42×C7—21no—
123C2×C42×C7C2311yescharacteristic
124C2×C42×C7C2311yescharacteristic
125C2×C42×C7C2311yescharacteristic
126#6510—28no—
127C2×#1144—24no—
128C2×#1144—42no—
129C2×#1144C2314yes—
130C2×#1144C2314yes—
131C2×#1143—24no—
132C2×#1143—42no—
133C2×#1143—42no—
134C2×#1143—42no—
135C2×#1143C2314yes—
136C2×#1143C2314yes—
137C2×#1143C2314yes—
138C2×#1143C2314yes—
139C2×#1142—42no—
140C2×#1142C2314yes—
141C2×#1141—24no—
142C2×#1141—42no—
143C2×#1141C2314yes—
144C2×#1141C2314yes—
145C2×(C2×D7)⋊C4—21no—
146C2×(C2×D7)⋊C4—21no—
147C2×(C2×D7)⋊C4—21no—
148C2×(C2×D7)⋊C4—21no—
149C2×(C2×D7)⋊C4—21no—
150C2×(C2×D7)⋊C4—21no—
151C2×C4⋊Dic7C2311yescharacteristic
152C2×Dic7⋊C4—21no—
153C2×C4×Dic7—21no—
154C22×C7⋊C8C2311yescharacteristic
155C22×C7⋊C8C2311yescharacteristic
156C22×C7⋊C8C2311yescharacteristic
157C22×C7⋊C8C2311yescharacteristic
158#6457—28no—
159#6457—28no—
160#6456—28no—
161#6438—22no—
162#6438—22no—
163#6438C2314yes—
164#6438C2314yes—
165#6437—22no—
166#6437C2314yes—
167C4×D28—22no—
168C4×D28—22no—
169C4×D28C2314yes—
170C4×D28C2314yes—
171C4×Dic14—22no—
172C4×Dic14C2314yes—
173#6409C2314yes—
174#6409C2314yes—
175#6406C2314yes—
176#6384C2314yes—
177#6383C2314yes—
178#6383C2314yes—
179#6382C2314yes—
180C4⋊(C7⋊C8)C2314yes—
181C4⋊(C7⋊C8)C2314yes—
182C4⋊(C7⋊C8)C2314yes—
183#6377C2314yes—
184#6377C2314yes—
185C4×C7⋊C8C2314yes—
186C2×#559—71no—
187C2×#556D711yescharacteristic, complemented
188#3401—716no—
189C2×#497—71no—
190C2×#496—71no—
191C2×#495—71no—
192C2×#464—71no—
193C2×#464—71no—
194C2×#460—71no—
195C2×#463—71no—
196C2×#463—71no—
197C2×#461—71no—
198C2×#446—71no—
199C2×#442—71no—
200C2×#441—71no—
201C2×C4×SD16—71no—
202C24×C7—21no—
203C23×D7—21no—
204C23×D7—21no—
205C2×C7×Q8—21no—
206C2×C7×Q8—21no—
207C2×C7×Q8—22no—
208C2×C7×Q8—22no—
209C2×C7×Q8—22no—
210C2×C7×Q8—22no—
211C2×C7×Q8—42no—
212C2×C7×Q8C2×D414yes—
213C2×C7×Q8C2412yes—
214C2×C7×Q8C2412yes—
215C2×C7×D4—21no—
216C2×C7×D4—22no—
217C2×C7×D4—22no—
218C2×C7×D4C2412yes—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7—21no—
222C22×C4×C7—24no—
223C22×C4×C7—44no—
224C22×C4×C7C2×D411yescharacteristic
225C22×C4×C7C2×D411yescharacteristic
226C22×C4×C7C2×D411yescharacteristic
227C22×C4×C7C2×D411yescharacteristic
228C22×C4×C7C2×D411yescharacteristic
229C22×C4×C7C2×D411yescharacteristic
230C22×C4×C7C2411yescharacteristic
231C22×Dic7—21no—
232C22×Dic7—21no—
233C2×D28—22no—
234C2×D28—22no—
235C2×D28—22no—
236C2×D28—22no—
237C2×D28—21no—
238C2×D28—21no—
239C2×D28—24no—
240C2×D28—24no—
241C2×D28—44no—
242C2×D28—82no—
243C2×D28C2412yes—
244C2×D28C2412yes—
245C2×C4×D7—24no—
246C2×C4×D7—24no—
247C2×C4×D7—82no—
248C2×C4×D7—82no—
249C2×Dic14—22no—
250C2×Dic14—22no—
251C2×Dic14—21no—
252C2×Dic14C2412yes—
253C7×C4⋊C4—24no—
254C7×C4⋊C4—24no—
255C7×C4⋊C4—24no—
256C7×C4⋊C4—24no—
257C7×C4⋊C4—21no—
258C7×C4⋊C4C2×D414yes—
259C7×C4⋊C4C2×D414yes—
260C7×C4⋊C4C2×D414yes—
261C7×C4⋊C4C2412yes—
262C7×C22⋊C4—24no—
263C7×C22⋊C4—24no—
264C7×C22⋊C4—24no—
265C7×C22⋊C4—24no—
266C7×C22⋊C4—24no—
267C42×C7—24no—
268C42×C7—24no—
269C42×C7C2×D412yes—
270C42×C7C2×D412yes—
271C42×C7C2×D412yes—
272C42×C7C2412yes—
273C42×C7C2412yes—
274C42×C7C2412yes—
275#1144—28no—
276#1144—44no—
277#1143—28no—
278#1143—44no—
279#1143—44no—
280#1143—44no—
281#1142—44no—
282#1141—28no—
283#1141—44no—
284(C2×D7)⋊C4—24no—
285(C2×D7)⋊C4—24no—
286(C2×D7)⋊C4—24no—
287(C2×D7)⋊C4—24no—
288(C2×D7)⋊C4—24no—
289(C2×D7)⋊C4—24no—
290C4⋊Dic7—21no—
291C4⋊Dic7C2412yes—
292Dic7⋊C4—24no—
293C4×Dic7—24no—
294C2×C7⋊C8—22no—
295C2×C7⋊C8—22no—
296C2×C7⋊C8—22no—
297C2×C7⋊C8#4114yes—
298C2×C7⋊C8C2412yes—
299C2×C7⋊C8C2412yes—
300C2×C7⋊C8C2412yes—
301C2×C7⋊C8C2412yes—
302C22×Q16—71no—
303C22×Q16—71no—
304C22×SD16—71no—
305C22×SD16—71no—
306C22×SD16—71no—
307C22×SD16—71no—
308C22×SD16—71no—
309C22×D8—71no—
310C22×D8—71no—
311#559—78no—
312#559—144no—
313#556—24no—
314#556C2×D718yescomplemented
315C2×C4⋊Q8C2×D711yescharacteristic
316C2×#127—71no—
317C2×#126—21no—
318C2×#126—21no—
319C2×#124—71no—
320C2×#124—71no—
321C2×#124—141no—
322C2×#124C2×D711yescharacteristic
323C2×#124C2×D711yescharacteristic
324C2×#123—141no—
325C2×#123—141no—
326C2×C22⋊Q8—21no—
327C2×C4×Q8—71no—
328C2×C4×Q8C2×D711yescharacteristic
329C2×C4×Q8C2×D711yescharacteristic
330C2×C4×Q8C2×D711yescharacteristic
331C2×C4×D4—71no—
332C2×C4×D4—71no—
333C2×C4×D4—141no—
334C2×C4×D4C2×D711yescharacteristic
335C2×#117—21no—
336#497—78no—
337#496—78no—
338#495—78no—
339#464—78no—
340#464—78no—
341#463—78no—
342#463—78no—
343#461—78no—
344#460—78no—
345#446—78no—
346#442—78no—
347#441—78no—
348C4×SD16—78no—
349C2×#106—71no—
350C2×C4⋊C8—71no—
351C2×C4⋊C8—71no—
352C2×C4⋊C8—71no—
353C2×#103—71no—
354C2×#103—71no—
355C2×#103—71no—
356C2×#102—71no—
357C2×#102—71no—
358C2×#102—71no—
359C2×#97—71no—
360C2×#97—71no—
361C2×C4×C8—71no—
362C23×C7—22no—
363C23×C7—42no—
364C23×C7—42no—
365C23×C7—42no—
366C23×C7C22×D411yescharacteristic
367C22×D7—22no—
368C22×D7—22no—
369C22×D7—42no—
370C22×D7—42no—
371C22×D7—42no—
372C22×D7—42no—
373C22×D7—42no—
374C22×D7—42no—
375C7×Q8—22no—
376C7×Q8—22no—
377C7×Q8—22no—
378C7×Q8—22no—
379C7×Q8—44no—
380C7×Q8—42no—
381C7×Q8—42no—
382C7×D4—22no—
383C7×D4—22no—
384C7×D4—42no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—48no—
395C2×C4×C7—42no—
396C2×C4×C7—42no—
397C2×C4×C7—42no—
398C2×C4×C7C22×D412yes—
399C2×C4×C7C22×D412yes—
400C2×C4×C7C22×D412yes—
401C2×C4×C7C22×D412yes—
402C2×C4×C7C22×D412yes—
403C2×C4×C7C22×D412yes—
404C2×C4×C7C22×D411yescharacteristic
405C2×C4×C7C2×#4112yes—
406C2×C4×C7H(5,𝔽2)12yes—
407C2×C4×C7C2511yescharacteristic
408C2×Dic7—22no—
409C2×Dic7—22no—
410C2×Dic7—42no—
411C2×Dic7—42no—
412D28—22no—
413D28—22no—
414D28—22no—
415D28—22no—
416D28—48no—
417D28—42no—
418D28—42no—
419D28—84no—
420C4×D7—84no—
421C4×D7—84no—
422Dic14—22no—
423Dic14—22no—
424Dic14—42no—
425C7⋊C8—22no—
426C7⋊C8—22no—
427C7⋊C8—22no—
428C7⋊C8C2×#4114yes—
429C22×Q8—71no—
430C22×Q8C22⋊D711yescharacteristic
431C22×Q8C22×D711yescharacteristic
432C22×Q8C22×D711yescharacteristic
433C22×D4—71no—
434C22×D4—71no—
435C22×D4—141no—
436C22×D4—141no—
437C22×D4C22×D711yescharacteristic
438C23×C4—21no—
439C23×C4—141no—
440C23×C4—141no—
441C2×Q16—74no—
442C2×Q16—74no—
443C2×Q16—144no—
444C2×Q16—282no—
445C2×SD16—74no—
446C2×SD16—74no—
447C2×SD16—74no—
448C2×SD16—74no—
449C2×SD16—74no—
450C2×SD16—144no—
451C2×SD16—282no—
452C2×SD16—282no—
453C2×SD16—282no—
454C2×SD16—282no—
455C2×D8—74no—
456C2×D8—74no—
457C2×D8—144no—
458C2×D8—282no—
459C22×C8—71no—
460C22×C8—71no—
461C22×C8—71no—
462C22×C8—71no—
463C4⋊Q8—22no—
464C4⋊Q8C22×D714yes—
465#127—74no—
466#127—142no—
467#126—28no—
468#126—28no—
469#124—22no—
470#124—22no—
471#124—74no—
472#124—74no—
473#124—148no—
474#124—142no—
475#124—142no—
476#124C22×D714yes—
477#124C22×D714yes—
478#123—148no—
479#123—148no—
480C22⋊Q8—28no—
481C4×Q8—22no—
482C4×Q8—22no—
483C4×Q8—74no—
484C4×Q8—142no—
485C4×Q8C22⋊D714yes—
486C4×Q8C22×D714yes—
487C4×Q8C22×D714yes—
488C4×Q8C22×D714yes—
489C4×D4—22no—
490C4×D4—74no—
491C4×D4—74no—
492C4×D4—148no—
493C4×D4—142no—
494C4×D4—142no—
495C4×D4C22×D714yes—
496#117—28no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—71no—
502C2×C4⋊C4—141no—
503C2×C4⋊C4C22⋊D711yescharacteristic
504C2×C4⋊C4C22⋊D711yescharacteristic
505C2×C4⋊C4C22⋊D711yescharacteristic
506C2×C4⋊C4C22×D711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—141no—
513C2×C22⋊C4—141no—
514C2×C22⋊C4—141no—
515C2×C22⋊C4—141no—
516C2×C22⋊C4—141no—
517C2×C22⋊C4—141no—
518C2×C42—21no—
519C2×C42—21no—
520C2×C42—141no—
521C2×C42C22×D711yescharacteristic
522C2×C42C22×D711yescharacteristic
523C2×C42C22×D711yescharacteristic
524#106—74no—
525C4⋊C8—74no—
526C4⋊C8—74no—
527C4⋊C8—74no—
528#103—74no—
529#103—74no—
530#103—74no—
531#102—74no—
532#102—74no—
533#102—74no—
534#97—74no—
535#97—74no—
536C4×C8—74no—
537C22×C7—42no—
538C22×C7—42no—
539C22×C7—42no—
540C22×C7—84no—
541C22×C7#55012yes—
542C22×C7#57512yes—
543C22×C7#57712yes—
544C22×C7C23×D411yescharacteristic
545C2×D7—42no—
546C2×D7—42no—
547C2×D7—42no—
548C2×D7—42no—
549C2×D7—42no—
550C2×D7—42no—
551C2×D7—84no—
552C2×D7—84no—
553C4×C7—22no—
554C4×C7—22no—
555C4×C7—22no—
556C4×C7—22no—
557C4×C7—22no—
558C4×C7—22no—
559C4×C7—42no—
560C4×C7—42no—
561C4×C7—42no—
562C4×C7#55012yes—
563C4×C7C22×#4111yescharacteristic
564C4×C7C2×H(5,𝔽2)11yescharacteristic
565Dic7—42no—
566Dic7—42no—
567C24—21no—
568C24—141no—
569C24—141no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—42no—
577C2×Q8—72no—
578C2×Q8—141no—
579C2×Q8—142no—
580C2×Q8—142no—
581C2×Q8C2×C22⋊D714yes—
582C2×Q8C23×D712yes—
583C2×Q8C23×D712yes—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—72no—
588C2×D4—72no—
589C2×D4—142no—
590C2×D4—142no—
591C2×D4—142no—
592C2×D4—142no—
593C2×D4—144no—
594C2×D4—141no—
595C2×D4—141no—
596C2×D4—144no—
597C2×D4—284no—
598C2×D4—562no—
599C2×D4C23×D712yes—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—24no—
604C22×C4—44no—
605C22×C4—141no—
606C22×C4—141no—
607C22×C4—144no—
608C22×C4—144no—
609C22×C4—562no—
610C22×C4—562no—
611C22×C4C2×C22⋊D711yescharacteristic
612C22×C4C2×C22⋊D711yescharacteristic
613C22×C4C2×C22⋊D711yescharacteristic
614C22×C4C2×C22⋊D711yescharacteristic
615C22×C4C2×C22⋊D711yescharacteristic
616C22×C4C2×C22⋊D711yescharacteristic
617C22×C4C23×D711yescharacteristic
618Q16—148no—
619Q16—284no—
620SD16—148no—
621SD16—284no—
622SD16—284no—
623SD16—284no—
624SD16—284no—
625D8—148no—
626D8—284no—
627C2×C8—74no—
628C2×C8—72no—
629C2×C8—72no—
630C2×C8—72no—
631C2×C8—72no—
632C2×C8—142no—
633C2×C8—142no—
634C2×C8—142no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—24no—
639C4⋊C4—21no—
640C4⋊C4—72no—
641C4⋊C4—144no—
642C4⋊C4—141no—
643C4⋊C4C2×C22⋊D714yes—
644C4⋊C4C2×C22⋊D714yes—
645C4⋊C4C2×C22⋊D714yes—
646C4⋊C4C23×D712yes—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—144no—
653C22⋊C4—144no—
654C22⋊C4—144no—
655C22⋊C4—144no—
656C22⋊C4—144no—
657C22⋊C4—144no—
658C42—24no—
659C42—24no—
660C42—144no—
661C42C2×C22⋊D712yes—
662C42C2×C22⋊D712yes—
663C42C2×C22⋊D712yes—
664C42C23×D712yes—
665C42C23×D712yes—
666C42C23×D712yes—
667C2×C7—82no—
668C2×C7#340114yescomplemented
669C2×C7C2×#55011yescharacteristic
670C2×C7C2×#57511yescharacteristic
671C2×C7C2×#57711yescharacteristic
672D7—82no—
673D7—82no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—142no—
679C23—142no—
680C23—282no—
681C23—282no—
682C23—282no—
683C23—282no—
684C23—282no—
685C23—282no—
686C23C22×C22⋊D711yescharacteristic
687Q8—22no—
688Q8—22no—
689Q8—22no—
690Q8—22no—
691Q8—44no—
692Q8—42no—
693Q8—42no—
694Q8—142no—
695Q8—142no—
696Q8—282no—
697D4—22no—
698D4—22no—
699D4—42no—
700D4—142no—
701D4—142no—
702D4—142no—
703D4—142no—
704D4—288no—
705D4—282no—
706D4—282no—
707D4—564no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
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—142no—
722C2×C4—142no—
723C2×C4—282no—
724C2×C4—282no—
725C2×C4—564no—
726C2×C4—564no—
727C2×C4D7×#4112yes—
728C2×C4#655312yes—
729C2×C4C22×C22⋊D712yes—
730C2×C4C22×C22⋊D712yes—
731C2×C4C22×C22⋊D712yes—
732C2×C4C22×C22⋊D712yes—
733C2×C4C22×C22⋊D712yes—
734C2×C4C22×C22⋊D712yes—
735C2×C4C22×C22⋊D711yescharacteristic
736C2×C4C24×D711yescharacteristic
737C8—74no—
738C8—142no—
739C8—142no—
740C8—142no—
741C7C2×#340111yescharacteristic, complemented, Sylow
742C22—42no—
743C22—42no—
744C22—42no—
745C22—84no—
746C22—282no—
747C22—282no—
748C22—282no—
749C22—282no—
750C22—282no—
751C22—282no—
752C22—564no—
753C22—564no—
754C22#9051312yes—
755C22#9052512yes—
756C22#9052812yes—
757C22C23×C22⋊D711yescharacteristic
758C4—22no—
759C4—22no—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—42no—
765C4—42no—
766C4—42no—
767C4—282no—
768C4—282no—
769C4#9052512yes—
770C4C2×D7×#4111yescharacteristic
771C4C2×#655311yescharacteristic
772C2—82no—
773C2—562no—
774C2—562no—
775C2#1174111714yesdirect product factor
776C2C2×#9051311yescharacteristic
777C2C2×#9052511yescharacteristic
778C2C2×#9052811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#556C2
socleC23×C7C22×D4
prime radicalC2×#89830C2
hypercenterC2×#556D7
hypocenterC7C2×#3401
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×C7×#556C2semidirect
2. C2×#90276C2semidirect
3. #11741117C2direct (N × H)
4. C2×#89855C2semidirect
5. C2×#89858C2semidirect
6. C2×#89826C2semidirect
7. C2×#89829C2semidirect
9. C2×#89831C2semidirect
10. C2×#89800C2semidirect
11. C2×#89799C2semidirect
12. C2×#89796C2semidirect
13. C2×#89802C2semidirect
14. C2×C4×#1143C2semidirect
15. C2×#89788C2semidirect
16. C2×#89786C2semidirect
18. C7×#556C22semidirect
41. #90276C22semidirect
54. #89858C22semidirect
55. #89855C22semidirect
56. #89831C22semidirect
58. #89829C22semidirect
59. #89826C22semidirect
60. #89802C22semidirect
61. #89800C22semidirect
62. #89799C22semidirect
63. C4×#1143C22semidirect
64. #89796C22semidirect
65. #89788C22semidirect
66. #89786C22semidirect
187. C2×#556D7semidirect
314. #556C2×D7semidirect
668. C2×C7#3401semidirect
741. C7C2×#3401semidirect
775. C2#11741117direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5562
C2×#902762
#117411172
C2×#898552
C2×#898582
C2×#898262
C2×#898292
C2×#898302
C2×#898312
C2×#898002
C2×#897992
C2×#897962
C2×#898022
C2×C4×#11432
C2×#897882
C2×#897862
C2×#34017