Finite Group Databasebeta

← C2×#11740910 #14226706

Subgroups — C2×#11740910 #14226706

Order 1792.

1946 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#542C211yesmaximal, characteristic, complemented
2C2×#90226C211yesmaximal, characteristic, complemented
3#11740910C2116yesmaximal, direct product factor
4C2×#89856C211yesmaximal, characteristic, complemented
5C2×#89859C211yesmaximal, characteristic, complemented
6C2×#89829C211yesmaximal, characteristic, complemented
7C2×#89829C211yesmaximal, characteristic, complemented
8C2×#89821C211yesmaximal, characteristic, complemented
9C2×#89820C211yesmaximal, characteristic, complemented
10C2×#89811C211yesmaximal, characteristic, complemented
11C2×#89810C211yesmaximal, characteristic, complemented
12C2×#89799C211yesmaximal, characteristic, complemented
13C2×#89794C211yesmaximal, characteristic, complemented
14C2×#89787C211yesmaximal, characteristic, complemented
15C2×#89781C211yesmaximal, characteristic, complemented
16C2×#89771C211yesmaximal, characteristic, complemented
17C7×#542—24no—
18C7×#542C2218yescomplemented
19C2×C7×C4⋊Q8C2211yescharacteristic
20C2×C7×#126—21no—
21C2×C7×#124—21no—
22C2×C7×#124C2211yescharacteristic
23C2×C7×#123—21no—
24C2×C7×C22⋊Q8—21no—
25C2×C7×C22⋊Q8C2211yescharacteristic
26C2×C7×#121C2211yescharacteristic
27C2×C4×C7×Q8C2211yescharacteristic
28C2×C4×C7×D4C2211yescharacteristic
29C2×C7×#117C2211yescharacteristic
30C22×#1143C2211yescharacteristic
31C22×#1143C2211yescharacteristic
32C22×#1141C2211yescharacteristic
33C22×#1141C2211yescharacteristic
34C2×#6493C2211yescharacteristic
35C2×#6493C2211yescharacteristic
36C22×#1136C2211yescharacteristic
37C23×C7⋊C8C2211yescharacteristic
38#90226—24no—
39#90226C2218yescomplemented
40C2×#6457—21no—
41C2×#6457—21no—
42C2×#6447—21no—
43C2×#6447—21no—
44C2×#6437C2211yescharacteristic
45C2×C4×D28C2211yescharacteristic
46C2×C4×D28C2211yescharacteristic
47C2×#6433C2211yescharacteristic
48C2×#6409C2211yescharacteristic
49C2×#6409C2211yescharacteristic
50C2×#6406C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52#89859C2218yescomplemented
53#89856C2218yescomplemented
54#89829C2218yescomplemented
55#89829C2218yescomplemented
56#89821C2218yescomplemented
57#89820C2218yescomplemented
58#89811C2218yescomplemented
59#89810C2218yescomplemented
60#89799C2218yescomplemented
61#89794C2218yescomplemented
62#89787C2218yescomplemented
63#89781C2218yescomplemented
64#89771C2218yescomplemented
65C2×#6383C2211yescharacteristic
66C2×#6383C2211yescharacteristic
67C2×#6383C2211yescharacteristic
68C2×#6383C2211yescharacteristic
69C2×#6382C2211yescharacteristic
70C2×#6382C2211yescharacteristic
71C2×#6381C2211yescharacteristic
72C2×#6381C2211yescharacteristic
73C2×C4⋊(C7⋊C8)C2211yescharacteristic
74C2×C4⋊(C7⋊C8)C2211yescharacteristic
75C2×C4⋊(C7⋊C8)C2211yescharacteristic
76C2×C4⋊(C7⋊C8)C2211yescharacteristic
77C2×#3257—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8C2311yescharacteristic
80C22×C7×D4—21no—
81C22×C7×D4C2311yescharacteristic
82C23×C4×C7—21no—
83C23×C4×C7C2311yescharacteristic
84C22×C22⋊D7—21no—
85C22×C22⋊D7—21no—
86C22×D28—21no—
87C22×D28—21no—
88C22×D28C2311yescharacteristic
89C22×D28C2311yescharacteristic
90C22×C4×D7—21no—
91C22×C4×D7—21no—
92C7×C4⋊Q8—22no—
93C7×C4⋊Q8C2314yes—
94C7×#126—28no—
95C7×#124—28no—
96C7×#124—22no—
97C7×#124C2314yes—
98C7×#123—28no—
99C7×C22⋊Q8—22no—
100C7×C22⋊Q8—28no—
101C7×C22⋊Q8C2314yes—
102C7×#121—22no—
103C7×#121C2314yes—
104C4×C7×Q8—22no—
105C4×C7×Q8C2314yes—
106C4×C7×D4—22no—
107C4×C7×D4C2314yes—
108C7×#117D414yes—
109C7×#117C2314yes—
110C2×C7×C4⋊C4—21no—
111C2×C7×C4⋊C4—21no—
112C2×C7×C4⋊C4—21no—
113C2×C7×C4⋊C4D411yescharacteristic
114C2×C7×C4⋊C4D411yescharacteristic
115C2×C7×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
122C2×C7×C22⋊C4D411yescharacteristic
123C2×C7×C22⋊C4D411yescharacteristic
124C2×C42×C7—21no—
125C2×C42×C7C2311yescharacteristic
126C2×C42×C7C2311yescharacteristic
127C2×#1143—42no—
128C2×#1143—42no—
129C2×#1143C2314yes—
130C2×#1143C2314yes—
131C2×#1141—42no—
132C2×#1141—42no—
133C2×#1141C2314yes—
134C2×#1141C2314yes—
135#6493—22no—
136#6493—22no—
137#6493C2314yes—
138#6493C2314yes—
139C2×(C2×D7)⋊C4—21no—
140C2×(C2×D7)⋊C4—21no—
141C2×(C2×D7)⋊C4—21no—
142C2×(C2×D7)⋊C4—21no—
143C2×C4⋊Dic7C2311yescharacteristic
144C2×C4⋊Dic7C2311yescharacteristic
145C2×Dic7⋊C4—21no—
146C2×Dic7⋊C4—21no—
147C2×#1136—42no—
148C2×#1136C2314yes—
149C22×C7⋊C8—42no—
150C22×C7⋊C8C2311yescharacteristic
151C22×C7⋊C8C2311yescharacteristic
152C22×C7⋊C8C2311yescharacteristic
153C22×C7⋊C8C2311yescharacteristic
154C22×C7⋊C8C2314yes—
155#6457—28no—
156#6457—28no—
157#6447—28no—
158#6447—28no—
159#6437—22no—
160#6437C2314yes—
161C4×D28—22no—
162C4×D28—22no—
163C4×D28C2314yes—
164C4×D28C2314yes—
165#6433—22no—
166#6433C2314yes—
167#6409C2314yes—
168#6409C2314yes—
169#6406C2314yes—
170#6406C2314yes—
171#6383C2314yes—
172#6383C2314yes—
173#6383C2314yes—
174#6383C2314yes—
175#6382C2314yes—
176#6382C2314yes—
177#6381C2314yes—
178#6381C2314yes—
179C4⋊(C7⋊C8)C2314yes—
180C4⋊(C7⋊C8)C2314yes—
181C4⋊(C7⋊C8)C2314yes—
182C4⋊(C7⋊C8)C2314yes—
183C2×#542D711yescharacteristic, complemented
184C2×#540—71no—
185#3257—716no—
186C2×#479—71no—
187C2×#478—71no—
188C2×#476—71no—
189C2×#474—71no—
190C2×#469—71no—
191C2×#468—71no—
192C2×#466—71no—
193C2×#465—71no—
194C2×#460—71no—
195C2×#463—71no—
196C2×#463—71no—
197C2×#459—71no—
198C2×#424—71no—
199C24×C7—21no—
200C24×C7C2×D411yescharacteristic
201C23×D7—21no—
202C23×D7—21no—
203C2×C7×Q8—21no—
204C2×C7×Q8—24no—
205C2×C7×Q8—22no—
206C2×C7×Q8—22no—
207C2×C7×Q8—82no—
208C2×C7×Q8C2412yes—
209C2×C7×D4—24no—
210C2×C7×D4—21no—
211C2×C7×D4—22no—
212C2×C7×D4—22no—
213C2×C7×D4—82no—
214C2×C7×D4C2412yes—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7—24no—
221C22×C4×C7—82no—
222C22×C4×C7C2×D411yescharacteristic
223C22×C4×C7C2×D411yescharacteristic
224C22×C4×C7C2×D411yescharacteristic
225C22×C4×C7C2×D411yescharacteristic
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—82no—
233C2×C22⋊D7—82no—
234C22×Dic7—21no—
235C22×Dic7—21no—
236C2×D28—22no—
237C2×D28—22no—
238C2×D28—22no—
239C2×D28—22no—
240C2×D28—21no—
241C2×D28—21no—
242C2×D28—24no—
243C2×D28—24no—
244C2×D28—82no—
245C2×D28—82no—
246C2×D28C2412yes—
247C2×D28C2412yes—
248C2×C4×D7—24no—
249C2×C4×D7—24no—
250C2×C4×D7—82no—
251C2×C4×D7—82no—
252C7×C4⋊C4—24no—
253C7×C4⋊C4—24no—
254C7×C4⋊C4—24no—
255C7×C4⋊C4—21no—
256C7×C4⋊C4—21no—
257C7×C4⋊C4C2×D414yes—
258C7×C4⋊C4C2×D414yes—
259C7×C4⋊C4C2412yes—
260C7×C4⋊C4C2412yes—
261C7×C22⋊C4—24no—
262C7×C22⋊C4—24no—
263C7×C22⋊C4—24no—
264C7×C22⋊C4—24no—
265C7×C22⋊C4—24no—
266C7×C22⋊C4C2×D414yes—
267C7×C22⋊C4C2×D414yes—
268C42×C7—24no—
269C42×C7C2×D412yes—
270C42×C7C2×D412yes—
271C42×C7C2412yes—
272C42×C7C2412yes—
273#1143—44no—
274#1143—44no—
275#1141—44no—
276#1141—44no—
277(C2×D7)⋊C4—24no—
278(C2×D7)⋊C4—24no—
279(C2×D7)⋊C4—24no—
280(C2×D7)⋊C4—24no—
281C4⋊Dic7—21no—
282C4⋊Dic7—21no—
283C4⋊Dic7C2412yes—
284C4⋊Dic7C2412yes—
285Dic7⋊C4—24no—
286Dic7⋊C4—24no—
287#1136—44no—
288C2×C7⋊C8—22no—
289C2×C7⋊C8—22no—
290C2×C7⋊C8—22no—
291C2×C7⋊C8—22no—
292C2×C7⋊C8—44no—
293C2×C7⋊C8C2412yes—
294C2×C7⋊C8C2412yes—
295C2×C7⋊C8C2412yes—
296C2×C7⋊C8C2412yes—
297C22×SD16—71no—
298C22×SD16—71no—
299C22×D8—71no—
300C22×D8—71no—
301C22×M16—71no—
302C23×C8—71no—
303#542—24no—
304#542C2×D718yescomplemented
305#540—78no—
306#540—144no—
307C2×C4⋊Q8C2×D711yescharacteristic
308C2×#127—71no—
309C2×#126—21no—
310C2×#125—71no—
311C2×#124—21no—
312C2×#124C2×D711yescharacteristic
313C2×#123—21no—
314C2×#123—141no—
315C2×#123—141no—
316C2×C22⋊Q8—21no—
317C2×C22⋊Q8C2×D711yescharacteristic
318C2×#121—71no—
319C2×#121—71no—
320C2×#121—141no—
321C2×#121—141no—
322C2×#121C2×D711yescharacteristic
323C2×C4×Q8C2×D711yescharacteristic
324C2×C4×D4—71no—
325C2×C4×D4—71no—
326C2×C4×D4C2×D711yescharacteristic
327C2×#117C2×D711yescharacteristic
328#479—78no—
329#478—78no—
330#476—78no—
331#474—78no—
332#469—78no—
333#468—78no—
334#466—78no—
335#465—78no—
336#463—78no—
337#463—78no—
338#460—78no—
339#459—78no—
340C2×#107—71no—
341C2×#107—71no—
342C2×#106—71no—
343C2×#106—71no—
344#424—78no—
345C2×C4⋊C8—71no—
346C2×C4⋊C8—71no—
347C2×C4⋊C8—71no—
348C2×C4⋊C8—71no—
349C2×#103—71no—
350C2×#103—71no—
351C2×#102—71no—
352C2×#102—71no—
353C2×#102—71no—
354C2×#102—71no—
355C2×#102—71no—
356C2×#102—71no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—42no—
362C23×C7—42no—
363C23×C7—42no—
364C23×C7C22×D412yes—
365C23×C7C22×D411yescharacteristic
366C22×D7—22no—
367C22×D7—22no—
368C22×D7—42no—
369C22×D7—42no—
370C22×D7—42no—
371C22×D7—42no—
372C22×D7—42no—
373C22×D7—42no—
374C7×Q8—22no—
375C7×Q8—22no—
376C7×Q8—42no—
377C7×Q8—84no—
378C7×D4—22no—
379C7×D4—22no—
380C7×D4—42no—
381C7×D4—84no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—24no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—42no—
394C2×C4×C7—42no—
395C2×C4×C7—42no—
396C2×C4×C7—84no—
397C2×C4×C7C22×D412yes—
398C2×C4×C7C22×D412yes—
399C2×C4×C7C22×D412yes—
400C2×C4×C7C22×D412yes—
401C2×C4×C7C22×D412yes—
402C2×C4×C7C22×D411yescharacteristic
403C2×C4×C7H(5,𝔽2)12yes—
404C2×C4×C72−1+412yes—
405C2×C4×C7C2511yescharacteristic
406C22⋊D7—84no—
407C22⋊D7—84no—
408C2×Dic7—22no—
409C2×Dic7—22no—
410C2×Dic7—42no—
411C2×Dic7—42no—
412D28—22no—
413D28—22no—
414D28—22no—
415D28—22no—
416D28—42no—
417D28—42no—
418D28—84no—
419D28—84no—
420C4×D7—84no—
421C4×D7—84no—
422C7⋊C8—22no—
423C7⋊C8—22no—
424C7⋊C8—22no—
425C7⋊C8—22no—
426C22×Q8—21no—
427C22×Q8C22×D711yescharacteristic
428C22×D4—21no—
429C22×D4—71no—
430C22×D4—71no—
431C22×D4—141no—
432C22×D4—141no—
433C22×D4—141no—
434C22×D4—141no—
435C22×D4C22×D711yescharacteristic
436C23×C4—21no—
437C23×C4—141no—
438C23×C4—141no—
439C23×C4C22×D711yescharacteristic
440C2×SD16—74no—
441C2×SD16—74no—
442C2×SD16—282no—
443C2×SD16—282no—
444C2×D8—74no—
445C2×D8—74no—
446C2×D8—282no—
447C2×D8—282no—
448C2×M16—74no—
449C2×M16—282no—
450C22×C8—71no—
451C22×C8—71no—
452C22×C8—71no—
453C22×C8—71no—
454C22×C8—74no—
455C22×C8—282no—
456C4⋊Q8—22no—
457C4⋊Q8C22×D714yes—
458#127—74no—
459#127—142no—
460#126—28no—
461#125—74no—
462#125—142no—
463#124—28no—
464#124—22no—
465#124C22×D714yes—
466#123—28no—
467#123—148no—
468#123—148no—
469C22⋊Q8—22no—
470C22⋊Q8—28no—
471C22⋊Q8C22×D714yes—
472#121—22no—
473#121—74no—
474#121—74no—
475#121—142no—
476#121—142no—
477#121—148no—
478#121—148no—
479#121C22×D714yes—
480C4×Q8—22no—
481C4×Q8C22×D714yes—
482C4×D4—22no—
483C4×D4—74no—
484C4×D4—74no—
485C4×D4—142no—
486C4×D4—142no—
487C4×D4C22×D714yes—
488#117C22⋊D714yes—
489#117C22×D714yes—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—71no—
494C2×C4⋊C4—71no—
495C2×C4⋊C4—141no—
496C2×C4⋊C4—141no—
497C2×C4⋊C4C22⋊D711yescharacteristic
498C2×C4⋊C4C22⋊D711yescharacteristic
499C2×C4⋊C4C22×D711yescharacteristic
500C2×C4⋊C4C22×D711yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—141no—
507C2×C22⋊C4—141no—
508C2×C22⋊C4—141no—
509C2×C22⋊C4—141no—
510C2×C22⋊C4C22⋊D711yescharacteristic
511C2×C22⋊C4C22⋊D711yescharacteristic
512C2×C42—21no—
513C2×C42C22×D711yescharacteristic
514C2×C42C22×D711yescharacteristic
515#107—74no—
516#107—74no—
517#106—74no—
518#106—74no—
519C4⋊C8—74no—
520C4⋊C8—74no—
521C4⋊C8—74no—
522C4⋊C8—74no—
523#103—74no—
524#103—74no—
525#102—74no—
526#102—74no—
527#102—74no—
528#102—74no—
529#102—74no—
530#102—74no—
531C22×C7—22no—
532C22×C7—22no—
533C22×C7—22no—
534C22×C7—44no—
535C22×C7—42no—
536C22×C7—42no—
537C22×C7—42no—
538C22×C7—84no—
539C22×C7#53712yes—
540C22×C7#57612yes—
541C22×C7#57712yes—
542C22×C7C23×D411yescharacteristic
543C2×D7—42no—
544C2×D7—42no—
545C2×D7—42no—
546C2×D7—42no—
547C2×D7—42no—
548C2×D7—42no—
549C2×D7—84no—
550C2×D7—84no—
551C4×C7—22no—
552C4×C7—22no—
553C4×C7—22no—
554C4×C7—22no—
555C4×C7—22no—
556C4×C7—42no—
557C4×C7—42no—
558C4×C7—42no—
559C4×C7#53712yes—
560C4×C7C2×H(5,𝔽2)11yescharacteristic
561C4×C7C2×2−1+411yescharacteristic
562Dic7—42no—
563Dic7—42no—
564C24—21no—
565C24—141no—
566C24—141no—
567C24C2×C22⋊D711yescharacteristic
568C2×Q8—21no—
569C2×Q8—24no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—82no—
573C2×Q8C23×D712yes—
574C2×D4—24no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—72no—
579C2×D4—72no—
580C2×D4—82no—
581C2×D4—144no—
582C2×D4—144no—
583C2×D4—142no—
584C2×D4—142no—
585C2×D4—142no—
586C2×D4—142no—
587C2×D4—141no—
588C2×D4—141no—
589C2×D4—144no—
590C2×D4—144no—
591C2×D4—562no—
592C2×D4—562no—
593C2×D4—562no—
594C2×D4—562no—
595C2×D4C23×D712yes—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—82no—
603C22×C4—141no—
604C22×C4—141no—
605C22×C4—144no—
606C22×C4—144no—
607C22×C4—562no—
608C22×C4—562no—
609C22×C4C2×C22⋊D712yes—
610C22×C4C2×C22⋊D711yescharacteristic
611C22×C4C2×C22⋊D711yescharacteristic
612C22×C4C2×C22⋊D711yescharacteristic
613C22×C4C2×C22⋊D711yescharacteristic
614C22×C4C2×C22⋊D711yescharacteristic
615C22×C4C23×D712yes—
616C22×C4C23×D711yescharacteristic
617SD16—284no—
618SD16—284no—
619D8—284no—
620D8—284no—
621M16—284no—
622C2×C8—72no—
623C2×C8—72no—
624C2×C8—72no—
625C2×C8—72no—
626C2×C8—142no—
627C2×C8—142no—
628C2×C8—142no—
629C2×C8—142no—
630C2×C8—284no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—72no—
637C4⋊C4—72no—
638C4⋊C4—144no—
639C4⋊C4—144no—
640C4⋊C4—141no—
641C4⋊C4—141no—
642C4⋊C4C2×C22⋊D714yes—
643C4⋊C4C2×C22⋊D714yes—
644C4⋊C4C23×D712yes—
645C4⋊C4C23×D712yes—
646C22⋊C4—24no—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—144no—
652C22⋊C4—144no—
653C22⋊C4—144no—
654C22⋊C4—144no—
655C22⋊C4C2×C22⋊D714yes—
656C22⋊C4C2×C22⋊D714yes—
657C42—24no—
658C42C2×C22⋊D712yes—
659C42C2×C22⋊D712yes—
660C42C23×D712yes—
661C42C23×D712yes—
662C2×C7—42no—
663C2×C7—82no—
664C2×C7#325714yescomplemented
665C2×C7C2×#53711yescharacteristic
666C2×C7C2×#57611yescharacteristic
667C2×C7C2×#57711yescharacteristic
668D7—82no—
669D7—82no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—142no—
678C23—142no—
679C23—282no—
680C23—282no—
681C23—282no—
682C23—282no—
683C23—282no—
684C23—282no—
685C23C22×C22⋊D712yes—
686C23C22×C22⋊D711yescharacteristic
687Q8—22no—
688Q8—22no—
689Q8—42no—
690Q8—84no—
691D4—22no—
692D4—22no—
693D4—42no—
694D4—84no—
695D4—142no—
696D4—142no—
697D4—142no—
698D4—142no—
699D4—282no—
700D4—282no—
701D4—564no—
702D4—564no—
703D4—564no—
704D4—564no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—84no—
720C2×C4—142no—
721C2×C4—142no—
722C2×C4—282no—
723C2×C4—282no—
724C2×C4—564no—
725C2×C4—564no—
726C2×C4#655312yes—
727C2×C4#655412yes—
728C2×C4C22×C22⋊D712yes—
729C2×C4C22×C22⋊D712yes—
730C2×C4C22×C22⋊D712yes—
731C2×C4C22×C22⋊D712yes—
732C2×C4C22×C22⋊D712yes—
733C2×C4C22×C22⋊D711yescharacteristic
734C2×C4C24×D711yescharacteristic
735C8—142no—
736C8—142no—
737C8—142no—
738C8—142no—
739C7C2×#325711yescharacteristic, complemented, Sylow
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—84no—
748C22—282no—
749C22—282no—
750C22—282no—
751C22—282no—
752C22—282no—
753C22—282no—
754C22—564no—
755C22—564no—
756C22#9052412yes—
757C22#9052612yes—
758C22#9052812yes—
759C22C23×C22⋊D711yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—42no—
766C4—42no—
767C4—42no—
768C4—282no—
769C4—282no—
770C4#9052412yes—
771C4C2×#655311yescharacteristic
772C4C2×#655411yescharacteristic
773C2—42no—
774C2—82no—
775C2—562no—
776C2—562no—
777C2#1174091014yesdirect product factor
778C2C2×#9052411yescharacteristic
779C2C2×#9052611yescharacteristic
780C2C2×#9052811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#542C2
socleC23×C7C22×D4
hypercenterC2×#542D7
hypocenterC7C2×#3257
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×C7×#542C2semidirect
2. C2×#90226C2semidirect
3. #11740910C2direct (N × H)
4. C2×#89856C2semidirect
5. C2×#89859C2semidirect
6. C2×#89829C2semidirect
7. C2×#89829C2semidirect
8. C2×#89821C2semidirect
9. C2×#89820C2semidirect
10. C2×#89811C2semidirect
11. C2×#89810C2semidirect
12. C2×#89799C2semidirect
13. C2×#89794C2semidirect
14. C2×#89787C2semidirect
15. C2×#89781C2semidirect
16. C2×#89771C2semidirect
18. C7×#542C22semidirect
39. #90226C22semidirect
52. #89859C22semidirect
53. #89856C22semidirect
54. #89829C22semidirect
55. #89829C22semidirect
56. #89821C22semidirect
57. #89820C22semidirect
58. #89811C22semidirect
59. #89810C22semidirect
60. #89799C22semidirect
61. #89794C22semidirect
62. #89787C22semidirect
63. #89781C22semidirect
64. #89771C22semidirect
183. C2×#542D7semidirect
304. #542C2×D7semidirect
664. C2×C7#3257semidirect
739. C7C2×#3257semidirect
777. C2#11740910direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5422
C2×#902262
#117409102
C2×#898562
C2×#898592
C2×#898292
C2×#898212
C2×#898202
C2×#898112
C2×#898102
C2×#897992
C2×#897942
C2×#897872
C2×#897812
C2×#897712
C2×#32577