Finite Group Databasebeta

← C2×#11741084 #14233545

Subgroups — C2×#11741084 #14233545

Order 1792.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#554C211yesmaximal, characteristic, complemented
2C2×#90276C211yesmaximal, characteristic, complemented
3#11741084C2116yesmaximal, direct product factor
4C2×#89859C211yesmaximal, characteristic, complemented
5C2×#89861C211yesmaximal, characteristic, complemented
6C2×#89835C211yesmaximal, characteristic, complemented
7C2×#89838C211yesmaximal, characteristic, complemented
8C2×#89839C211yesmaximal, characteristic, complemented
9C2×#89840C211yesmaximal, characteristic, complemented
10C2×#89796C211yesmaximal, characteristic, complemented
11C2×#89788C211yesmaximal, characteristic, complemented
12C2×#89788C211yesmaximal, characteristic, complemented
13C2×#89787C211yesmaximal, characteristic
14C2×#89786C211yesmaximal, characteristic, complemented
15C2×#89790C211yesmaximal, characteristic, complemented
16C2×C4×#1141C211yesmaximal, characteristic, complemented
17C7×#554—24no—
18C7×#554C2218yescomplemented
19C2×C7×C4⋊Q8C2211yescharacteristic
20C2×C7×#125C2211yescharacteristic
21C2×C7×#125C2211yescharacteristic
22C2×C7×C22⋊Q8—21no—
23C2×C7×C22⋊Q8—21no—
24C2×C7×C22⋊Q8—21no—
25C2×C4×C7×Q8C2211yescharacteristic
26C2×C4×C7×D4C2211yescharacteristic
27C2×C4×C7×D4C2211yescharacteristic
28C2×C4×C7×D4C2211yescharacteristic
29C22×C7×C4⋊C4—21no—
30C2×#6510—21no—
31C22×#1142C2211yescharacteristic
32C22×#1141C2211yescharacteristic
33C22×#1141C2211yescharacteristic
34#90276—24no—
35#90276C2218yescomplemented
36C2×#6457—21no—
37C2×#6457—21no—
38C2×#6456—21no—
39C2×#6438C2211yescharacteristic
40C2×#6438C2211yescharacteristic
41C2×#6437C2211yescharacteristic
42C2×C4×D28C2211yescharacteristic
43C2×C4×D28C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C2×#6406C2211yescharacteristic
46#89861C2218yescomplemented
47#89859C2218yescomplemented
48#89840C2218yescomplemented
49#89839C2218yescomplemented
50#89838C2218yescomplemented
51#89835C2218yescomplemented
52#89796C2218yescomplemented
53#89790C2218yescomplemented
54#89788C2218yescomplemented
55#89788C2218yescomplemented
56#89787C2218yes—
57#89786C2218yescomplemented
58C4×#1141C2218yescomplemented
59C2×#6384C2211yescharacteristic
60C2×#6384C2211yescharacteristic
61C2×#6384C2211yescharacteristic
62C2×#6383C2211yescharacteristic
63C2×#6383C2211yescharacteristic
64C2×#6383C2211yescharacteristic
65C2×#6383C2211yescharacteristic
66C2×#6383C2211yescharacteristic
67C2×#6383C2211yescharacteristic
68C2×#6382C2211yescharacteristic
69C2×#6381C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71C2×C4⋊(C7⋊C8)C2211yescharacteristic
72C2×C4⋊(C7⋊C8)C2211yescharacteristic
73C2×C4⋊(C7⋊C8)C2211yescharacteristic
74C2×#6377C2211yescharacteristic
75C2×#6377C2211yescharacteristic
76C2×C4×C7⋊C8C2211yescharacteristic
77C2×#3370—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8D411yescharacteristic
80C22×C7×D4C2311yescharacteristic
81C23×C4×C7—21no—
82C23×C4×C7—21no—
83C23×C4×C7—21no—
84C22×D28—21no—
85C22×D28—21no—
86C22×D28C2311yescharacteristic
87C22×D28C2311yescharacteristic
88C22×C4×D7—21no—
89C22×C4×D7—21no—
90C22×Dic14C2311yescharacteristic
91C7×C4⋊Q8—22no—
92C7×C4⋊Q8C2314yes—
93C7×#125—22no—
94C7×#125—22no—
95C7×#125C2314yes—
96C7×#125C2314yes—
97C7×C22⋊Q8—28no—
98C7×C22⋊Q8—28no—
99C7×C22⋊Q8—28no—
100C4×C7×Q8D414yes—
101C4×C7×Q8C2314yes—
102C4×C7×D4—22no—
103C4×C7×D4—22no—
104C4×C7×D4—22no—
105C4×C7×D4C2314yes—
106C4×C7×D4C2314yes—
107C4×C7×D4C2314yes—
108C2×C7×C4⋊C4—21no—
109C2×C7×C4⋊C4—21no—
110C2×C7×C4⋊C4—21no—
111C2×C7×C4⋊C4—21no—
112C2×C7×C4⋊C4—21no—
113C2×C7×C4⋊C4—28no—
114C2×C7×C4⋊C4D411yescharacteristic
115C2×C7×C4⋊C4D411yescharacteristic
116C2×C7×C4⋊C4D411yescharacteristic
117C2×C7×C4⋊C4C2311yescharacteristic
118C2×C7×C4⋊C4C2311yescharacteristic
119C2×C7×C4⋊C4C2311yescharacteristic
120C2×C7×C22⋊C4—21no—
121C2×C7×C22⋊C4—21no—
122C2×C7×C22⋊C4—21no—
123C2×C42×C7C2311yescharacteristic
124C2×C42×C7C2311yescharacteristic
125C2×C42×C7C2311yescharacteristic
126#6510—28no—
127C2×#1142—24no—
128C2×#1142C2314yes—
129C2×#1141—24no—
130C2×#1141—24no—
131C2×#1141C2314yes—
132C2×#1141C2314yes—
133C2×(C2×D7)⋊C4—21no—
134C2×(C2×D7)⋊C4—21no—
135C2×(C2×D7)⋊C4—21no—
136C2×(C2×D7)⋊C4—21no—
137C2×(C2×D7)⋊C4—21no—
138C2×(C2×D7)⋊C4—21no—
139C2×C4⋊Dic7C2311yescharacteristic
140C2×Dic7⋊C4—21no—
141C2×C4×Dic7—21no—
142C22×C7⋊C8C2311yescharacteristic
143C22×C7⋊C8C2311yescharacteristic
144C22×C7⋊C8C2311yescharacteristic
145C22×C7⋊C8C2311yescharacteristic
146#6457—28no—
147#6457—28no—
148#6456—28no—
149#6438—22no—
150#6438—22no—
151#6438C2314yes—
152#6438C2314yes—
153#6437—22no—
154#6437C2314yes—
155C4×D28—22no—
156C4×D28—22no—
157C4×D28C2314yes—
158C4×D28C2314yes—
159C4×Dic14—22no—
160C4×Dic14C2314yes—
161#6406C2314yes—
162#6384C2314yes—
163#6384C2314yes—
164#6384C2314yes—
165#6383C2314yes—
166#6383C2314yes—
167#6383C2314yes—
168#6383C2314yes—
169#6383C2314yes—
170#6383C2314yes—
171#6382C2314yes—
172#6381C2314yes—
173#6381C2314yes—
174C4⋊(C7⋊C8)C2314yes—
175C4⋊(C7⋊C8)C2314yes—
176C4⋊(C7⋊C8)C2314yes—
177#6377C2314yes—
178#6377C2314yes—
179C4×C7⋊C8C2314yes—
180C2×#559—71no—
181C2×#554D711yescharacteristic, complemented
182#3370—716no—
183C2×#490—71no—
184C2×#489—71no—
185C2×#488—71no—
186C2×#479—71no—
187C2×#478—71no—
188C2×#474—71no—
189C2×#463—71no—
190C2×#463—71no—
191C2×#459—71no—
192C2×#446—71no—
193C2×#442—71no—
194C2×#440—71no—
195C2×C4×D8—71no—
196C24×C7—21no—
197C23×D7—21no—
198C23×D7—21no—
199C2×C7×Q8—24no—
200C2×C7×Q8—42no—
201C2×C7×Q8—82no—
202C2×C7×Q8C2×D414yes—
203C2×C7×D4—21no—
204C2×C7×D4—22no—
205C2×C7×D4#4114yes—
206C2×C7×D4C2412yes—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—24no—
211C22×C4×C7—24no—
212C22×C4×C7—24no—
213C22×C4×C7—44no—
214C22×C4×C7—82no—
215C22×C4×C7—82no—
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2×D411yescharacteristic
219C22×C4×C7C2×D411yescharacteristic
220C22×C4×C7C2×D411yescharacteristic
221C22×C4×C7C2×D411yescharacteristic
222C22×C4×C7C2411yescharacteristic
223C22×Dic7—21no—
224C22×Dic7—21no—
225C2×D28—22no—
226C2×D28—22no—
227C2×D28—22no—
228C2×D28—22no—
229C2×D28—21no—
230C2×D28—21no—
231C2×D28—24no—
232C2×D28—24no—
233C2×D28—44no—
234C2×D28—82no—
235C2×D28C2412yes—
236C2×D28C2412yes—
237C2×C4×D7—24no—
238C2×C4×D7—24no—
239C2×C4×D7—82no—
240C2×C4×D7—82no—
241C2×Dic14—22no—
242C2×Dic14—22no—
243C2×Dic14—21no—
244C2×Dic14C2412yes—
245C7×C4⋊C4—24no—
246C7×C4⋊C4—24no—
247C7×C4⋊C4—24no—
248C7×C4⋊C4—24no—
249C7×C4⋊C4—24no—
250C7×C4⋊C4—21no—
251C7×C4⋊C4—21no—
252C7×C4⋊C4—21no—
253C7×C4⋊C4C2×D414yes—
254C7×C4⋊C4C2×D414yes—
255C7×C4⋊C4C2×D414yes—
256C7×C4⋊C4C2412yes—
257C7×C4⋊C4C2412yes—
258C7×C4⋊C4C2412yes—
259C7×C22⋊C4—24no—
260C7×C22⋊C4—24no—
261C7×C22⋊C4—24no—
262C42×C7C2×D412yes—
263C42×C7C2×D412yes—
264C42×C7C2×D412yes—
265C42×C7C2412yes—
266C42×C7C2412yes—
267C42×C7C2412yes—
268#1142—28no—
269#1141—28no—
270#1141—28no—
271(C2×D7)⋊C4—24no—
272(C2×D7)⋊C4—24no—
273(C2×D7)⋊C4—24no—
274(C2×D7)⋊C4—24no—
275(C2×D7)⋊C4—24no—
276(C2×D7)⋊C4—24no—
277C4⋊Dic7—21no—
278C4⋊Dic7C2412yes—
279Dic7⋊C4—24no—
280C4×Dic7—24no—
281C2×C7⋊C8—22no—
282C2×C7⋊C8—22no—
283C2×C7⋊C8—22no—
284C2×C7⋊C8—22no—
285C2×C7⋊C8C2412yes—
286C2×C7⋊C8C2412yes—
287C2×C7⋊C8C2412yes—
288C2×C7⋊C8C2412yes—
289C22×SD16—71no—
290C22×D8—71no—
291C22×D8—71no—
292#559—78no—
293#559—144no—
294#554—24no—
295#554C2×D718yescomplemented
296C2×C4⋊Q8C2×D711yescharacteristic
297C2×#127—71no—
298C2×#125C2×D711yescharacteristic
299C2×#125C2×D711yescharacteristic
300C2×#124—71no—
301C2×#124—71no—
302C2×#124—141no—
303C2×#123—141no—
304C2×#123—141no—
305C2×C22⋊Q8—21no—
306C2×C22⋊Q8—21no—
307C2×C22⋊Q8—21no—
308C2×C4×Q8—71no—
309C2×C4×Q8C2×D711yescharacteristic
310C2×C4×D4—71no—
311C2×C4×D4—71no—
312C2×C4×D4—141no—
313C2×C4×D4C2×D711yescharacteristic
314C2×C4×D4C2×D711yescharacteristic
315C2×C4×D4C2×D711yescharacteristic
316C22×C4⋊C4—21no—
317#490—78no—
318#489—78no—
319#488—78no—
320#479—78no—
321#478—78no—
322#474—78no—
323#463—78no—
324#463—78no—
325#459—78no—
326#446—78no—
327#442—78no—
328#440—78no—
329C4×D8—78no—
330C2×#107—71no—
331C2×#107—71no—
332C2×#106—71no—
333C2×C4⋊C8—71no—
334C2×C4⋊C8—71no—
335C2×C4⋊C8—71no—
336C2×#103—71no—
337C2×#103—71no—
338C2×#103—71no—
339C2×#102—71no—
340C2×#102—71no—
341C2×#102—71no—
342C2×#102—71no—
343C2×#102—71no—
344C2×#102—71no—
345C2×#102—71no—
346C2×#97—71no—
347C2×#97—71no—
348C2×C4×C8—71no—
349C23×C7—24no—
350C23×C7—22no—
351C23×C7—42no—
352C23×C7—42no—
353C23×C7C22×D411yescharacteristic
354C22×D7—22no—
355C22×D7—22no—
356C22×D7—42no—
357C22×D7—42no—
358C22×D7—42no—
359C22×D7—42no—
360C22×D7—42no—
361C22×D7—42no—
362C7×Q8—44no—
363C7×Q8—84no—
364C7×D4—24no—
365C7×D4—22no—
366C7×D4C2×#4114yes—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—48no—
377C2×C4×C7—42no—
378C2×C4×C7—42no—
379C2×C4×C7—42no—
380C2×C4×C7—84no—
381C2×C4×C7—84no—
382C2×C4×C7C22×D412yes—
383C2×C4×C7C22×D412yes—
384C2×C4×C7C22×D412yes—
385C2×C4×C7C22×D412yes—
386C2×C4×C7C22×D412yes—
387C2×C4×C7C22×D412yes—
388C2×C4×C7C22×D411yescharacteristic
389C2×C4×C7C2×#4112yes—
390C2×C4×C72−1+412yes—
391C2×C4×C7C2511yescharacteristic
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—42no—
395C2×Dic7—42no—
396D28—22no—
397D28—22no—
398D28—22no—
399D28—22no—
400D28—48no—
401D28—42no—
402D28—42no—
403D28—84no—
404C4×D7—84no—
405C4×D7—84no—
406Dic14—22no—
407Dic14—22no—
408Dic14—42no—
409C7⋊C8—22no—
410C7⋊C8—22no—
411C7⋊C8—22no—
412C7⋊C8—22no—
413C22×Q8—21no—
414C22×Q8—71no—
415C22×Q8C22⋊D711yescharacteristic
416C22×D4—71no—
417C22×D4—71no—
418C22×D4—141no—
419C22×D4—141no—
420C22×D4C22×D711yescharacteristic
421C23×C4—21no—
422C23×C4—21no—
423C23×C4—21no—
424C23×C4—141no—
425C23×C4—141no—
426C2×SD16—74no—
427C2×SD16—144no—
428C2×D8—74no—
429C2×D8—74no—
430C2×D8—144no—
431C2×D8—144no—
432C22×C8—71no—
433C22×C8—71no—
434C22×C8—71no—
435C22×C8—71no—
436C4⋊Q8—22no—
437C4⋊Q8C22×D714yes—
438#127—74no—
439#127—142no—
440#125—22no—
441#125—22no—
442#125C22×D714yes—
443#125C22×D714yes—
444#124—74no—
445#124—74no—
446#124—148no—
447#124—142no—
448#124—142no—
449#123—148no—
450#123—148no—
451C22⋊Q8—28no—
452C22⋊Q8—28no—
453C22⋊Q8—28no—
454C4×Q8—74no—
455C4×Q8—142no—
456C4×Q8C22⋊D714yes—
457C4×Q8C22×D714yes—
458C4×D4—22no—
459C4×D4—22no—
460C4×D4—22no—
461C4×D4—74no—
462C4×D4—74no—
463C4×D4—148no—
464C4×D4—142no—
465C4×D4—142no—
466C4×D4C22×D714yes—
467C4×D4C22×D714yes—
468C4×D4C22×D714yes—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—28no—
475C2×C4⋊C4—71no—
476C2×C4⋊C4—141no—
477C2×C4⋊C4C22⋊D711yescharacteristic
478C2×C4⋊C4C22⋊D711yescharacteristic
479C2×C4⋊C4C22⋊D711yescharacteristic
480C2×C4⋊C4C22×D711yescharacteristic
481C2×C4⋊C4C22×D711yescharacteristic
482C2×C4⋊C4C22×D711yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—141no—
487C2×C22⋊C4—141no—
488C2×C22⋊C4—141no—
489C2×C22⋊C4—141no—
490C2×C22⋊C4—141no—
491C2×C22⋊C4—141no—
492C2×C42—141no—
493C2×C42C22×D711yescharacteristic
494C2×C42C22×D711yescharacteristic
495C2×C42C22×D711yescharacteristic
496#107—74no—
497#107—74no—
498#106—74no—
499C4⋊C8—74no—
500C4⋊C8—74no—
501C4⋊C8—74no—
502#103—74no—
503#103—74no—
504#103—74no—
505#102—74no—
506#102—74no—
507#102—74no—
508#102—74no—
509#102—74no—
510#102—74no—
511#102—74no—
512#97—74no—
513#97—74no—
514C4×C8—74no—
515C22×C7—24no—
516C22×C7—48no—
517C22×C7—42no—
518C22×C7—42no—
519C22×C7#54812yes—
520C22×C7#57512yes—
521C22×C7#57612yes—
522C22×C7C23×D411yescharacteristic
523C2×D7—42no—
524C2×D7—42no—
525C2×D7—42no—
526C2×D7—42no—
527C2×D7—42no—
528C2×D7—42no—
529C2×D7—84no—
530C2×D7—84no—
531C4×C7—22no—
532C4×C7—22no—
533C4×C7—22no—
534C4×C7—22no—
535C4×C7—22no—
536C4×C7—22no—
537C4×C7—42no—
538C4×C7—42no—
539C4×C7—42no—
540C4×C7#54812yes—
541C4×C7C22×#4111yescharacteristic
542C4×C7C2×2−1+411yescharacteristic
543Dic7—42no—
544Dic7—42no—
545C24—21no—
546C24—141no—
547C24—141no—
548C2×Q8—24no—
549C2×Q8—42no—
550C2×Q8—72no—
551C2×Q8—82no—
552C2×Q8—141no—
553C2×Q8—142no—
554C2×Q8—142no—
555C2×Q8C2×C22⋊D714yes—
556C2×D4—22no—
557C2×D4—21no—
558C2×D4—72no—
559C2×D4—72no—
560C2×D4—142no—
561C2×D4—142no—
562C2×D4—142no—
563C2×D4—142no—
564C2×D4—144no—
565C2×D4—141no—
566C2×D4—141no—
567C2×D4—144no—
568C2×D4—284no—
569C2×D4—562no—
570C2×D4#116114yes—
571C2×D4C23×D712yes—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—44no—
579C22×C4—82no—
580C22×C4—82no—
581C22×C4—141no—
582C22×C4—141no—
583C22×C4—144no—
584C22×C4—144no—
585C22×C4—562no—
586C22×C4—562no—
587C22×C4C2×C22⋊D711yescharacteristic
588C22×C4C2×C22⋊D711yescharacteristic
589C22×C4C2×C22⋊D711yescharacteristic
590C22×C4C2×C22⋊D711yescharacteristic
591C22×C4C2×C22⋊D711yescharacteristic
592C22×C4C2×C22⋊D711yescharacteristic
593C22×C4C23×D711yescharacteristic
594SD16—148no—
595D8—148no—
596D8—148no—
597C2×C8—72no—
598C2×C8—72no—
599C2×C8—72no—
600C2×C8—72no—
601C2×C8—142no—
602C2×C8—142no—
603C2×C8—142no—
604C2×C8—142no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—72no—
614C4⋊C4—144no—
615C4⋊C4—141no—
616C4⋊C4C2×C22⋊D714yes—
617C4⋊C4C2×C22⋊D714yes—
618C4⋊C4C2×C22⋊D714yes—
619C4⋊C4C23×D712yes—
620C4⋊C4C23×D712yes—
621C4⋊C4C23×D712yes—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—144no—
626C22⋊C4—144no—
627C22⋊C4—144no—
628C22⋊C4—144no—
629C22⋊C4—144no—
630C22⋊C4—144no—
631C42—144no—
632C42C2×C22⋊D712yes—
633C42C2×C22⋊D712yes—
634C42C2×C22⋊D712yes—
635C42C23×D712yes—
636C42C23×D712yes—
637C42C23×D712yes—
638C2×C7—44no—
639C2×C7#337014yescomplemented
640C2×C7C2×#54811yescharacteristic
641C2×C7C2×#57511yescharacteristic
642C2×C7C2×#57611yescharacteristic
643D7—82no—
644D7—82no—
645C23—24no—
646C23—22no—
647C23—42no—
648C23—42no—
649C23—142no—
650C23—142no—
651C23—282no—
652C23—282no—
653C23—282no—
654C23—282no—
655C23—282no—
656C23—282no—
657C23C22×C22⋊D711yescharacteristic
658Q8—44no—
659Q8—84no—
660Q8—142no—
661Q8—142no—
662Q8—282no—
663D4—24no—
664D4—22no—
665D4—142no—
666D4—142no—
667D4—142no—
668D4—142no—
669D4—288no—
670D4—282no—
671D4—282no—
672D4—564no—
673D4C2×#116114yes—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—48no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—84no—
688C2×C4—84no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—282no—
692C2×C4—282no—
693C2×C4—564no—
694C2×C4—564no—
695C2×C4C2×#116112yes—
696C2×C4#655112yes—
697C2×C4C22×C22⋊D712yes—
698C2×C4C22×C22⋊D712yes—
699C2×C4C22×C22⋊D712yes—
700C2×C4C22×C22⋊D712yes—
701C2×C4C22×C22⋊D712yes—
702C2×C4C22×C22⋊D712yes—
703C2×C4C22×C22⋊D711yescharacteristic
704C2×C4C24×D711yescharacteristic
705C8—142no—
706C8—142no—
707C8—142no—
708C8—142no—
709C7C2×#337011yescharacteristic, complemented, Sylow
710C22—24no—
711C22—42no—
712C22—42no—
713C22—48no—
714C22—282no—
715C22—282no—
716C22—282no—
717C22—282no—
718C22—282no—
719C22—282no—
720C22—564no—
721C22—564no—
722C22#9050812yes—
723C22#9051312yes—
724C22#9052612yes—
725C22C23×C22⋊D711yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—282no—
736C4—282no—
737C4#9050812yes—
738C4C22×#116111yescharacteristic
739C4C2×#655111yescharacteristic
740C2—44no—
741C2—562no—
742C2—562no—
743C2#1174108414yesdirect product factor
744C2C2×#9050811yescharacteristic
745C2C2×#9051311yescharacteristic
746C2C2×#9052611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#554C2
socleC23×C7C22×D4
prime radicalC2×#89787C2
hypercenterC2×#554D7
hypocenterC7C2×#3370
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×C7×#554C2semidirect
2. C2×#90276C2semidirect
3. #11741084C2direct (N × H)
4. C2×#89859C2semidirect
5. C2×#89861C2semidirect
6. C2×#89835C2semidirect
7. C2×#89838C2semidirect
8. C2×#89839C2semidirect
9. C2×#89840C2semidirect
10. C2×#89796C2semidirect
11. C2×#89788C2semidirect
12. C2×#89788C2semidirect
14. C2×#89786C2semidirect
15. C2×#89790C2semidirect
16. C2×C4×#1141C2semidirect
18. C7×#554C22semidirect
35. #90276C22semidirect
46. #89861C22semidirect
47. #89859C22semidirect
48. #89840C22semidirect
49. #89839C22semidirect
50. #89838C22semidirect
51. #89835C22semidirect
52. #89796C22semidirect
53. #89790C22semidirect
54. #89788C22semidirect
55. #89788C22semidirect
57. #89786C22semidirect
58. C4×#1141C22semidirect
181. C2×#554D7semidirect
295. #554C2×D7semidirect
639. C2×C7#3370semidirect
709. C7C2×#3370semidirect
743. C2#11741084direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5542
C2×#902762
#117410842
C2×#898592
C2×#898612
C2×#898352
C2×#898382
C2×#898392
C2×#898402
C2×#897962
C2×#897882
C2×#897872
C2×#897862
C2×#897902
C2×C4×#11412
C2×#33707