Finite Group Databasebeta

← C2×#11741090 #14233561

Subgroups — C2×#11741090 #14233561

Order 1792.

1886 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#554C211yesmaximal, characteristic, complemented
2C2×#90275C211yesmaximal, characteristic, complemented
3#11741090C2116yesmaximal, direct product factor
4C2×#89866C211yesmaximal, characteristic, complemented
5C2×#89861C211yesmaximal, characteristic, complemented
6C2×#89835C211yesmaximal, characteristic, complemented
7C2×#89838C211yesmaximal, characteristic, complemented
8C2×#89841C211yesmaximal, characteristic, complemented
9C2×#89840C211yesmaximal, characteristic, complemented
10C2×#89796C211yesmaximal, characteristic, complemented
11C2×#89791C211yesmaximal, characteristic, complemented
12C2×C4×#1142C211yesmaximal, characteristic, complemented
13C2×#89788C211yesmaximal, characteristic
14C2×#89788C211yesmaximal, characteristic
15C2×#89786C211yesmaximal, characteristic
16C2×#89790C211yesmaximal, 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×#6509—21no—
31C22×#1142C2211yescharacteristic
32C22×#1142C2211yescharacteristic
33C22×#1141C2211yescharacteristic
34#90275—24no—
35#90275C2218yescomplemented
36C2×#6461—21no—
37C2×#6461—21no—
38C2×#6455—21no—
39C2×#6438C2211yescharacteristic
40C2×#6438C2211yescharacteristic
41C2×C4×D28C2211yescharacteristic
42C2×#6432C2211yescharacteristic
43C2×C4×Dic14C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C2×#6406C2211yescharacteristic
46#89866C2218yescomplemented
47#89861C2218yescomplemented
48#89841C2218yescomplemented
49#89840C2218yescomplemented
50#89838C2218yescomplemented
51#89835C2218yescomplemented
52#89796C2218yescomplemented
53#89791C2218yescomplemented
54#89790C2218yescomplemented
55C4×#1142C2218yescomplemented
56#89788C2218yes—
57#89788C2218yes—
58#89786C2218yes—
59C2×#6384C2211yescharacteristic
60C2×#6384C2211yescharacteristic
61C2×#6384C2211yescharacteristic
62C2×#6384C2211yescharacteristic
63C2×#6384C2211yescharacteristic
64C2×#6384C2211yescharacteristic
65C2×#6383C2211yescharacteristic
66C2×#6383C2211yescharacteristic
67C2×#6383C2211yescharacteristic
68C2×#6382C2211yescharacteristic
69C2×#6382C2211yescharacteristic
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×#3376—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×D28C2311yescharacteristic
85C22×C4×D7—21no—
86C22×Dic14C2311yescharacteristic
87C22×Dic14C2311yescharacteristic
88C7×C4⋊Q8—22no—
89C7×C4⋊Q8C2314yes—
90C7×#125—22no—
91C7×#125—22no—
92C7×#125C2314yes—
93C7×#125C2314yes—
94C7×C22⋊Q8—28no—
95C7×C22⋊Q8—28no—
96C7×C22⋊Q8—28no—
97C4×C7×Q8D414yes—
98C4×C7×Q8C2314yes—
99C4×C7×D4—22no—
100C4×C7×D4—22no—
101C4×C7×D4—22no—
102C4×C7×D4C2314yes—
103C4×C7×D4C2314yes—
104C4×C7×D4C2314yes—
105C2×C7×C4⋊C4—21no—
106C2×C7×C4⋊C4—21no—
107C2×C7×C4⋊C4—21no—
108C2×C7×C4⋊C4—21no—
109C2×C7×C4⋊C4—21no—
110C2×C7×C4⋊C4—28no—
111C2×C7×C4⋊C4D411yescharacteristic
112C2×C7×C4⋊C4D411yescharacteristic
113C2×C7×C4⋊C4D411yescharacteristic
114C2×C7×C4⋊C4C2311yescharacteristic
115C2×C7×C4⋊C4C2311yescharacteristic
116C2×C7×C4⋊C4C2311yescharacteristic
117C2×C7×C22⋊C4—21no—
118C2×C7×C22⋊C4—21no—
119C2×C7×C22⋊C4—21no—
120C2×C42×C7C2311yescharacteristic
121C2×C42×C7C2311yescharacteristic
122C2×C42×C7C2311yescharacteristic
123#6509—28no—
124C2×#1142—24no—
125C2×#1142—24no—
126C2×#1142C2314yes—
127C2×#1142C2314yes—
128C2×#1141—24no—
129C2×#1141C2314yes—
130C2×(C2×D7)⋊C4—21no—
131C2×(C2×D7)⋊C4—21no—
132C2×(C2×D7)⋊C4—21no—
133C2×(C2×D7)⋊C4—21no—
134C2×(C2×D7)⋊C4—21no—
135C2×C4⋊Dic7—21no—
136C2×C4⋊Dic7—21no—
137C2×C4⋊Dic7C2311yescharacteristic
138C2×Dic7⋊C4—21no—
139C2×Dic7⋊C4—21no—
140C2×C4×Dic7—21no—
141C2×C4×Dic7—21no—
142C22×C7⋊C8C2311yescharacteristic
143C22×C7⋊C8C2311yescharacteristic
144C22×C7⋊C8C2311yescharacteristic
145C22×C7⋊C8C2311yescharacteristic
146#6461—28no—
147#6461—28no—
148#6455—28no—
149#6438—22no—
150#6438—22no—
151#6438C2314yes—
152#6438C2314yes—
153C4×D28—22no—
154C4×D28C2314yes—
155#6432—22no—
156#6432C2314yes—
157C4×Dic14—22no—
158C4×Dic14—22no—
159C4×Dic14C2314yes—
160C4×Dic14C2314yes—
161#6406C2314yes—
162#6384C2314yes—
163#6384C2314yes—
164#6384C2314yes—
165#6384C2314yes—
166#6384C2314yes—
167#6384C2314yes—
168#6383C2314yes—
169#6383C2314yes—
170#6383C2314yes—
171#6382C2314yes—
172#6382C2314yes—
173#6381C2314yes—
174C4⋊(C7⋊C8)C2314yes—
175C4⋊(C7⋊C8)C2314yes—
176C4⋊(C7⋊C8)C2314yes—
177#6377C2314yes—
178#6377C2314yes—
179C4×C7⋊C8C2314yes—
180C2×#556—71no—
181C2×#554D711yescharacteristic, complemented
182#3376—716no—
183C2×#491—71no—
184C2×#489—71no—
185C2×#488—71no—
186C2×#479—71no—
187C2×#475—71no—
188C2×#478—71no—
189C2×#463—71no—
190C2×#463—71no—
191C2×#461—71no—
192C2×#446—71no—
193C2×#442—71no—
194C2×#440—71no—
195C2×C4×SD16—71no—
196C24×C7—21no—
197C23×D7—21no—
198C2×C7×Q8—24no—
199C2×C7×Q8—42no—
200C2×C7×Q8—82no—
201C2×C7×Q8C2×D414yes—
202C2×C7×D4—21no—
203C2×C7×D4—22no—
204C2×C7×D4#4114yes—
205C2×C7×D4C2412yes—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—24no—
210C22×C4×C7—24no—
211C22×C4×C7—24no—
212C22×C4×C7—44no—
213C22×C4×C7—82no—
214C22×C4×C7—82no—
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2×D411yescharacteristic
219C22×C4×C7C2×D411yescharacteristic
220C22×C4×C7C2×D411yescharacteristic
221C22×C4×C7C2411yescharacteristic
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C2×D28—22no—
226C2×D28—22no—
227C2×D28—21no—
228C2×D28C2412yes—
229C2×C4×D7—24no—
230C2×C4×D7—44no—
231C2×Dic14—22no—
232C2×Dic14—22no—
233C2×Dic14—22no—
234C2×Dic14—22no—
235C2×Dic14—21no—
236C2×Dic14—21no—
237C2×Dic14C2412yes—
238C2×Dic14C2412yes—
239C7×C4⋊C4—24no—
240C7×C4⋊C4—24no—
241C7×C4⋊C4—24no—
242C7×C4⋊C4—24no—
243C7×C4⋊C4—24no—
244C7×C4⋊C4—21no—
245C7×C4⋊C4—21no—
246C7×C4⋊C4—21no—
247C7×C4⋊C4C2×D414yes—
248C7×C4⋊C4C2×D414yes—
249C7×C4⋊C4C2×D414yes—
250C7×C4⋊C4C2412yes—
251C7×C4⋊C4C2412yes—
252C7×C4⋊C4C2412yes—
253C7×C22⋊C4—24no—
254C7×C22⋊C4—24no—
255C7×C22⋊C4—24no—
256C42×C7C2×D412yes—
257C42×C7C2×D412yes—
258C42×C7C2×D412yes—
259C42×C7C2412yes—
260C42×C7C2412yes—
261C42×C7C2412yes—
262#1142—28no—
263#1142—28no—
264#1141—28no—
265(C2×D7)⋊C4—24no—
266(C2×D7)⋊C4—24no—
267(C2×D7)⋊C4—24no—
268(C2×D7)⋊C4—24no—
269(C2×D7)⋊C4—24no—
270C4⋊Dic7—21no—
271C4⋊Dic7—24no—
272C4⋊Dic7—24no—
273C4⋊Dic7C2412yes—
274Dic7⋊C4—24no—
275Dic7⋊C4—24no—
276C4×Dic7—24no—
277C4×Dic7—24no—
278C2×C7⋊C8—22no—
279C2×C7⋊C8—22no—
280C2×C7⋊C8—22no—
281C2×C7⋊C8—22no—
282C2×C7⋊C8C2412yes—
283C2×C7⋊C8C2412yes—
284C2×C7⋊C8C2412yes—
285C2×C7⋊C8C2412yes—
286C22×SD16—71no—
287C22×SD16—71no—
288C22×D8—71no—
289#556—78no—
290#556—144no—
291#554—24no—
292#554C2×D718yescomplemented
293C2×C4⋊Q8—71no—
294C2×C4⋊Q8C2×D711yescharacteristic
295C2×#126—141no—
296C2×#126—141no—
297C2×#125C2×D711yescharacteristic
298C2×#125C2×D711yescharacteristic
299C2×#124—71no—
300C2×#124—71no—
301C2×C22⋊Q8—21no—
302C2×C22⋊Q8—21no—
303C2×C22⋊Q8—21no—
304C2×C22⋊Q8—141no—
305C2×C4×Q8—71no—
306C2×C4×Q8—71no—
307C2×C4×Q8C2×D711yescharacteristic
308C2×C4×D4—71no—
309C2×C4×D4C2×D711yescharacteristic
310C2×C4×D4C2×D711yescharacteristic
311C2×C4×D4C2×D711yescharacteristic
312C2×#117—141no—
313C22×C4⋊C4—21no—
314#491—78no—
315#489—78no—
316#488—78no—
317#479—78no—
318#478—78no—
319#475—78no—
320#463—78no—
321#463—78no—
322#461—78no—
323#446—78no—
324#442—78no—
325#440—78no—
326C4×SD16—78no—
327C2×#107—71no—
328C2×#106—71no—
329C2×#106—71no—
330C2×C4⋊C8—71no—
331C2×C4⋊C8—71no—
332C2×C4⋊C8—71no—
333C2×#103—71no—
334C2×#103—71no—
335C2×#103—71no—
336C2×#103—71no—
337C2×#103—71no—
338C2×#103—71no—
339C2×#102—71no—
340C2×#102—71no—
341C2×#102—71no—
342C2×#102—71no—
343C2×#97—71no—
344C2×#97—71no—
345C2×C4×C8—71no—
346C23×C7—24no—
347C23×C7—22no—
348C23×C7—42no—
349C23×C7—42no—
350C23×C7C22×D411yescharacteristic
351C22×D7—22no—
352C22×D7—42no—
353C22×D7—42no—
354C22×D7—42no—
355C7×Q8—44no—
356C7×Q8—84no—
357C7×D4—24no—
358C7×D4—22no—
359C7×D4C2×#4114yes—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—48no—
370C2×C4×C7—42no—
371C2×C4×C7—42no—
372C2×C4×C7—42no—
373C2×C4×C7—84no—
374C2×C4×C7—84no—
375C2×C4×C7C22×D412yes—
376C2×C4×C7C22×D412yes—
377C2×C4×C7C22×D412yes—
378C2×C4×C7C22×D412yes—
379C2×C4×C7C22×D412yes—
380C2×C4×C7C22×D412yes—
381C2×C4×C7C22×D411yescharacteristic
382C2×C4×C7C2×#4112yes—
383C2×C4×C72−1+412yes—
384C2×C4×C7C2511yescharacteristic
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—42no—
389C2×Dic7—42no—
390C2×Dic7—42no—
391D28—22no—
392D28—22no—
393D28—42no—
394C4×D7—48no—
395Dic14—22no—
396Dic14—22no—
397Dic14—22no—
398Dic14—22no—
399Dic14—42no—
400Dic14—42no—
401C7⋊C8—22no—
402C7⋊C8—22no—
403C7⋊C8—22no—
404C7⋊C8—22no—
405C22×Q8—21no—
406C22×Q8—71no—
407C22×Q8—71no—
408C22×Q8C22⋊D711yescharacteristic
409C22×D4—71no—
410C22×D4C22×D711yescharacteristic
411C23×C4—21no—
412C23×C4—21no—
413C23×C4—21no—
414C23×C4—141no—
415C2×SD16—74no—
416C2×SD16—74no—
417C2×SD16—144no—
418C2×SD16—144no—
419C2×D8—74no—
420C2×D8—144no—
421C22×C8—71no—
422C22×C8—71no—
423C22×C8—71no—
424C22×C8—71no—
425C4⋊Q8—22no—
426C4⋊Q8—74no—
427C4⋊Q8—142no—
428C4⋊Q8C22×D714yes—
429#126—148no—
430#126—148no—
431#125—22no—
432#125—22no—
433#125C22×D714yes—
434#125C22×D714yes—
435#124—74no—
436#124—74no—
437#124—142no—
438#124—142no—
439C22⋊Q8—28no—
440C22⋊Q8—28no—
441C22⋊Q8—28no—
442C22⋊Q8—148no—
443C4×Q8—74no—
444C4×Q8—74no—
445C4×Q8—142no—
446C4×Q8—142no—
447C4×Q8C22⋊D714yes—
448C4×Q8C22×D714yes—
449C4×D4—22no—
450C4×D4—22no—
451C4×D4—22no—
452C4×D4—74no—
453C4×D4—142no—
454C4×D4C22×D714yes—
455C4×D4C22×D714yes—
456C4×D4C22×D714yes—
457#117—148no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—28no—
464C2×C4⋊C4—71no—
465C2×C4⋊C4—141no—
466C2×C4⋊C4—141no—
467C2×C4⋊C4—141no—
468C2×C4⋊C4—141no—
469C2×C4⋊C4C22⋊D711yescharacteristic
470C2×C4⋊C4C22⋊D711yescharacteristic
471C2×C4⋊C4C22⋊D711yescharacteristic
472C2×C4⋊C4C22×D711yescharacteristic
473C2×C4⋊C4C22×D711yescharacteristic
474C2×C4⋊C4C22×D711yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—141no—
479C2×C22⋊C4—141no—
480C2×C22⋊C4—141no—
481C2×C22⋊C4—141no—
482C2×C22⋊C4—141no—
483C2×C42—141no—
484C2×C42—141no—
485C2×C42C22×D711yescharacteristic
486C2×C42C22×D711yescharacteristic
487C2×C42C22×D711yescharacteristic
488#107—74no—
489#106—74no—
490#106—74no—
491C4⋊C8—74no—
492C4⋊C8—74no—
493C4⋊C8—74no—
494#103—74no—
495#103—74no—
496#103—74no—
497#103—74no—
498#103—74no—
499#103—74no—
500#102—74no—
501#102—74no—
502#102—74no—
503#102—74no—
504#97—74no—
505#97—74no—
506C4×C8—74no—
507C22×C7—24no—
508C22×C7—48no—
509C22×C7—42no—
510C22×C7—42no—
511C22×C7#54812yes—
512C22×C7#57512yes—
513C22×C7#57712yes—
514C22×C7C23×D411yescharacteristic
515C2×D7—42no—
516C2×D7—42no—
517C2×D7—42no—
518C2×D7—84no—
519C4×C7—22no—
520C4×C7—22no—
521C4×C7—22no—
522C4×C7—22no—
523C4×C7—22no—
524C4×C7—22no—
525C4×C7—42no—
526C4×C7—42no—
527C4×C7—42no—
528C4×C7#54812yes—
529C4×C7C22×#4111yescharacteristic
530C4×C7C2×2−1+411yescharacteristic
531Dic7—42no—
532Dic7—42no—
533Dic7—42no—
534C24—21no—
535C24—141no—
536C2×Q8—24no—
537C2×Q8—42no—
538C2×Q8—72no—
539C2×Q8—72no—
540C2×Q8—82no—
541C2×Q8—141no—
542C2×Q8—141no—
543C2×Q8—142no—
544C2×Q8—142no—
545C2×Q8—142no—
546C2×Q8—142no—
547C2×Q8C2×C22⋊D714yes—
548C2×D4—22no—
549C2×D4—21no—
550C2×D4—72no—
551C2×D4—142no—
552C2×D4—142no—
553C2×D4—141no—
554C2×D4#116114yes—
555C2×D4C23×D712yes—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—44no—
563C22×C4—82no—
564C22×C4—82no—
565C22×C4—141no—
566C22×C4—141no—
567C22×C4—141no—
568C22×C4—144no—
569C22×C4—284no—
570C22×C4C2×C22⋊D711yescharacteristic
571C22×C4C2×C22⋊D711yescharacteristic
572C22×C4C2×C22⋊D711yescharacteristic
573C22×C4C2×C22⋊D711yescharacteristic
574C22×C4C2×C22⋊D711yescharacteristic
575C22×C4C2×C22⋊D711yescharacteristic
576C22×C4C23×D711yescharacteristic
577SD16—148no—
578SD16—148no—
579D8—148no—
580C2×C8—72no—
581C2×C8—72no—
582C2×C8—72no—
583C2×C8—72no—
584C2×C8—142no—
585C2×C8—142no—
586C2×C8—142no—
587C2×C8—142no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—72no—
597C4⋊C4—144no—
598C4⋊C4—144no—
599C4⋊C4—141no—
600C4⋊C4—144no—
601C4⋊C4—144no—
602C4⋊C4C2×C22⋊D714yes—
603C4⋊C4C2×C22⋊D714yes—
604C4⋊C4C2×C22⋊D714yes—
605C4⋊C4C23×D712yes—
606C4⋊C4C23×D712yes—
607C4⋊C4C23×D712yes—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—144no—
612C22⋊C4—144no—
613C22⋊C4—144no—
614C22⋊C4—144no—
615C22⋊C4—144no—
616C42—144no—
617C42—144no—
618C42C2×C22⋊D712yes—
619C42C2×C22⋊D712yes—
620C42C2×C22⋊D712yes—
621C42C23×D712yes—
622C42C23×D712yes—
623C42C23×D712yes—
624C2×C7—44no—
625C2×C7#337614yescomplemented
626C2×C7C2×#54811yescharacteristic
627C2×C7C2×#57511yescharacteristic
628C2×C7C2×#57711yescharacteristic
629D7—82no—
630C23—24no—
631C23—22no—
632C23—42no—
633C23—42no—
634C23—142no—
635C23—282no—
636C23—282no—
637C23—282no—
638C23C22×C22⋊D711yescharacteristic
639Q8—44no—
640Q8—84no—
641Q8—142no—
642Q8—142no—
643Q8—142no—
644Q8—142no—
645Q8—282no—
646Q8—282no—
647D4—24no—
648D4—22no—
649D4—142no—
650D4—142no—
651D4—282no—
652D4C2×#116114yes—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—48no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—84no—
667C2×C4—84no—
668C2×C4—142no—
669C2×C4—142no—
670C2×C4—142no—
671C2×C4—288no—
672C2×C4—282no—
673C2×C4—282no—
674C2×C4—282no—
675C2×C4C2×#116112yes—
676C2×C4#655112yes—
677C2×C4C22×C22⋊D712yes—
678C2×C4C22×C22⋊D712yes—
679C2×C4C22×C22⋊D712yes—
680C2×C4C22×C22⋊D712yes—
681C2×C4C22×C22⋊D712yes—
682C2×C4C22×C22⋊D712yes—
683C2×C4C22×C22⋊D711yescharacteristic
684C2×C4C24×D711yescharacteristic
685C8—142no—
686C8—142no—
687C8—142no—
688C8—142no—
689C7C2×#337611yescharacteristic, complemented, Sylow
690C22—24no—
691C22—42no—
692C22—42no—
693C22—48no—
694C22—282no—
695C22—282no—
696C22—282no—
697C22—564no—
698C22#9050812yes—
699C22#9051312yes—
700C22#9052712yes—
701C22C23×C22⋊D711yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—282no—
712C4—282no—
713C4—282no—
714C4#9050812yes—
715C4C22×#116111yescharacteristic
716C4C2×#655111yescharacteristic
717C2—44no—
718C2—562no—
719C2#1174109014yesdirect product factor
720C2C2×#9050811yescharacteristic
721C2C2×#9051311yescharacteristic
722C2C2×#9052711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#554C2
socleC23×C7C22×D4
prime radicalC22×#1141C22
hypercenterC2×#554D7
hypocenterC7C2×#3376
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×#90275C2semidirect
3. #11741090C2direct (N × H)
4. C2×#89866C2semidirect
5. C2×#89861C2semidirect
6. C2×#89835C2semidirect
7. C2×#89838C2semidirect
8. C2×#89841C2semidirect
9. C2×#89840C2semidirect
10. C2×#89796C2semidirect
11. C2×#89791C2semidirect
12. C2×C4×#1142C2semidirect
16. C2×#89790C2semidirect
18. C7×#554C22semidirect
35. #90275C22semidirect
46. #89866C22semidirect
47. #89861C22semidirect
48. #89841C22semidirect
49. #89840C22semidirect
50. #89838C22semidirect
51. #89835C22semidirect
52. #89796C22semidirect
53. #89791C22semidirect
54. #89790C22semidirect
55. C4×#1142C22semidirect
181. C2×#554D7semidirect
292. #554C2×D7semidirect
625. C2×C7#3376semidirect
689. C7C2×#3376semidirect
719. C2#11741090direct (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×#902752
#117410902
C2×#898662
C2×#898612
C2×#898352
C2×#898382
C2×#898412
C2×#898402
C2×#897962
C2×#897912
C2×C4×#11422
C2×#897882
C2×#897862
C2×#897902
C2×#33767