Finite Group Databasebeta

← C2×#11740907 #14222121

Subgroups — C2×#11740907 #14222121

Order 1792.

2134 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#542C211yesmaximal, characteristic, complemented
2C2×#90214C211yesmaximal, characteristic, complemented
3#11740907C2116yesmaximal, direct product factor
4C2×#89866C211yesmaximal, characteristic, complemented
5C2×#89856C211yesmaximal, characteristic, complemented
6C2×#89826C211yesmaximal, characteristic, complemented
7C2×#89829C211yesmaximal, characteristic, complemented
8C2×#89819C211yesmaximal, characteristic, complemented
9C2×#89815C211yesmaximal, characteristic, complemented
10C2×#89809C211yesmaximal, characteristic
11C2×#89806C211yesmaximal, characteristic, complemented
12C2×#89802C211yesmaximal, characteristic, complemented
13C2×C4×#1143C211yesmaximal, characteristic, complemented
14C2×C4×#1142C211yesmaximal, characteristic, complemented
15C2×#89786C211yesmaximal, characteristic, complemented
16C2×#89772C211yesmaximal, characteristic, complemented
17C22×#1157C2211yescharacteristic
18C7×#542—24no—
19C7×#542C2218yescomplemented
20C2×C7×C4⋊Q8C2211yescharacteristic
21C2×C7×#126—21no—
22C2×C7×#124—21no—
23C2×C7×#124C2211yescharacteristic
24C2×C7×#123—21no—
25C2×C7×C22⋊Q8—21no—
26C2×C7×C22⋊Q8C2211yescharacteristic
27C2×C7×#121C2211yescharacteristic
28C2×C4×C7×Q8C2211yescharacteristic
29C2×C4×C7×D4C2211yescharacteristic
30C2×C7×#117C2211yescharacteristic
31C22×#1144C2211yescharacteristic
32C22×#1143C2211yescharacteristic
33C22×#1142C2211yescharacteristic
34C22×#1141C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36#90214—24no—
37#90214C2218yescomplemented
38C2×#6455—21no—
39C2×D7×C4⋊C4—21no—
40C2×(C22⋊D7)⋊C4—21no—
41C2×(C22⋊D7)⋊C4—21no—
42C2×C4×D28C2211yescharacteristic
43C2×C4×D28C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C2×C4×Dic14C2211yescharacteristic
46C2×#6409C2211yescharacteristic
47C2×#6409C2211yescharacteristic
48C2×#6406C2211yescharacteristic
49C2×#6406C2211yescharacteristic
50C2×C22⋊(C7⋊C8)C2211yescharacteristic
51C2×C22⋊(C7⋊C8)C2211yescharacteristic
52#89866C2218yescomplemented
53#89856C2218yescomplemented
54#89829C2218yescomplemented
55#89826C2218yescomplemented
56#89819C2218yescomplemented
57#89815C2218yescomplemented
58#89809C2218yes—
59#89806C2218yescomplemented
60#89802C2218yescomplemented
61C4×#1143C2218yescomplemented
62C4×#1142C2218yescomplemented
63#89786C2218yescomplemented
64#89772C2218yescomplemented
65C2×#6384C2211yescharacteristic
66C2×#6384C2211yescharacteristic
67C2×#6383C2211yescharacteristic
68C2×#6383C2211yescharacteristic
69C2×#6382C2211yescharacteristic
70C2×#6382C2211yescharacteristic
71C2×#6382C2211yescharacteristic
72C2×#6382C2211yescharacteristic
73C2×C4⋊(C7⋊C8)C2211yescharacteristic
74C2×C4⋊(C7⋊C8)C2211yescharacteristic
75C2×#6377C2211yescharacteristic
76C2×C4×C7⋊C8C2211yescharacteristic
77C2×#3125—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—
85C23×Dic7—21no—
86C2×#1157—22no—
87C2×#1157—24no—
88C2×#1157—24no—
89C2×#1157C2314yes—
90C22×D28C2311yescharacteristic
91C22×C4×D7—21no—
92C22×C4×D7—21no—
93C22×C4×D7—21no—
94C22×Dic14C2311yescharacteristic
95C7×C4⋊Q8—22no—
96C7×C4⋊Q8C2314yes—
97C7×#126—28no—
98C7×#124—28no—
99C7×#124—22no—
100C7×#124C2314yes—
101C7×#123—28no—
102C7×C22⋊Q8—22no—
103C7×C22⋊Q8—28no—
104C7×C22⋊Q8C2314yes—
105C7×#121—22no—
106C7×#121C2314yes—
107C4×C7×Q8—22no—
108C4×C7×Q8C2314yes—
109C4×C7×D4—22no—
110C4×C7×D4C2314yes—
111C7×#117D414yes—
112C7×#117C2314yes—
113C2×C7×C4⋊C4—21no—
114C2×C7×C4⋊C4—21no—
115C2×C7×C4⋊C4—21no—
116C2×C7×C4⋊C4D411yescharacteristic
117C2×C7×C4⋊C4D411yescharacteristic
118C2×C7×C4⋊C4C2311yescharacteristic
119C2×C7×C4⋊C4C2311yescharacteristic
120C2×C7×C22⋊C4—21no—
121C2×C7×C22⋊C4—21no—
122C2×C7×C22⋊C4—21no—
123C2×C7×C22⋊C4—21no—
124C2×C7×C22⋊C4—21no—
125C2×C7×C22⋊C4D411yescharacteristic
126C2×C7×C22⋊C4D411yescharacteristic
127C2×C42×C7—21no—
128C2×C42×C7C2311yescharacteristic
129C2×C42×C7C2311yescharacteristic
130C2×#1144—24no—
131C2×#1144C2314yes—
132C2×#1143—24no—
133C2×#1143C2314yes—
134C2×#1142—24no—
135C2×#1142C2314yes—
136C2×#1141—24no—
137C2×#1141C2314yes—
138C2×(C2×D7)⋊C4—21no—
139C2×(C2×D7)⋊C4—21no—
140C2×C4⋊Dic7—21no—
141C2×C4⋊Dic7—22no—
142C2×C4⋊Dic7C2311yescharacteristic
143C2×C4⋊Dic7C2311yescharacteristic
144C2×C4⋊Dic7C2314yes—
145C2×Dic7⋊C4—21no—
146C2×Dic7⋊C4—21no—
147C2×C4×Dic7—21no—
148C2×C4×Dic7—21no—
149C22×C7⋊C8C2311yescharacteristic
150C22×C7⋊C8C2311yescharacteristic
151C22×C7⋊C8C2311yescharacteristic
152C22×C7⋊C8C2311yescharacteristic
153#6455—28no—
154D7×C4⋊C4—28no—
155(C22⋊D7)⋊C4—28no—
156(C22⋊D7)⋊C4—28no—
157C4×D28—22no—
158C4×D28—22no—
159C4×D28C2314yes—
160C4×D28C2314yes—
161C4×Dic14—22no—
162C4×Dic14—22no—
163C4×Dic14C2314yes—
164C4×Dic14C2314yes—
165#6409C2314yes—
166#6409C2314yes—
167#6406C2314yes—
168#6406C2314yes—
169C22⋊(C7⋊C8)C2314yes—
170C22⋊(C7⋊C8)C2314yes—
171#6384C2314yes—
172#6384C2314yes—
173#6383C2314yes—
174#6383C2314yes—
175#6382C2314yes—
176#6382C2314yes—
177#6382C2314yes—
178#6382C2314yes—
179C4⋊(C7⋊C8)C2314yes—
180C4⋊(C7⋊C8)C2314yes—
181#6377C2314yes—
182C4×C7⋊C8C2314yes—
183C2×#542D711yescharacteristic, complemented
184C2×#520—71no—
185#3125—716no—
186C2×#481—71no—
187C2×#483—71no—
188C2×#475—71no—
189C2×#476—71no—
190C2×#464—71no—
191C2×#463—71no—
192C2×#452—71no—
193C2×#449—71no—
194C2×#442—71no—
195C2×#441—71no—
196C2×C4×SD16—71no—
197C2×C4×SD16—71no—
198C2×#433—71no—
199C24×C7—21no—
200C24×C7C2×D411yescharacteristic
201C23×D7—21no—
202C2×C7×Q8—21no—
203C2×C7×Q8—24no—
204C2×C7×Q8—22no—
205C2×C7×Q8—22no—
206C2×C7×Q8—82no—
207C2×C7×Q8C2412yes—
208C2×C7×D4—24no—
209C2×C7×D4—21no—
210C2×C7×D4—22no—
211C2×C7×D4—22no—
212C2×C7×D4—82no—
213C2×C7×D4C2412yes—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7—24no—
220C22×C4×C7—82no—
221C22×C4×C7C2×D411yescharacteristic
222C22×C4×C7C2×D411yescharacteristic
223C22×C4×C7C2×D411yescharacteristic
224C22×C4×C7C2×D411yescharacteristic
225C22×C4×C7C2×D411yescharacteristic
226C22×C4×C7C2×D412yes—
227C22×C4×C7C2412yes—
228C22×C4×C7C2411yescharacteristic
229C2×C22⋊D7—28no—
230C2×C22⋊D7—24no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—21no—
234C22×Dic7—24no—
235C22×Dic7—82no—
236#1157—216no—
237#1157—28no—
238#1157—28no—
239C2×D28—21no—
240C2×D28—22no—
241C2×D28#4114yes—
242C2×D28C2412yes—
243C2×C4×D7—28no—
244C2×C4×D7—24no—
245C2×C4×D7—24no—
246C2×C4×D7—24no—
247C2×C4×D7—82no—
248C2×C4×D7—82no—
249C2×Dic14—21no—
250C2×Dic14—22no—
251C2×Dic14#4114yes—
252C2×Dic14C2412yes—
253C7×C4⋊C4—24no—
254C7×C4⋊C4—24no—
255C7×C4⋊C4—24no—
256C7×C4⋊C4—21no—
257C7×C4⋊C4—21no—
258C7×C4⋊C4C2×D414yes—
259C7×C4⋊C4C2×D414yes—
260C7×C4⋊C4C2412yes—
261C7×C4⋊C4C2412yes—
262C7×C22⋊C4—24no—
263C7×C22⋊C4—24no—
264C7×C22⋊C4—24no—
265C7×C22⋊C4—24no—
266C7×C22⋊C4—24no—
267C7×C22⋊C4C2×D414yes—
268C7×C22⋊C4C2×D414yes—
269C42×C7—24no—
270C42×C7C2×D412yes—
271C42×C7C2×D412yes—
272C42×C7C2412yes—
273C42×C7C2412yes—
274#1144—28no—
275#1143—28no—
276#1142—28no—
277#1141—28no—
278(C2×D7)⋊C4—24no—
279(C2×D7)⋊C4—24no—
280C4⋊Dic7—21no—
281C4⋊Dic7—21no—
282C4⋊Dic7—24no—
283C4⋊Dic7C2412yes—
284C4⋊Dic7C2412yes—
285Dic7⋊C4—24no—
286Dic7⋊C4—24no—
287C4×Dic7—24no—
288C4×Dic7—24no—
289C2×C7⋊C8—22no—
290C2×C7⋊C8—22no—
291C2×C7⋊C8—22no—
292C2×C7⋊C8—22no—
293C2×C7⋊C8C2412yes—
294C2×C7⋊C8C2412yes—
295C2×C7⋊C8C2412yes—
296C2×C7⋊C8C2412yes—
297C22×#41—71no—
298C22×Q16—71no—
299C22×SD16—71no—
300C22×SD16—71no—
301C22×D8—71no—
302#542—24no—
303#542C2×D718yescomplemented
304C2×C4⋊Q8C2×D711yescharacteristic
305C2×#126—21no—
306C2×#124—21no—
307C2×#124C2×D711yescharacteristic
308C2×#123—21no—
309C2×C22⋊Q8—21no—
310C2×C22⋊Q8C2×D711yescharacteristic
311C2×#121C2×D711yescharacteristic
312#520—78no—
313#520—144no—
314C2×C4×Q8—71no—
315C2×C4×Q8—71no—
316C2×C4×Q8C2×D711yescharacteristic
317C2×C4×D4—71no—
318C2×C4×D4—71no—
319C2×C4×D4—141no—
320C2×C4×D4—141no—
321C2×C4×D4C2×D711yescharacteristic
322C2×#117—141no—
323C2×#117C2×D711yescharacteristic
324C22×C4⋊C4—71no—
325C22×C4⋊C4—141no—
326#483—78no—
327#481—78no—
328#476—78no—
329#475—78no—
330#464—78no—
331#463—78no—
332#452—78no—
333#449—78no—
334#442—78no—
335#441—78no—
336C4×SD16—78no—
337C4×SD16—78no—
338#433—78no—
339C2×#106—71no—
340C2×#106—71no—
341C2×#106—71no—
342C2×#106—71no—
343C2×C4⋊C8—71no—
344C2×C4⋊C8—71no—
345C2×#103—71no—
346C2×#103—71no—
347C2×#103—71no—
348C2×#103—71no—
349C2×#102—71no—
350C2×#102—71no—
351C2×#102—71no—
352C2×#102—71no—
353C2×C22⋊C8—71no—
354C2×C22⋊C8—71no—
355C2×#97—71no—
356C2×C4×C8—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—24no—
367C22×D7—22no—
368C22×D7—42no—
369C22×D7—42no—
370C7×Q8—22no—
371C7×Q8—22no—
372C7×Q8—42no—
373C7×Q8—84no—
374C7×D4—22no—
375C7×D4—22no—
376C7×D4—42no—
377C7×D4—84no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—24no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—42no—
390C2×C4×C7—42no—
391C2×C4×C7—42no—
392C2×C4×C7—84no—
393C2×C4×C7C22×D412yes—
394C2×C4×C7C22×D412yes—
395C2×C4×C7C22×D412yes—
396C2×C4×C7C22×D412yes—
397C2×C4×C7C22×D412yes—
398C2×C4×C7C22×D411yescharacteristic
399C2×C4×C7C2×#4112yes—
400C2×C4×C7C2×#4112yes—
401C2×C4×C7C2511yescharacteristic
402C22⋊D7—216no—
403C2×Dic7—24no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—42no—
408C2×Dic7—42no—
409C2×Dic7—84no—
410D28—24no—
411D28—22no—
412D28C2×#4114yes—
413C4×D7—216no—
414C4×D7—84no—
415C4×D7—84no—
416Dic14—24no—
417Dic14—22no—
418Dic14C2×#4114yes—
419C7⋊C8—22no—
420C7⋊C8—22no—
421C7⋊C8—22no—
422C7⋊C8—22no—
423C2×#41—74no—
424C2×#41—144no—
425C2×#41—144no—
426C2×#41—142no—
427C22×Q8—21no—
428C22×Q8—71no—
429C22×Q8C22×D711yescharacteristic
430C22×D4—21no—
431C22×D4—71no—
432C22×D4—141no—
433C22×D4C22×D711yescharacteristic
434C23×C4—21no—
435C23×C4—141no—
436C23×C4—141no—
437C23×C4—141no—
438C23×C4—141no—
439C23×C4C22×D711yescharacteristic
440C2×Q16—74no—
441C2×Q16—144no—
442C2×SD16—74no—
443C2×SD16—74no—
444C2×SD16—144no—
445C2×SD16—144no—
446C2×D8—74no—
447C2×D8—144no—
448C22×C8—71no—
449C22×C8—71no—
450C22×C8—71no—
451C22×C8—71no—
452C4⋊Q8—22no—
453C4⋊Q8C22×D714yes—
454#126—28no—
455#124—28no—
456#124—22no—
457#124C22×D714yes—
458#123—28no—
459C22⋊Q8—22no—
460C22⋊Q8—28no—
461C22⋊Q8C22×D714yes—
462#121—22no—
463#121C22×D714yes—
464C4×Q8—22no—
465C4×Q8—74no—
466C4×Q8—74no—
467C4×Q8—142no—
468C4×Q8—142no—
469C4×Q8C22×D714yes—
470C4×D4—22no—
471C4×D4—74no—
472C4×D4—74no—
473C4×D4—148no—
474C4×D4—148no—
475C4×D4—142no—
476C4×D4—142no—
477C4×D4C22×D714yes—
478#117—148no—
479#117C22⋊D714yes—
480#117C22×D714yes—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—71no—
485C2×C4⋊C4—71no—
486C2×C4⋊C4—74no—
487C2×C4⋊C4—141no—
488C2×C4⋊C4—142no—
489C2×C4⋊C4—141no—
490C2×C4⋊C4—141no—
491C2×C4⋊C4—148no—
492C2×C4⋊C4C22⋊D711yescharacteristic
493C2×C4⋊C4C22⋊D711yescharacteristic
494C2×C4⋊C4C22×D711yescharacteristic
495C2×C4⋊C4C22×D711yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—141no—
502C2×C22⋊C4—141no—
503C2×C22⋊C4C22⋊D711yescharacteristic
504C2×C22⋊C4C22⋊D711yescharacteristic
505C2×C42—21no—
506C2×C42—141no—
507C2×C42—141no—
508C2×C42C22×D711yescharacteristic
509C2×C42C22×D711yescharacteristic
510#106—74no—
511#106—74no—
512#106—74no—
513#106—74no—
514C4⋊C8—74no—
515C4⋊C8—74no—
516#103—74no—
517#103—74no—
518#103—74no—
519#103—74no—
520#102—74no—
521#102—74no—
522#102—74no—
523#102—74no—
524C22⋊C8—74no—
525C22⋊C8—74no—
526#97—74no—
527C4×C8—74no—
528C22×C7—22no—
529C22×C7—22no—
530C22×C7—22no—
531C22×C7—44no—
532C22×C7—42no—
533C22×C7—42no—
534C22×C7—42no—
535C22×C7—84no—
536C22×C7#52512yes—
537C22×C7#57712yes—
538C22×C7#57712yes—
539C22×C7C23×D411yescharacteristic
540C2×D7—24no—
541C2×D7—48no—
542C2×D7—42no—
543C2×D7—42no—
544C4×C7—22no—
545C4×C7—22no—
546C4×C7—22no—
547C4×C7—22no—
548C4×C7—22no—
549C4×C7—42no—
550C4×C7—42no—
551C4×C7—42no—
552C4×C7#52512yes—
553C4×C7C22×#4111yescharacteristic
554C4×C7C22×#4111yescharacteristic
555Dic7—24no—
556Dic7—42no—
557Dic7—42no—
558C24—21no—
559C24—141no—
560C24C2×C22⋊D711yescharacteristic
561#41—148no—
562#41—148no—
563#41—1416no—
564C2×Q8—21no—
565C2×Q8—24no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—74no—
569C2×Q8—72no—
570C2×Q8—82no—
571C2×Q8—142no—
572C2×Q8—141no—
573C2×Q8C23×D712yes—
574C2×D4—24no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—74no—
579C2×D4—72no—
580C2×D4—82no—
581C2×D4—148no—
582C2×D4—144no—
583C2×D4—142no—
584C2×D4—141no—
585C2×D4C23×D712yes—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—24no—
592C22×C4—82no—
593C22×C4—148no—
594C22×C4—141no—
595C22×C4—144no—
596C22×C4—141no—
597C22×C4—141no—
598C22×C4—144no—
599C22×C4—144no—
600C22×C4—144no—
601C22×C4—562no—
602C22×C4—562no—
603C22×C4—562no—
604C22×C4C2×C22⋊D712yes—
605C22×C4C2×C22⋊D711yescharacteristic
606C22×C4C2×C22⋊D711yescharacteristic
607C22×C4C2×C22⋊D711yescharacteristic
608C22×C4C2×C22⋊D711yescharacteristic
609C22×C4C2×C22⋊D711yescharacteristic
610C22×C4C23×D712yes—
611C22×C4C23×D711yescharacteristic
612Q16—148no—
613SD16—148no—
614SD16—148no—
615D8—148no—
616C2×C8—72no—
617C2×C8—72no—
618C2×C8—72no—
619C2×C8—72no—
620C2×C8—142no—
621C2×C8—142no—
622C2×C8—142no—
623C2×C8—142no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—72no—
630C4⋊C4—72no—
631C4⋊C4—144no—
632C4⋊C4—144no—
633C4⋊C4—144no—
634C4⋊C4—141no—
635C4⋊C4—141no—
636C4⋊C4C2×C22⋊D714yes—
637C4⋊C4C2×C22⋊D714yes—
638C4⋊C4C23×D712yes—
639C4⋊C4C23×D712yes—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4—144no—
646C22⋊C4—144no—
647C22⋊C4C2×C22⋊D714yes—
648C22⋊C4C2×C22⋊D714yes—
649C42—24no—
650C42—144no—
651C42—144no—
652C42C2×C22⋊D712yes—
653C42C2×C22⋊D712yes—
654C42C23×D712yes—
655C42C23×D712yes—
656C2×C7—42no—
657C2×C7—82no—
658C2×C7#312514yescomplemented
659C2×C7C2×#52511yescharacteristic
660C2×C7C2×#57711yescharacteristic
661C2×C7C2×#57711yescharacteristic
662D7—44no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—144no—
671C23—142no—
672C23—282no—
673C23—282no—
674C23C22×C22⋊D712yes—
675C23C22×C22⋊D711yescharacteristic
676Q8—22no—
677Q8—22no—
678Q8—42no—
679Q8—74no—
680Q8—84no—
681Q8—144no—
682Q8—142no—
683D4—22no—
684D4—22no—
685D4—42no—
686D4—74no—
687D4—84no—
688D4—1416no—
689D4—144no—
690D4—142no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—84no—
706C2×C4—1416no—
707C2×C4—144no—
708C2×C4—142no—
709C2×C4—142no—
710C2×C4—142no—
711C2×C4—282no—
712C2×C4—282no—
713C2×C4—564no—
714C2×C4—564no—
715C2×C4—564no—
716C2×C4D7×#4112yes—
717C2×C4D7×#4112yes—
718C2×C4C22×C22⋊D712yes—
719C2×C4C22×C22⋊D712yes—
720C2×C4C22×C22⋊D712yes—
721C2×C4C22×C22⋊D712yes—
722C2×C4C22×C22⋊D712yes—
723C2×C4C22×C22⋊D711yescharacteristic
724C2×C4C24×D711yescharacteristic
725C8—142no—
726C8—142no—
727C8—142no—
728C8—142no—
729C7C2×#312511yescharacteristic, complemented, Sylow
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—84no—
738C22—144no—
739C22—282no—
740C22—282no—
741C22—288no—
742C22#9051912yes—
743C22#9052712yes—
744C22#9052812yes—
745C22C23×C22⋊D711yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—144no—
755C4—282no—
756C4—282no—
757C4#9051912yes—
758C4C2×D7×#4111yescharacteristic
759C4C2×D7×#4111yescharacteristic
760C2—42no—
761C2—82no—
762C2—284no—
763C2#1174090714yesdirect product factor
764C2C2×#9051911yescharacteristic
765C2C2×#9052711yescharacteristic
766C2C2×#9052811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#542C2
socleC23×C7C22×D4
prime radicalC2×#89809C2
hypercenterC2×#542D7
hypocenterC7C2×#3125
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×#90214C2semidirect
3. #11740907C2direct (N × H)
4. C2×#89866C2semidirect
5. C2×#89856C2semidirect
6. C2×#89826C2semidirect
7. C2×#89829C2semidirect
8. C2×#89819C2semidirect
9. C2×#89815C2semidirect
11. C2×#89806C2semidirect
12. C2×#89802C2semidirect
13. C2×C4×#1143C2semidirect
14. C2×C4×#1142C2semidirect
15. C2×#89786C2semidirect
16. C2×#89772C2semidirect
19. C7×#542C22semidirect
37. #90214C22semidirect
52. #89866C22semidirect
53. #89856C22semidirect
54. #89829C22semidirect
55. #89826C22semidirect
56. #89819C22semidirect
57. #89815C22semidirect
59. #89806C22semidirect
60. #89802C22semidirect
61. C4×#1143C22semidirect
62. C4×#1142C22semidirect
63. #89786C22semidirect
64. #89772C22semidirect
183. C2×#542D7semidirect
303. #542C2×D7semidirect
658. C2×C7#3125semidirect
729. C7C2×#3125semidirect
763. C2#11740907direct (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×#902142
#117409072
C2×#898662
C2×#898562
C2×#898262
C2×#898292
C2×#898192
C2×#898152
C2×#898092
C2×#898062
C2×#898022
C2×C4×#11432
C2×C4×#11422
C2×#897862
C2×#897722
C2×#31257