Finite Group Databasebeta

← C2×#11736569 #14232215

Subgroups — C2×#11736569 #14232215

Order 1792.

2158 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90198C211yesmaximal, characteristic
2C2×#90202C211yesmaximal, characteristic, complemented
3C22×C7×#106C211yesmaximal, characteristic, complemented
4C2×#89886C211yesmaximal, characteristic, complemented
5C2×C8×C22⋊D7C211yesmaximal, characteristic, complemented
6C2×#89743C211yesmaximal, characteristic, complemented
7C2×#89740C211yesmaximal, characteristic, complemented
8C2×#89626C211yesmaximal, characteristic, complemented
9C2×#89642C211yesmaximal, characteristic, complemented
10#11736569C2116yesmaximal, direct product factor
11C2×#89635C211yesmaximal, characteristic, complemented
12C2×#89634C211yesmaximal, characteristic, complemented
13C2×#89636C211yesmaximal, characteristic, complemented
14C2×D7×#106C211yesmaximal, characteristic, complemented
15C2×#89627C211yesmaximal, characteristic, complemented
16C2×#89624C211yesmaximal, characteristic, complemented
17C22×#1157—21no—
18C23×C7×C8C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C2×#6493C2211yescharacteristic
22C2×#6492—21no—
23C2×C4×C22⋊D7—21no—
24C2×C4×C22⋊D7C2211yescharacteristic
25C2×#6487—21no—
26C2×#6487C2211yescharacteristic
27C22×#1132C2211yescharacteristic
28C22×C8×D7C2211yescharacteristic
29#90202—24no—
30#90202C2218yescomplemented
31C2×#6460C2211yescharacteristic
32C2×#6459—21no—
33C2×#6459—21no—
34#90198—24no—
35#90198C2218yes—
36C2×#6458C2211yescharacteristic
37C2×#6457—21no—
38C2×#6456C2211yescharacteristic
39C2×D7×C4⋊C4C2211yescharacteristic
40C2×D7×C4⋊C4C2211yescharacteristic
41C2×#6452—21no—
42C2×#6451C2211yescharacteristic
43C2×#6451C2211yescharacteristic
44C2×#6450C2211yescharacteristic
45C2×C7×#106C2211yescharacteristic
46C2×C7×#106C2211yescharacteristic
47C2×C7×#106C2211yescharacteristic
48C2×C7×#106C2211yescharacteristic
49C2×C7×#106C2218yescomplemented
50C2×C22⋊(C7⋊C8)C2211yescharacteristic
51#89886C2218yescomplemented
52C2×#6395C2211yescharacteristic
53C8×C22⋊D7C2218yescomplemented
54C2×(C2×D7)⋊C8C2211yescharacteristic
55C2×#6391C2211yescharacteristic
56C2×#6390C2211yescharacteristic
57C2×Dic7⋊C8C2211yescharacteristic
58C2×C8×Dic7C2211yescharacteristic
59#89743C2218yescomplemented
60C2×#6384C2211yescharacteristic
61C2×#6384C2211yescharacteristic
62#89740C2218yescomplemented
63C2×#6383C2211yescharacteristic
64C2×#6383C2211yescharacteristic
65C2×#6382C2211yescharacteristic
66C2×#6382C2211yescharacteristic
67C2×#6382C2211yescharacteristic
68C2×#6382C2211yescharacteristic
69#89642C2218yescomplemented
70#89636C2218yescomplemented
71#89635C2218yescomplemented
72#89634C2218yescomplemented
73D7×#106C2218yescomplemented
74#89627C2218yescomplemented
75#89626C2218yescomplemented
76#89624C2218yescomplemented
77C2×#3335—71nomaximal, Sylow
78C23×C4×C7—21no—
79C23×C4×C7—21no—
80C23×C4×C7C2311yescharacteristic
81C22×C22⋊D7—21no—
82C22×C22⋊D7D411yescharacteristic
83C2×#1157—28no—
84C2×#1157—48no—
85C22×D28—21no—
86C22×D28C2311yescharacteristic
87C22×C4×D7—21no—
88C22×C4×D7—21no—
89C22×C4×D7—21no—
90C22×C4×D7C2311yescharacteristic
91C22×Dic14—21no—
92C22×Dic14—21no—
93C22×Dic14C2311yescharacteristic
94C22×C7×C8—24no—
95C22×C7×C8C2311yescharacteristic
96C22×C7×C8C2314yes—
97C22×C7×C8C2311yescharacteristic
98C2×C7×C4⋊C4—21no—
99C2×C7×C4⋊C4—21no—
100C2×C7×C4⋊C4—22no—
101C2×C7×C4⋊C4—22no—
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C4⋊C4C2311yescharacteristic
104C2×C7×C4⋊C4C2311yescharacteristic
105C2×C7×C4⋊C4C2311yescharacteristic
106C2×C7×C4⋊C4C2314yes—
107C2×C7×C4⋊C4C2314yes—
108C2×C22⋊Dic7—21no—
109C2×C22⋊Dic7D411yescharacteristic
110#6493—22no—
111#6493C2314yes—
112#6492—28no—
113C4×C22⋊D7—28no—
114C4×C22⋊D7D414yes—
115C4×C22⋊D7C2314yes—
116C2×(C2×D7)⋊C4—21no—
117C2×(C2×D7)⋊C4—21no—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4—21no—
120C2×(C2×D7)⋊C4D411yescharacteristic
121C2×C4⋊Dic7—21no—
122C2×C4⋊Dic7C2311yescharacteristic
123C2×C4⋊Dic7C2311yescharacteristic
124#6487—22no—
125#6487—28no—
126#6487C2314yes—
127C2×Dic7⋊C4—21no—
128C2×Dic7⋊C4—21no—
129C2×Dic7⋊C4—21no—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4D411yescharacteristic
134C2×C4×Dic7—21no—
135C2×C4×Dic7C2311yescharacteristic
136C22×C7⋊C8C2311yescharacteristic
137C22×C7⋊C8C2311yescharacteristic
138C2×#1132—24no—
139C2×#1132C2314yes—
140C2×C8×D7—24no—
141C2×C8×D7C2314yes—
142#6460—22no—
143#6460C2314yes—
144#6459—28no—
145#6459—28no—
146#6458—22no—
147#6458C2314yes—
148#6457—28no—
149#6456—22no—
150#6456C2314yes—
151D7×C4⋊C4—22no—
152D7×C4⋊C4—22no—
153D7×C4⋊C4C2314yes—
154D7×C4⋊C4C2314yes—
155#6452—28no—
156#6451—22no—
157#6451—22no—
158#6451C2314yes—
159#6451C2314yes—
160#6450—22no—
161#6450C2314yes—
162C7×#106C2314yes—
163C7×#106C2314yes—
164C7×#106C2314yes—
165C7×#106C2314yes—
166C22⋊(C7⋊C8)C2314yes—
167#6395C2314yes—
168(C2×D7)⋊C8C2314yes—
169#6391C2314yes—
170#6390C2314yes—
171Dic7⋊C8C2314yes—
172C8×Dic7C2314yes—
173#6384C2314yes—
174#6384C2314yes—
175#6383C2314yes—
176#6383C2314yes—
177#6382C2314yes—
178#6382C2314yes—
179#6382C2314yes—
180#6382C2314yes—
181C2×#554—71no—
182C2×#547—71no—
183#3335—716no—
184C2×#498—71no—
185C2×#481—71no—
186C2×#481—71no—
187C2×#483—71no—
188C2×#483—71no—
189C2×#475—71no—
190C2×#476—71no—
191C2×#465—71no—
192C2×#465—71no—
193C2×C4×SD16—71no—
194C2×C8×D4—71no—
195C22×#106—71no—
196C22×#106D711yescharacteristic, complemented
197C24×C7C2×D411yescharacteristic
198C23×D7—21no—
199C23×D7C2×D411yescharacteristic
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—24no—
207C22×C4×C7—24no—
208C22×C4×C7—44no—
209C22×C4×C7—82no—
210C22×C4×C7C2×D411yescharacteristic
211C22×C4×C7C2×D412yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2411yescharacteristic
214C2×C22⋊D7—24no—
215C2×C22⋊D7—44no—
216C2×C22⋊D7SD1618yescomplemented
217C2×C22⋊D7C2×D414yes—
218C22×Dic7—21no—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7C2×D411yescharacteristic
222C22×Dic7C2×D411yescharacteristic
223C22×Dic7C2×D411yescharacteristic
224#1157—432no—
225C2×D28—22no—
226C2×D28—22no—
227C2×D28—24no—
228C2×D28—21no—
229C2×D28—44no—
230C2×D28C2412yes—
231C2×C4×D7—22no—
232C2×C4×D7—22no—
233C2×C4×D7—24no—
234C2×C4×D7—24no—
235C2×C4×D7—24no—
236C2×C4×D7—44no—
237C2×C4×D7—44no—
238C2×C4×D7—82no—
239C2×C4×D7C2×D412yes—
240C2×C4×D7C2412yes—
241C2×Dic14—22no—
242C2×Dic14—22no—
243C2×Dic14—21no—
244C2×Dic14—24no—
245C2×Dic14—24no—
246C2×Dic14—44no—
247C2×Dic14—82no—
248C2×Dic14C2412yes—
249C2×C7×C8—22no—
250C2×C7×C8—28no—
251C2×C7×C8#4114yescomplemented
252C2×C7×C8C2412yes—
253C2×C7×C8C2412yes—
254C7×C4⋊C4—21no—
255C7×C4⋊C4—21no—
256C7×C4⋊C4—21no—
257C7×C4⋊C4—24no—
258C7×C4⋊C4—21no—
259C7×C4⋊C4—24no—
260C7×C4⋊C4C2412yes—
261C7×C4⋊C4C2412yes—
262C7×C4⋊C4C2412yes—
263C7×C4⋊C4C2412yes—
264C22⋊Dic7—24no—
265C22⋊Dic7C2×D414yes—
266(C2×D7)⋊C4—24no—
267(C2×D7)⋊C4—24no—
268(C2×D7)⋊C4—24no—
269(C2×D7)⋊C4—24no—
270(C2×D7)⋊C4C2×D414yes—
271C4⋊Dic7—21no—
272C4⋊Dic7—21no—
273C4⋊Dic7—24no—
274C4⋊Dic7C2412yes—
275C4⋊Dic7C2412yes—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282Dic7⋊C4C2×D414yes—
283C4×Dic7—24no—
284C4×Dic7C2×D412yes—
285C4×Dic7C2412yes—
286C2×C7⋊C8—22no—
287C2×C7⋊C8—22no—
288C2×C7⋊C8C2412yes—
289C2×C7⋊C8C2412yes—
290#1132—28no—
291C8×D7—28no—
292C22×#41—141no—
293C22×SD16—71no—
294C23×C8—71no—
295C23×C8C2×D711yescharacteristic
296#554—78no—
297#554—144no—
298#547—78no—
299#547—144no—
300C2×C4⋊Q8—71no—
301C2×C4⋊Q8—71no—
302C2×#125—141no—
303C2×#123—141no—
304C2×#123—141no—
305C2×C22⋊Q8—71no—
306C2×C22⋊Q8—71no—
307C2×C22⋊Q8—141no—
308C2×C22⋊Q8—141no—
309C2×C22⋊Q8—141no—
310C2×#121—71no—
311C2×#121—71no—
312C2×C4×Q8—71no—
313C2×C4×D4—71no—
314C2×C4×D4—71no—
315C2×C4×D4—141no—
316C22×C4⋊C4—71no—
317C22×C4⋊C4—71no—
318C22×C4⋊C4C2×D711yescharacteristic
319C22×C4⋊C4C2×D711yescharacteristic
320#498—78no—
321#483—78no—
322#483—78no—
323#481—78no—
324#481—78no—
325#476—78no—
326#475—78no—
327#465—78no—
328#465—78no—
329C4×SD16—78no—
330C8×D4—78no—
331C2×#106—71no—
332C2×#106—71no—
333C2×#106—71no—
334C2×#106—71no—
335C2×#106—71no—
336C2×#106—78no—
337C2×#106C2×D711yescharacteristic
338C2×#106C2×D711yescharacteristic
339C2×#106C2×D711yescharacteristic
340C2×#106C2×D711yescharacteristic
341C2×#106C2×D718yescomplemented
342C2×C4⋊C8—71no—
343C2×#103—71no—
344C2×#103—71no—
345C2×#103—71no—
346C2×#102—71no—
347C2×#102—71no—
348C2×#102—71no—
349C2×C22⋊C8—71no—
350C2×C22⋊C8—71no—
351C2×C4×C8—71no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7C2×SD1614yes—
355C23×C7C22×D412yes—
356C23×C7C22×D411yescharacteristic
357C22×D7—22no—
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—42no—
361C22×D7—42no—
362C22×D7—42no—
363C22×D7C2×SD1614yes—
364C22×D7C22×D412yes—
365C2×C4×C7—22no—
366C2×C4×C7—24no—
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—42no—
374C2×C4×C7—42no—
375C2×C4×C7—48no—
376C2×C4×C7—42no—
377C2×C4×C7—42no—
378C2×C4×C7—84no—
379C2×C4×C7C22×D412yes—
380C2×C4×C7C22×D411yescharacteristic
381C2×C4×C7C2×#4112yes—
382C2×C4×C72−1+412yes—
383C2×C4×C7C2511yescharacteristic
384C22⋊D7—48no—
385C22⋊D7C2×SD16116yescomplemented
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—42no—
392C2×Dic7—42no—
393C2×Dic7—42no—
394C2×Dic7C2×SD1614yes—
395C2×Dic7C22×D412yes—
396C2×Dic7C22×D412yes—
397C2×Dic7C22×D412yes—
398D28—22no—
399D28—22no—
400D28—48no—
401D28—42no—
402C4×D7—24no—
403C4×D7—22no—
404C4×D7—22no—
405C4×D7—48no—
406C4×D7—48no—
407C4×D7—84no—
408Dic14—22no—
409Dic14—22no—
410Dic14—42no—
411Dic14—48no—
412Dic14—84no—
413C7×C8—22no—
414C7×C8C2×#4114yescomplemented
415C7⋊C8—22no—
416C7⋊C8—22no—
417C2×#41—148no—
418C2×#41—288no—
419C22×Q8—71no—
420C22×Q8—141no—
421C22×Q8—141no—
422C22×D4—71no—
423C22×D4—71no—
424C22×D4—141no—
425C22×D4—141no—
426C23×C4—21no—
427C23×C4—21no—
428C23×C4—71no—
429C23×C4—141no—
430C23×C4—141no—
431C23×C4—141no—
432C23×C4C22×D711yescharacteristic
433C2×SD16—74no—
434C2×SD16—144no—
435C22×C8—24no—
436C22×C8—71no—
437C22×C8—71no—
438C22×C8—74no—
439C22×C8—144no—
440C22×C8C22×D711yescharacteristic
441C22×C8C22×D714yes—
442C22×C8C22×D711yescharacteristic
443C4⋊Q8—74no—
444C4⋊Q8—74no—
445C4⋊Q8—142no—
446C4⋊Q8—142no—
447#125—148no—
448#123—148no—
449#123—148no—
450C22⋊Q8—74no—
451C22⋊Q8—74no—
452C22⋊Q8—148no—
453C22⋊Q8—148no—
454C22⋊Q8—148no—
455C22⋊Q8—142no—
456C22⋊Q8—142no—
457#121—74no—
458#121—74no—
459#121—142no—
460#121—142no—
461C4×Q8—74no—
462C4×Q8—142no—
463C4×D4—74no—
464C4×D4—74no—
465C4×D4—74no—
466C4×D4—142no—
467C4×D4—148no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—71no—
473C2×C4⋊C4—71no—
474C2×C4⋊C4—71no—
475C2×C4⋊C4—74no—
476C2×C4⋊C4—74no—
477C2×C4⋊C4—142no—
478C2×C4⋊C4—142no—
479C2×C4⋊C4—141no—
480C2×C4⋊C4—141no—
481C2×C4⋊C4—141no—
482C2×C4⋊C4—141no—
483C2×C4⋊C4—141no—
484C2×C4⋊C4—141no—
485C2×C4⋊C4—141no—
486C2×C4⋊C4C22×D711yescharacteristic
487C2×C4⋊C4C22×D711yescharacteristic
488C2×C4⋊C4C22×D711yescharacteristic
489C2×C4⋊C4C22×D711yescharacteristic
490C2×C4⋊C4C22×D714yes—
491C2×C4⋊C4C22×D714yes—
492C2×C22⋊C4—71no—
493C2×C22⋊C4—71no—
494C2×C22⋊C4—141no—
495C2×C22⋊C4—141no—
496C2×C22⋊C4—141no—
497C2×C22⋊C4—141no—
498C2×C22⋊C4—141no—
499C2×C42—71no—
500C2×C42—141no—
501#106—74no—
502#106—74no—
503#106—74no—
504#106—74no—
505#106—74no—
506#106C22×D714yes—
507#106C22×D714yes—
508#106C22×D714yes—
509#106C22×D714yes—
510C4⋊C8—74no—
511#103—74no—
512#103—74no—
513#103—74no—
514#102—74no—
515#102—74no—
516#102—74no—
517C22⋊C8—74no—
518C22⋊C8—74no—
519C4×C8—74no—
520C22×C7—28no—
521C22×C7—22no—
522C22×C7—22no—
523C22×C7#54712yes—
524C22×C7C22×SD1614yes—
525C22×C7C22×SD1612yes—
526C22×C7#57712yes—
527C22×C7C23×D411yescharacteristic
528C2×D7—28no—
529C2×D7—22no—
530C2×D7—22no—
531C2×D7—42no—
532C2×D7—42no—
533C2×D7—42no—
534C2×D7—84no—
535C2×D7C22×SD1614yes—
536C4×C7—22no—
537C4×C7—42no—
538C4×C7—42no—
539C4×C7—42no—
540C4×C7—42no—
541C4×C7#54712yes—
542C4×C7C22×#4111yescharacteristic
543C4×C7C2×2−1+411yescharacteristic
544Dic7—22no—
545Dic7—22no—
546Dic7—42no—
547Dic7—42no—
548Dic7—42no—
549Dic7C22×SD1614yes—
550C24—71no—
551C24—141no—
552C24D4×D711yescharacteristic
553#41—2832no—
554C2×Q8—72no—
555C2×Q8—144no—
556C2×Q8—144no—
557C2×Q8—141no—
558C2×Q8—142no—
559C2×Q8—142no—
560C2×Q8—284no—
561C2×Q8—562no—
562C2×D4—78no—
563C2×D4—74no—
564C2×D4—72no—
565C2×D4—144no—
566C2×D4—144no—
567C2×D4—142no—
568C2×D4—141no—
569C2×D4—142no—
570C2×D4—284no—
571C2×D4—284no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—44no—
581C22×C4—71no—
582C22×C4—71no—
583C22×C4—71no—
584C22×C4—72no—
585C22×C4—72no—
586C22×C4—82no—
587C22×C4—144no—
588C22×C4—144no—
589C22×C4—144no—
590C22×C4—142no—
591C22×C4—142no—
592C22×C4—141no—
593C22×C4—141no—
594C22×C4—141no—
595C22×C4—284no—
596C22×C4—284no—
597C22×C4—562no—
598C22×C4D4×D712yes—
599C22×C4D4×D711yescharacteristic
600C22×C4C23×D712yes—
601C22×C4C23×D711yescharacteristic
602SD16—148no—
603C2×C8—22no—
604C2×C8—28no—
605C2×C8—72no—
606C2×C8—72no—
607C2×C8—142no—
608C2×C8—142no—
609C2×C8—148no—
610C2×C8#115714yescomplemented
611C2×C8C23×D712yes—
612C2×C8C23×D712yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—74no—
620C4⋊C4—72no—
621C4⋊C4—72no—
622C4⋊C4—144no—
623C4⋊C4—144no—
624C4⋊C4—144no—
625C4⋊C4—144no—
626C4⋊C4—144no—
627C4⋊C4—144no—
628C4⋊C4—144no—
629C4⋊C4—141no—
630C4⋊C4—141no—
631C4⋊C4C23×D712yes—
632C4⋊C4C23×D712yes—
633C4⋊C4C23×D712yes—
634C4⋊C4C23×D712yes—
635C22⋊C4—74no—
636C22⋊C4—74no—
637C22⋊C4—144no—
638C22⋊C4—144no—
639C22⋊C4—144no—
640C22⋊C4—144no—
641C22⋊C4—144no—
642C42—72no—
643C42—72no—
644C42—144no—
645C2×C7—24no—
646C2×C7#333514yescomplemented
647C2×C7C2×#54711yescharacteristic
648C2×C7C23×SD1611yescharacteristic
649C2×C7C2×#57711yescharacteristic
650D7—24no—
651D7—82no—
652C23—22no—
653C23—22no—
654C23—74no—
655C23—72no—
656C23—142no—
657C23—142no—
658C23—142no—
659C23—282no—
660C23—282no—
661C23—282no—
662C23D7×SD1614yes—
663C23C2×D4×D712yes—
664C23C2×D4×D711yescharacteristic
665Q8—142no—
666Q8—142no—
667Q8—288no—
668Q8—282no—
669Q8—564no—
670D4—716no—
671D4—142no—
672D4—142no—
673D4—288no—
674D4—288no—
675D4—282no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—48no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—74no—
690C2×C4—72no—
691C2×C4—72no—
692C2×C4—72no—
693C2×C4—84no—
694C2×C4—142no—
695C2×C4—142no—
696C2×C4—144no—
697C2×C4—142no—
698C2×C4—142no—
699C2×C4—142no—
700C2×C4—142no—
701C2×C4—142no—
702C2×C4—288no—
703C2×C4—288no—
704C2×C4—282no—
705C2×C4—282no—
706C2×C4—282no—
707C2×C4—564no—
708C2×C4C2×#115712yes—
709C2×C4C2×D4×D712yes—
710C2×C4C2×D4×D711yescharacteristic
711C2×C4#655112yes—
712C2×C4C24×D711yescharacteristic
713C8—22no—
714C8—142no—
715C8—142no—
716C8C2×#115714yescomplemented
717C7C2×#333511yescharacteristic, complemented, Sylow
718C22—22no—
719C22—22no—
720C22—28no—
721C22—74no—
722C22—142no—
723C22—142no—
724C22—148no—
725C22—282no—
726C22—282no—
727C22—282no—
728C22—564no—
729C22#9019812yes—
730C22C2×D7×SD1614yes—
731C22C2×D7×SD1612yes—
732C22#9045312yes—
733C22C22×D4×D711yescharacteristic
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—74no—
740C4—142no—
741C4—142no—
742C4—282no—
743C4—282no—
744C4—282no—
745C4#9019812yes—
746C4C22×#115711yescharacteristic
747C4C2×#655111yescharacteristic
748C2—24no—
749C2—144no—
750C2—562no—
751C2#1173656914yesdirect product factor
752C2C2×#9019811yescharacteristic
753C2C22×D7×SD1611yescharacteristic
754C2C2×#9045311yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC22×C7×#106C2
socleC23×C7C22×D4
prime radicalC2×#90198C2
hypercenterC22×#106D7
hypocenterC7C2×#3335
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
2. C2×#90202C2semidirect
3. C22×C7×#106C2semidirect
4. C2×#89886C2semidirect
5. C2×C8×C22⋊D7C2semidirect
6. C2×#89743C2semidirect
7. C2×#89740C2semidirect
8. C2×#89626C2semidirect
9. C2×#89642C2semidirect
10. #11736569C2direct (N × H)
11. C2×#89635C2semidirect
12. C2×#89634C2semidirect
13. C2×#89636C2semidirect
14. C2×D7×#106C2semidirect
15. C2×#89627C2semidirect
16. C2×#89624C2semidirect
30. #90202C22semidirect
49. C2×C7×#106C22semidirect
51. #89886C22semidirect
53. C8×C22⋊D7C22semidirect
59. #89743C22semidirect
62. #89740C22semidirect
69. #89642C22semidirect
70. #89636C22semidirect
71. #89635C22semidirect
72. #89634C22semidirect
73. D7×#106C22semidirect
74. #89627C22semidirect
75. #89626C22semidirect
76. #89624C22semidirect
196. C22×#106D7semidirect
216. C2×C22⋊D7SD16semidirect
251. C2×C7×C8#41semidirect
341. C2×#106C2×D7semidirect
385. C22⋊D7C2×SD16semidirect
414. C7×C8C2×#41semidirect
610. C2×C8#1157semidirect
646. C2×C7#3335semidirect
716. C8C2×#1157semidirect
717. C7C2×#3335semidirect
751. C2#11736569direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#901982
C2×#902022
C22×C7×#1062
C2×#898862
C2×C8×C22⋊D72
C2×#897432
C2×#897402
C2×#896262
C2×#896422
#117365692
C2×#896352
C2×#896342
C2×#896362
C2×D7×#1062
C2×#896272
C2×#896242
C2×#33357