Finite Group Databasebeta

← C2×#11738093 #14232214

Subgroups — C2×#11738093 #14232214

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×#90326C211yesmaximal, characteristic, complemented
2C2×#90302C211yesmaximal, characteristic
3C2×C7×#465C211yesmaximal, characteristic, complemented
4C2×#89943C211yesmaximal, characteristic, complemented
5C2×SD16×Dic7C211yesmaximal, characteristic, complemented
6C2×C8×C22⋊D7C211yesmaximal, characteristic, complemented
7C22×#6391C211yesmaximal, characteristic, complemented
8C2×#89815C211yesmaximal, characteristic, complemented
9C2×#89806C211yesmaximal, characteristic, complemented
10#11738093C2116yesmaximal, direct product factor
11C2×D7×#106C211yesmaximal, characteristic, complemented
12C2×#89627C211yesmaximal, characteristic, complemented
13C2×#89577C211yesmaximal, characteristic, complemented
14C2×#89563C211yesmaximal, characteristic, complemented
15C2×#89549C211yesmaximal, characteristic, complemented
16C2×#89533C211yesmaximal, characteristic, complemented
17C22×#1159—21no—
18C22×C7×SD16C2211yescharacteristic
19C23×C7×C8C2211yescharacteristic
20C2×C7×C22⋊Q8C2211yescharacteristic
21C2×C7×#121C2211yescharacteristic
22C2×#6509C2211yescharacteristic
23C2×Q8×Dic7C2211yescharacteristic
24C2×#6501C2211yescharacteristic
25C2×#6498—21no—
26C2×D4×Dic7C2211yescharacteristic
27C2×C4×C22⋊D7C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×C8×D7C2211yescharacteristic
31#90326—24no—
32#90326C2218yescomplemented
33#90302—24no—
34#90302C2218yes—
35C2×#6460—21no—
36C2×D7×C4⋊C4C2211yescharacteristic
37C2×D7×C4⋊C4C2211yescharacteristic
38C2×#6452—21no—
39C2×#6451C2211yescharacteristic
40C2×#6451C2211yescharacteristic
41C2×#6446—21no—
42C2×(C22⋊D7)⋊C4—21no—
43C2×#6441—21no—
44C2×#6441—21no—
45C7×#465C2218yescomplemented
46C2×C7×#106C2211yescharacteristic
47C2×C7×#103C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×#6409C2211yescharacteristic
50C2×#6409C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52C2×#6406C2211yescharacteristic
53C2×C22⋊(C7⋊C8)C2211yescharacteristic
54#89943C2218yescomplemented
55SD16×Dic7C2218yescomplemented
56C8×C22⋊D7C2218yescomplemented
57C2×(C2×D7)⋊C8C2211yescharacteristic
58C2×#6391C2211yescharacteristic
59C2×#6391C2211yescharacteristic
60C2×#6391C2211yescharacteristic
61C2×#6391C2211yescharacteristic
62C2×#6391C2218yescomplemented
63C2×Dic7⋊C8C2211yescharacteristic
64C2×C8×Dic7C2211yescharacteristic
65#89815C2218yescomplemented
66#89806C2218yescomplemented
67C2×#6382C2211yescharacteristic
68C2×#6382C2211yescharacteristic
69C2×#6382C2211yescharacteristic
70C2×#6382C2211yescharacteristic
71D7×#106C2218yescomplemented
72#89627C2218yescomplemented
73#89577C2218yescomplemented
74#89563C2218yescomplemented
75#89549C2218yescomplemented
76#89533C2218yescomplemented
77C2×#3335—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×D4—21no—
80C22×C7×D4C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C22×C22⋊D7—21no—
83C22×C22⋊D7D411yescharacteristic
84C23×Dic7—21no—
85C23×Dic7—21no—
86C23×Dic7—21no—
87C2×#1159—28no—
88C2×#1159—48no—
89C22×C4×D7—21no—
90C22×C4×D7—21no—
91C22×C4×D7C2311yescharacteristic
92C22×Dic14—21no—
93C22×Dic14—21no—
94C2×C7×SD16—24no—
95C2×C7×SD16C2314yes—
96C22×C7×C8—24no—
97C22×C7×C8C2311yescharacteristic
98C22×C7×C8C2314yes—
99C22×C7×C8C2311yescharacteristic
100C7×C22⋊Q8—22no—
101C7×C22⋊Q8C2314yes—
102C7×#121—22no—
103C7×#121C2314yes—
104C2×C7×C4⋊C4—21no—
105C2×C7×C4⋊C4C2311yescharacteristic
106C2×C7×C4⋊C4C2311yescharacteristic
107C2×C7×C22⋊C4—21no—
108C2×C7×C22⋊C4—21no—
109C2×C22⋊Dic7—21no—
110C2×C22⋊Dic7—21no—
111C2×C22⋊Dic7D411yescharacteristic
112#6509—22no—
113#6509C2314yes—
114Q8×Dic7—22no—
115Q8×Dic7C2314yes—
116#6501—22no—
117#6501C2314yes—
118#6498—28no—
119D4×Dic7—22no—
120D4×Dic7C2314yes—
121C4×C22⋊D7D414yes—
122C4×C22⋊D7C2314yes—
123C2×(C2×D7)⋊C4—21no—
124C2×(C2×D7)⋊C4D411yescharacteristic
125C2×C4⋊Dic7—21no—
126C2×C4⋊Dic7—21no—
127C2×C4⋊Dic7—22no—
128C2×C4⋊Dic7—22no—
129C2×C4⋊Dic7—21no—
130C2×C4⋊Dic7C2311yescharacteristic
131C2×C4⋊Dic7C2311yescharacteristic
132C2×C4⋊Dic7C2311yescharacteristic
133C2×C4⋊Dic7C2311yescharacteristic
134C2×C4⋊Dic7C2314yes—
135C2×C4⋊Dic7C2314yes—
136C2×Dic7⋊C4—21no—
137C2×Dic7⋊C4—21no—
138C2×Dic7⋊C4—21no—
139C2×Dic7⋊C4—21no—
140C2×Dic7⋊C4—21no—
141C2×Dic7⋊C4D411yescharacteristic
142C2×C4×Dic7—21no—
143C2×C4×Dic7C2311yescharacteristic
144C22×C7⋊C8C2311yescharacteristic
145C22×C7⋊C8C2311yescharacteristic
146C2×C8×D7—24no—
147C2×C8×D7C2314yes—
148#6460—28no—
149D7×C4⋊C4—22no—
150D7×C4⋊C4—22no—
151D7×C4⋊C4C2314yes—
152D7×C4⋊C4C2314yes—
153#6452—28no—
154#6451—22no—
155#6451—22no—
156#6451C2314yes—
157#6451C2314yes—
158#6446—28no—
159(C22⋊D7)⋊C4—28no—
160#6441—28no—
161#6441—28no—
162C7×#106C2314yes—
163C7×#103C2314yes—
164C7×#102C2314yes—
165#6409C2314yes—
166#6409C2314yes—
167#6406C2314yes—
168#6406C2314yes—
169C22⋊(C7⋊C8)C2314yes—
170(C2×D7)⋊C8C2314yes—
171#6391C2314yes—
172#6391C2314yes—
173#6391C2314yes—
174#6391C2314yes—
175Dic7⋊C8C2314yes—
176C8×Dic7C2314yes—
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×#465D711yescharacteristic, complemented
193C2×C4×SD16—71no—
194C2×C8×D4—71no—
195C22×#106—71no—
196C22×#106—71no—
197C24×C7—21no—
198C24×C7C2×D411yescharacteristic
199C23×D7C2×D411yescharacteristic
200C2×C7×Q8—21no—
201C2×C7×Q8—22no—
202C2×C7×Q8—22no—
203C2×C7×Q8C2412yes—
204C2×C7×D4—24no—
205C2×C7×D4—21no—
206C2×C7×D4—22no—
207C2×C7×D4—22no—
208C2×C7×D4—44no—
209C2×C7×D4C2412yes—
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2×D412yes—
217C22×C4×C7C2412yes—
218C22×C4×C7C2411yescharacteristic
219C2×C22⋊D7—24no—
220C2×C22⋊D7—44no—
221C2×C22⋊D7SD1618yescomplemented
222C2×C22⋊D7C2×D414yes—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—24no—
228C22×Dic7—24no—
229C22×Dic7—24no—
230C22×Dic7—44no—
231C22×Dic7—44no—
232C22×Dic7—82no—
233C22×Dic7C2×D411yescharacteristic
234C22×Dic7C2×D411yescharacteristic
235C22×Dic7C2×D411yescharacteristic
236#1159—432no—
237C2×C4×D7—22no—
238C2×C4×D7—22no—
239C2×C4×D7—24no—
240C2×C4×D7—24no—
241C2×C4×D7—44no—
242C2×C4×D7—82no—
243C2×C4×D7C2×D412yes—
244C2×C4×D7C2412yes—
245C2×Dic14—24no—
246C2×Dic14—24no—
247C2×Dic14—44no—
248C2×Dic14—82no—
249C7×SD16—28no—
250C2×C7×C8—22no—
251C2×C7×C8—28no—
252C2×C7×C8#4114yescomplemented
253C2×C7×C8C2412yes—
254C2×C7×C8C2412yes—
255C7×C4⋊C4—21no—
256C7×C4⋊C4—21no—
257C7×C4⋊C4—24no—
258C7×C4⋊C4C2412yes—
259C7×C4⋊C4C2412yes—
260C7×C22⋊C4—24no—
261C7×C22⋊C4—24no—
262C22⋊Dic7—24no—
263C22⋊Dic7—24no—
264C22⋊Dic7C2×D414yes—
265(C2×D7)⋊C4—24no—
266(C2×D7)⋊C4C2×D414yes—
267C4⋊Dic7—24no—
268C4⋊Dic7—21no—
269C4⋊Dic7—21no—
270C4⋊Dic7—24no—
271C4⋊Dic7—21no—
272C4⋊Dic7—21no—
273C4⋊Dic7—24no—
274C4⋊Dic7C2412yes—
275C4⋊Dic7C2412yes—
276C4⋊Dic7C2412yes—
277C4⋊Dic7C2412yes—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282Dic7⋊C4—24no—
283Dic7⋊C4C2×D414yes—
284C4×Dic7—24no—
285C4×Dic7C2×D412yes—
286C4×Dic7C2412yes—
287C2×C7⋊C8—22no—
288C2×C7⋊C8—22no—
289C2×C7⋊C8C2412yes—
290C2×C7⋊C8C2412yes—
291C8×D7—28no—
292C22×#41—141no—
293C22×SD16C2×D711yescharacteristic
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—141no—
307C2×C22⋊Q8—141no—
308C2×C22⋊Q8—141no—
309C2×C22⋊Q8C2×D711yescharacteristic
310C2×#121—71no—
311C2×#121C2×D711yescharacteristic
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⋊C4—71no—
319C22×C4⋊C4—71no—
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#465C2×D718yescomplemented
329C4×SD16—78no—
330C8×D4—78no—
331C2×#106—71no—
332C2×#106—78no—
333C2×#106—71no—
334C2×#106—71no—
335C2×#106—71no—
336C2×#106—71no—
337C2×#106—71no—
338C2×#106—71no—
339C2×#106—71no—
340C2×#106—78no—
341C2×#106C2×D711yescharacteristic
342C2×C4⋊C8—71no—
343C2×#103—71no—
344C2×#103—71no—
345C2×#103C2×D711yescharacteristic
346C2×#102—71no—
347C2×#102—71no—
348C2×#102C2×D711yescharacteristic
349C2×C22⋊C8—71no—
350C2×C22⋊C8—71no—
351C2×C4×C8—71no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—42no—
356C23×C7—42no—
357C23×C7—42no—
358C23×C7C2×SD1614yes—
359C23×C7C22×D412yes—
360C23×C7C22×D411yescharacteristic
361C22×D7—22no—
362C22×D7—22no—
363C22×D7C2×SD1614yes—
364C22×D7C22×D412yes—
365C7×Q8—22no—
366C7×Q8—22no—
367C7×Q8—42no—
368C7×D4—22no—
369C7×D4—22no—
370C7×D4—48no—
371C7×D4—42no—
372C2×C4×C7—22no—
373C2×C4×C7—24no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—42no—
380C2×C4×C7—42no—
381C2×C4×C7—42no—
382C2×C4×C7C22×D412yes—
383C2×C4×C7C22×D411yescharacteristic
384C2×C4×C7C2×#4112yes—
385C2×C4×C72−1+412yes—
386C2×C4×C7C2511yescharacteristic
387C22⋊D7—48no—
388C22⋊D7C2×SD16116yescomplemented
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—42no—
396C2×Dic7—42no—
397C2×Dic7—48no—
398C2×Dic7—42no—
399C2×Dic7—42no—
400C2×Dic7—48no—
401C2×Dic7—84no—
402C2×Dic7C2×SD1614yes—
403C2×Dic7C22×D412yes—
404C2×Dic7C22×D412yes—
405C2×Dic7C22×D412yes—
406C4×D7—24no—
407C4×D7—22no—
408C4×D7—22no—
409C4×D7—48no—
410C4×D7—84no—
411Dic14—48no—
412Dic14—84no—
413C7×C8—22no—
414C7×C8C2×#4114yescomplemented
415C7⋊C8—22no—
416C7⋊C8—22no—
417C2×#41—148no—
418C2×#41—288no—
419C22×Q8—141no—
420C22×Q8—141no—
421C22×Q8C22×D711yescharacteristic
422C22×D4—21no—
423C22×D4—71no—
424C22×D4—141no—
425C22×D4C22×D711yescharacteristic
426C23×C4—71no—
427C23×C4—141no—
428C23×C4—141no—
429C23×C4—141no—
430C23×C4—141no—
431C23×C4—141no—
432C23×C4C22×D711yescharacteristic
433C2×SD16—24no—
434C2×SD16C22×D714yes—
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—22no—
451C22⋊Q8—74no—
452C22⋊Q8—148no—
453C22⋊Q8—148no—
454C22⋊Q8—148no—
455C22⋊Q8—142no—
456C22⋊Q8C22×D714yes—
457#121—22no—
458#121—74no—
459#121—142no—
460#121C22×D714yes—
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—71no—
470C2×C4⋊C4—71no—
471C2×C4⋊C4—71no—
472C2×C4⋊C4—71no—
473C2×C4⋊C4—71no—
474C2×C4⋊C4—74no—
475C2×C4⋊C4—74no—
476C2×C4⋊C4—74no—
477C2×C4⋊C4—74no—
478C2×C4⋊C4—142no—
479C2×C4⋊C4—142no—
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⋊C4—141no—
487C2×C4⋊C4—141no—
488C2×C4⋊C4—142no—
489C2×C4⋊C4—142no—
490C2×C4⋊C4C22×D711yescharacteristic
491C2×C4⋊C4C22×D711yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—71no—
495C2×C22⋊C4—71no—
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#106—74no—
507#106—74no—
508#106—74no—
509#106C22×D714yes—
510C4⋊C8—74no—
511#103—74no—
512#103—74no—
513#103C22×D714yes—
514#102—74no—
515#102—74no—
516#102C22×D714yes—
517C22⋊C8—74no—
518C22⋊C8—74no—
519C4×C8—74no—
520C22×C7—28no—
521C22×C7—22no—
522C22×C7—22no—
523C22×C7—42no—
524C22×C7—42no—
525C22×C7—42no—
526C22×C7—84no—
527C22×C7#54712yes—
528C22×C7C22×SD1614yes—
529C22×C7C22×SD1612yes—
530C22×C7#57712yes—
531C22×C7C23×D411yescharacteristic
532C2×D7—28no—
533C2×D7—22no—
534C2×D7—22no—
535C2×D7C22×SD1614yes—
536C4×C7—22no—
537C4×C7—42no—
538C4×C7—42no—
539C4×C7—42no—
540C4×C7#54712yes—
541C4×C7C22×#4111yescharacteristic
542C4×C7C2×2−1+411yescharacteristic
543Dic7—22no—
544Dic7—22no—
545Dic7—42no—
546Dic7—42no—
547Dic7—42no—
548Dic7—42no—
549Dic7C22×SD1614yes—
550C24—21no—
551C24—71no—
552C24D4×D711yescharacteristic
553#41—2832no—
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—144no—
558C2×Q8—144no—
559C2×Q8—284no—
560C2×Q8—562no—
561C2×Q8C23×D712yes—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—44no—
567C2×D4—78no—
568C2×D4—74no—
569C2×D4—144no—
570C2×D4—284no—
571C2×D4C23×D712yes—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—71no—
578C22×C4—71no—
579C22×C4—71no—
580C22×C4—72no—
581C22×C4—72no—
582C22×C4—144no—
583C22×C4—144no—
584C22×C4—144no—
585C22×C4—142no—
586C22×C4—142no—
587C22×C4—144no—
588C22×C4—141no—
589C22×C4—141no—
590C22×C4—141no—
591C22×C4—141no—
592C22×C4—144no—
593C22×C4—284no—
594C22×C4—284no—
595C22×C4—284no—
596C22×C4—562no—
597C22×C4—562no—
598C22×C4D4×D712yes—
599C22×C4D4×D711yescharacteristic
600C22×C4C23×D712yes—
601C22×C4C23×D711yescharacteristic
602SD16—28no—
603C2×C8—22no—
604C2×C8—28no—
605C2×C8—72no—
606C2×C8—72no—
607C2×C8—142no—
608C2×C8—142no—
609C2×C8—148no—
610C2×C8#115914yescomplemented
611C2×C8C23×D712yes—
612C2×C8C23×D712yes—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—74no—
617C4⋊C4—72no—
618C4⋊C4—72no—
619C4⋊C4—72no—
620C4⋊C4—72no—
621C4⋊C4—144no—
622C4⋊C4—144no—
623C4⋊C4—144no—
624C4⋊C4—144no—
625C4⋊C4—144no—
626C4⋊C4—144no—
627C4⋊C4—141no—
628C4⋊C4—141no—
629C4⋊C4—141no—
630C4⋊C4—144no—
631C4⋊C4—144no—
632C4⋊C4—141no—
633C4⋊C4C23×D712yes—
634C4⋊C4C23×D712yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—74no—
638C22⋊C4—74no—
639C22⋊C4—144no—
640C22⋊C4—144no—
641C22⋊C4—144no—
642C42—72no—
643C42—72no—
644C42—144no—
645C2×C7—24no—
646C2×C7—82no—
647C2×C7#333514yescomplemented
648C2×C7C2×#54711yescharacteristic
649C2×C7C23×SD1611yescharacteristic
650C2×C7C2×#57711yescharacteristic
651D7—24no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—74no—
659C23—72no—
660C23—142no—
661C23—142no—
662C23D7×SD1614yes—
663C23C2×D4×D712yes—
664C23C2×D4×D711yescharacteristic
665Q8—22no—
666Q8—22no—
667Q8—42no—
668Q8—288no—
669Q8—564no—
670D4—22no—
671D4—22no—
672D4—48no—
673D4—42no—
674D4—716no—
675D4—288no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—74no—
687C2×C4—72no—
688C2×C4—72no—
689C2×C4—72no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—144no—
693C2×C4—142no—
694C2×C4—142no—
695C2×C4—142no—
696C2×C4—142no—
697C2×C4—142no—
698C2×C4—142no—
699C2×C4—288no—
700C2×C4—288no—
701C2×C4—282no—
702C2×C4—282no—
703C2×C4—288no—
704C2×C4—282no—
705C2×C4—282no—
706C2×C4—564no—
707C2×C4—564no—
708C2×C4C2×D4×D712yes—
709C2×C4C2×D4×D711yescharacteristic
710C2×C4C2×#115912yes—
711C2×C4#655412yes—
712C2×C4C24×D711yescharacteristic
713C8—22no—
714C8—142no—
715C8—142no—
716C8C2×#115914yescomplemented
717C7C2×#333511yescharacteristic, complemented, Sylow
718C22—22no—
719C22—28no—
720C22—22no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—74no—
725C22—84no—
726C22—142no—
727C22—148no—
728C22—142no—
729C22#9030212yes—
730C22C2×D7×SD1614yes—
731C22C2×D7×SD1612yes—
732C22#9046112yes—
733C22C22×D4×D711yescharacteristic
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—74no—
739C4—142no—
740C4—142no—
741C4—282no—
742C4—282no—
743C4—282no—
744C4—282no—
745C4#9030212yes—
746C4C22×#115911yescharacteristic
747C4C2×#655411yescharacteristic
748C2—24no—
749C2—82no—
750C2—144no—
751C2#1173809314yesdirect product factor
752C2C2×#9030211yescharacteristic
753C2C22×D7×SD1611yescharacteristic
754C2C2×#9046111yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#465C2
socleC23×C7C22×D4
prime radicalC2×#90302C2
hypercenterC2×#465D7
hypocenterC7C2×#3335
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#90326C2semidirect
3. C2×C7×#465C2semidirect
4. C2×#89943C2semidirect
5. C2×SD16×Dic7C2semidirect
6. C2×C8×C22⋊D7C2semidirect
7. C22×#6391C2semidirect
8. C2×#89815C2semidirect
9. C2×#89806C2semidirect
10. #11738093C2direct (N × H)
11. C2×D7×#106C2semidirect
12. C2×#89627C2semidirect
13. C2×#89577C2semidirect
14. C2×#89563C2semidirect
15. C2×#89549C2semidirect
16. C2×#89533C2semidirect
32. #90326C22semidirect
45. C7×#465C22semidirect
54. #89943C22semidirect
55. SD16×Dic7C22semidirect
56. C8×C22⋊D7C22semidirect
62. C2×#6391C22semidirect
65. #89815C22semidirect
66. #89806C22semidirect
71. D7×#106C22semidirect
72. #89627C22semidirect
73. #89577C22semidirect
74. #89563C22semidirect
75. #89549C22semidirect
76. #89533C22semidirect
192. C2×#465D7semidirect
221. C2×C22⋊D7SD16semidirect
252. C2×C7×C8#41semidirect
328. #465C2×D7semidirect
388. C22⋊D7C2×SD16semidirect
414. C7×C8C2×#41semidirect
610. C2×C8#1159semidirect
647. C2×C7#3335semidirect
716. C8C2×#1159semidirect
717. C7C2×#3335semidirect
751. C2#11738093direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903262
C2×#903022
C2×C7×#4652
C2×#899432
C2×SD16×Dic72
C2×C8×C22⋊D72
C22×#63912
C2×#898152
C2×#898062
#117380932
C2×D7×#1062
C2×#896272
C2×#895772
C2×#895632
C2×#895492
C2×#895332
C2×#33357