Finite Group Databasebeta

← C2×#11738613 #14221354

Subgroups — C2×#11738613 #14221354

Order 1792.

2234 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×#90380C211yesmaximal, characteristic, complemented
2C2×#90236C211yesmaximal, characteristic
3C2×C7×#478C211yesmaximal, characteristic, complemented
4C2×#89838C211yesmaximal, characteristic, complemented
5C2×#89779C211yesmaximal, characteristic, complemented
6#11738613C2116yesmaximal, direct product factor
7C2×#89662C211yesmaximal, characteristic, complemented
8C2×#89653C211yesmaximal, characteristic, complemented
9C2×#89643C211yesmaximal, characteristic, complemented
10C2×#89632C211yesmaximal, characteristic, complemented
11C2×#89614C211yesmaximal, characteristic, complemented
12C2×#89611C211yesmaximal, characteristic, complemented
13C2×#89542C211yesmaximal, characteristic
14C2×D7×#102C211yesmaximal, characteristic
15C2×#89535C211yesmaximal, characteristic, complemented
16C2×#89533C211yesmaximal, characteristic, complemented
17C22×D4×D7C2211yescharacteristic
18C2×C7×#125C2211yescharacteristic, complemented
19C2×C4×C7×D4C2211yescharacteristic
20C2×D4×Dic7C2211yescharacteristic
21C2×C4×C22⋊D7—21no—
22C22×(C2×D7)⋊C4—21no—
23C22×#1131C2211yescharacteristic
24C22×C8×D7C2211yescharacteristic
25#90380—24no—
26#90380C2218yescomplemented
27#90236—24no—
28#90236C2218yes—
29C2×#6460—21no—
30C2×#6459—21no—
31C2×#6456C2211yescharacteristic
32C2×#6455C2211yescharacteristic
33C2×#6455C2211yescharacteristic
34C2×D7×C4⋊C4C2211yescharacteristic
35C2×#6453C2211yescharacteristic, complemented
36C2×#6452—21no—
37C2×#6451—21no—
38C2×#6451C2211yescharacteristic, complemented
39C2×(C22⋊D7)⋊C4—21no—
40C2×D7×C22⋊C4—21no—
41C2×C4×D28C2211yescharacteristic
42C2×#6435C2211yescharacteristic
43C2×#6432C2211yescharacteristic, complemented
44C7×#478C2218yescomplemented
45C2×C7×#107C2211yescharacteristic, complemented
46C2×C7×#106C2211yescharacteristic, complemented
47C2×C7×C4⋊C8C2211yescharacteristic, complemented
48C2×C7×#102C2211yescharacteristic
49C2×C7×#102C2211yescharacteristic
50C2×#6406C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52C2×#6395C2211yescharacteristic
53C2×#6395C2211yescharacteristic
54C2×#6391C2211yescharacteristic, complemented
55C2×#6391C2211yescharacteristic, complemented
56C2×Dic7⋊C8C2211yescharacteristic, complemented
57C2×Dic7⋊C8C2211yescharacteristic, complemented
58#89838C2218yescomplemented
59#89779C2218yescomplemented
60C2×#6383C2211yescharacteristic
61C2×#6383C2211yescharacteristic
62C2×#6382C2211yescharacteristic, complemented
63C2×#6381C2211yescharacteristic, complemented
64C2×#6381C2211yescharacteristic, complemented
65C2×#6381C2211yescharacteristic, complemented
66C2×C4⋊(C7⋊C8)C2211yescharacteristic, complemented
67#89662C2218yescomplemented
68#89653C2218yescomplemented
69#89643C2218yescomplemented
70#89632C2218yescomplemented
71#89614C2218yescomplemented
72#89611C2218yescomplemented
73#89542C2218yes—
74D7×#102C2218yes—
75#89535C2218yescomplemented
76#89533C2218yescomplemented
77C2×#3081—71nomaximal, Sylow
78C24×D7—21no—
79C22×C7×D4C2311yescharacteristic
80C23×C4×C7—21no—
81C22×C22⋊D7—21no—
82C23×Dic7—21no—
83C2×D4×D7—22no—
84C2×D4×D7—24no—
85C2×D4×D7Q818yescomplemented
86C2×D4×D7C2314yes—
87C22×D28C2311yescharacteristic
88C22×C4×D7—21no—
89C22×C4×D7—21no—
90C22×C4×D7—21no—
91C22×C4×D7C2311yescharacteristic
92C22×Dic14—21no—
93C22×Dic14—21no—
94C22×C7×C8C2311yescharacteristic
95C22×C7×C8C2311yescharacteristic
96C7×#125—22no—
97C7×#125C2314yescomplemented
98C4×C7×D4—22no—
99C4×C7×D4C2314yes—
100C2×C7×C4⋊C4—21no—
101C2×C7×C4⋊C4—21no—
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C4⋊C4C2311yescharacteristic
104C2×C7×C4⋊C4C2311yescharacteristic
105C2×C7×C22⋊C4—21no—
106C2×C42×C7C2311yescharacteristic
107C2×C22⋊Dic7—21no—
108D4×Dic7—22no—
109D4×Dic7C2314yes—
110C4×C22⋊D7—28no—
111C2×(C2×D7)⋊C4—21no—
112C2×(C2×D7)⋊C4—21no—
113C2×(C2×D7)⋊C4—21no—
114C2×(C2×D7)⋊C4—21no—
115C2×(C2×D7)⋊C4—28no—
116C2×(C2×D7)⋊C4D411yescharacteristic
117C2×(C2×D7)⋊C4D411yescharacteristic
118C2×C4⋊Dic7—21no—
119C2×C4⋊Dic7—21no—
120C2×C4⋊Dic7C2311yescharacteristic
121C2×C4⋊Dic7C2311yescharacteristic
122C2×C4⋊Dic7C2311yescharacteristic
123C2×Dic7⋊C4—21no—
124C2×Dic7⋊C4—21no—
125C2×Dic7⋊C4—21no—
126C2×Dic7⋊C4D411yescharacteristic
127C2×Dic7⋊C4D411yescharacteristic
128C2×C4×Dic7—21no—
129C2×C4×Dic7—21no—
130C2×C4×Dic7C2311yescharacteristic
131C22×C7⋊C8C2311yescharacteristic
132C22×C7⋊C8C2311yescharacteristic
133C2×#1131—24no—
134C2×#1131C2314yes—
135C2×C8×D7—24no—
136C2×C8×D7C2314yes—
137#6460—28no—
138#6459—28no—
139#6456—22no—
140#6456C2314yes—
141#6455—22no—
142#6455—22no—
143#6455C2314yes—
144#6455C2314yes—
145D7×C4⋊C4—22no—
146D7×C4⋊C4C2314yes—
147#6453—22no—
148#6453C2314yescomplemented
149#6452—28no—
150#6451—28no—
151#6451—22no—
152#6451C2314yescomplemented
153(C22⋊D7)⋊C4—28no—
154D7×C22⋊C4—28no—
155C4×D28—22no—
156C4×D28C2314yes—
157#6435D414yes—
158#6435C2314yes—
159#6432—22no—
160#6432C2314yescomplemented
161C7×#107C2314yescomplemented
162C7×#106C2314yescomplemented
163C7×C4⋊C8C2314yescomplemented
164C7×#102C2314yes—
165C7×#102C2314yes—
166#6406C2314yes—
167#6406C2314yes—
168#6395C2314yes—
169#6395C2314yes—
170#6391C2314yescomplemented
171#6391C2314yescomplemented
172Dic7⋊C8C2314yescomplemented
173Dic7⋊C8C2314yescomplemented
174#6383C2314yes—
175#6383C2314yes—
176#6382C2314yescomplemented
177#6381C2314yescomplemented
178#6381C2314yescomplemented
179#6381C2314yescomplemented
180C4⋊(C7⋊C8)C2314yescomplemented
181C2×#544—71no—
182C2×#518—71no—
183#3081—716no—
184C2×#478—71no—
185C2×#478—71no—
186C2×#478—71no—
187C2×#478D711yescharacteristic, complemented
188C2×#476—71no—
189C2×#476—71no—
190C2×#474—71no—
191C2×#474—71no—
192C2×#428—71no—
193C2×#427—71no—
194C2×#424—71no—
195C2×#418—71no—
196C22×#102—71no—
197C24×C7—21no—
198C23×D7—21no—
199C23×D7—28no—
200C23×D7—24no—
201C23×D7—82no—
202C23×D7—82no—
203C23×D7C2×D411yescharacteristic
204C2×C7×D4—21no—
205C2×C7×D4—22no—
206C2×C7×D4C2×Q814yes—
207C2×C7×D4C2412yes—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—24no—
212C22×C4×C7—82no—
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2411yescharacteristic
216C2×C22⋊D7—28no—
217C2×C22⋊D7—24no—
218C22×Dic7—21no—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—24no—
222C22×Dic7—82no—
223C22×Dic7C2×D411yescharacteristic
224C22×Dic7C2×D411yescharacteristic
225C22×Dic7C2×D411yescharacteristic
226D4×D7—216no—
227D4×D7—28no—
228D4×D7C2×Q8116yescomplemented
229C2×D28—21no—
230C2×D28—22no—
231C2×D28C2×Q814yes—
232C2×D28C2412yes—
233C2×C4×D7—24no—
234C2×C4×D7—24no—
235C2×C4×D7—24no—
236C2×C4×D7—82no—
237C2×C4×D7—82no—
238C2×C4×D7—82no—
239C2×C4×D7C2×D412yes—
240C2×C4×D7C2×Q814yes—
241C2×C4×D7#4114yes—
242C2×C4×D7C2412yes—
243C2×Dic14—24no—
244C2×Dic14—24no—
245C2×Dic14—82no—
246C2×Dic14—82no—
247C2×C7×C8—22no—
248C2×C7×C8—22no—
249C2×C7×C8C2412yes—
250C2×C7×C8C2412yes—
251C7×C4⋊C4—21no—
252C7×C4⋊C4—24no—
253C7×C4⋊C4—24no—
254C7×C4⋊C4—21no—
255C7×C4⋊C4—21no—
256C7×C4⋊C4C2412yes—
257C7×C4⋊C4C2412yes—
258C7×C4⋊C4C2412yes—
259C7×C22⋊C4—24no—
260C42×C7C2×D412yes—
261C42×C7C2412yes—
262C22⋊Dic7—24no—
263(C2×D7)⋊C4—24no—
264(C2×D7)⋊C4—24no—
265(C2×D7)⋊C4—24no—
266(C2×D7)⋊C4—24no—
267(C2×D7)⋊C4C2×D414yes—
268(C2×D7)⋊C4C2×D414yes—
269C4⋊Dic7—21no—
270C4⋊Dic7—21no—
271C4⋊Dic7—24no—
272C4⋊Dic7—21no—
273C4⋊Dic7—24no—
274C4⋊Dic7C2412yes—
275C4⋊Dic7C2412yes—
276C4⋊Dic7C2412yes—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280Dic7⋊C4C2×D414yes—
281Dic7⋊C4C2×D414yes—
282C4×Dic7—24no—
283C4×Dic7—24no—
284C4×Dic7C2×D412yes—
285C4×Dic7C2412yes—
286C2×C7⋊C8—22no—
287C2×C7⋊C8—22no—
288C2×C7⋊C8C2412yes—
289C2×C7⋊C8C2412yes—
290#1131—28no—
291C8×D7—28no—
292C23×D4—71no—
293C22×M16—71no—
294C23×C8—71no—
295#544—78no—
296#544—144no—
297C2×C4⋊Q8—71no—
298C2×C4⋊Q8—71no—
299C2×C4⋊Q8—141no—
300C2×#125—71no—
301C2×#125—141no—
302C2×#125C2×D711yescharacteristic, complemented
303C2×C22⋊Q8—141no—
304C2×C22⋊Q8—141no—
305#518—78no—
306#518—144no—
307C2×C4×D4—71no—
308C2×C4×D4—71no—
309C2×C4×D4—71no—
310C2×C4×D4—141no—
311C2×C4×D4—141no—
312C2×C4×D4C2×D711yescharacteristic
313C2×#117—71no—
314C2×#117—71no—
315C2×#117—71no—
316C22×C4⋊C4—71no—
317C22×C22⋊C4—141no—
318C22×C22⋊C4—141no—
319#478—78no—
320#478—78no—
321#478—78no—
322#478C2×D718yescomplemented
323#476—78no—
324#476—78no—
325#474—78no—
326#474—78no—
327#428—78no—
328#427—78no—
329C2×#107—71no—
330C2×#107—71no—
331C2×#107—71no—
332C2×#107C2×D711yescharacteristic, complemented
333C2×#106—71no—
334C2×#106—71no—
335C2×#106—71no—
336C2×#106C2×D711yescharacteristic, complemented
337#424—78no—
338C2×C4⋊C8—71no—
339C2×C4⋊C8—71no—
340C2×C4⋊C8—71no—
341C2×C4⋊C8C2×D711yescharacteristic, complemented
342#418—78no—
343C2×#102—71no—
344C2×#102—71no—
345C2×#102—71no—
346C2×#102—71no—
347C2×#102—71no—
348C2×#102—71no—
349C2×#102—78no—
350C2×#102C2×D711yescharacteristic
351C2×#102C2×D711yescharacteristic
352C23×C7—24no—
353C23×C7—22no—
354C23×C7—42no—
355C23×C7—42no—
356C23×C7C22×D411yescharacteristic
357C22×D7—22no—
358C22×D7—22no—
359C22×D7—24no—
360C22×D7—22no—
361C22×D7—216no—
362C22×D7—42no—
363C22×D7—42no—
364C22×D7—816no—
365C22×D7—84no—
366C22×D7—84no—
367C22×D7C22⋊Q814yes—
368C22×D7C22×D412yes—
369C7×D4—24no—
370C7×D4—22no—
371C7×D4C22×Q814yes—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—42no—
378C2×C4×C7—42no—
379C2×C4×C7—42no—
380C2×C4×C7—84no—
381C2×C4×C7C22×D412yes—
382C2×C4×C7C22×D412yes—
383C2×C4×C7C22×D411yescharacteristic
384C2×C4×C7C22×Q812yes—
385C2×C4×C7C2×#4112yes—
386C2×C4×C7C2511yescharacteristic
387C22⋊D7—216no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—42no—
394C2×Dic7—42no—
395C2×Dic7—42no—
396C2×Dic7—84no—
397C2×Dic7C22⋊Q814yes—
398C2×Dic7C22×D412yes—
399C2×Dic7C22×D412yes—
400C2×Dic7C22×D412yes—
401D28—24no—
402D28—22no—
403D28C22×Q814yes—
404C4×D7—84no—
405C4×D7—84no—
406C4×D7—84no—
407C4×D7C22⋊Q818yes—
408C4×D7C22×Q814yes—
409C4×D7C2×#4114yes—
410Dic14—84no—
411Dic14—84no—
412C7×C8—22no—
413C7×C8—22no—
414C7⋊C8—22no—
415C7⋊C8—22no—
416C25—141no—
417C22×Q8—141no—
418C22×Q8—141no—
419C22×D4—78no—
420C22×D4—74no—
421C22×D4—71no—
422C22×D4—142no—
423C22×D4—144no—
424C22×D4—141no—
425C22×D4C22×D711yescharacteristic
426C23×C4—21no—
427C23×C4—71no—
428C23×C4—141no—
429C23×C4—141no—
430C23×C4—141no—
431C23×C4—141no—
432C2×M16—74no—
433C2×M16—144no—
434C22×C8—71no—
435C22×C8—71no—
436C22×C8—74no—
437C22×C8—144no—
438C22×C8C22×D711yescharacteristic
439C22×C8C22×D711yescharacteristic
440C4⋊Q8—74no—
441C4⋊Q8—74no—
442C4⋊Q8—142no—
443C4⋊Q8—148no—
444C4⋊Q8—142no—
445#125—22no—
446#125—74no—
447#125—142no—
448#125—148no—
449#125C22×D714yescomplemented
450C22⋊Q8—148no—
451C22⋊Q8—148no—
452C4×D4—22no—
453C4×D4—74no—
454C4×D4—74no—
455C4×D4—74no—
456C4×D4—142no—
457C4×D4—142no—
458C4×D4—148no—
459C4×D4—148no—
460C4×D4—142no—
461C4×D4C22×D714yes—
462#117—74no—
463#117—74no—
464#117—74no—
465#117—74no—
466#117—142no—
467#117—142no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—71no—
471C2×C4⋊C4—71no—
472C2×C4⋊C4—71no—
473C2×C4⋊C4—71no—
474C2×C4⋊C4—71no—
475C2×C4⋊C4—74no—
476C2×C4⋊C4—142no—
477C2×C4⋊C4—141no—
478C2×C4⋊C4—141no—
479C2×C4⋊C4—141no—
480C2×C4⋊C4—141no—
481C2×C4⋊C4—141no—
482C2×C4⋊C4C22×D711yescharacteristic
483C2×C4⋊C4C22×D711yescharacteristic
484C2×C4⋊C4C22×D711yescharacteristic
485C2×C22⋊C4—21no—
486C2×C22⋊C4—71no—
487C2×C22⋊C4—71no—
488C2×C22⋊C4—148no—
489C2×C22⋊C4—148no—
490C2×C22⋊C4—141no—
491C2×C22⋊C4—141no—
492C2×C22⋊C4—141no—
493C2×C22⋊C4—141no—
494C2×C22⋊C4—141no—
495C2×C42—71no—
496C2×C42—141no—
497C2×C42—141no—
498C2×C42C22×D711yescharacteristic
499#107—74no—
500#107—74no—
501#107—74no—
502#107C22×D714yescomplemented
503#106—74no—
504#106—74no—
505#106—74no—
506#106C22×D714yescomplemented
507C4⋊C8—74no—
508C4⋊C8—74no—
509C4⋊C8—74no—
510C4⋊C8C22×D714yescomplemented
511#102—74no—
512#102—74no—
513#102—74no—
514#102—74no—
515#102—74no—
516#102—74no—
517#102C22×D714yes—
518#102C22×D714yes—
519C22×C7—24no—
520C22×C7—48no—
521C22×C7—42no—
522C22×C7—42no—
523C22×C7C2×C22⋊Q812yes—
524C22×C7#57612yes—
525C22×C7#57712yes—
526C22×C7C23×D411yescharacteristic
527C2×D7—28no—
528C2×D7—22no—
529C2×D7—22no—
530C2×D7—24no—
531C2×D7—48no—
532C2×D7—42no—
533C2×D7—42no—
534C2×D7—816no—
535C2×D7C2×C22⋊Q814yes—
536C4×C7—22no—
537C4×C7—22no—
538C4×C7—42no—
539C4×C7—42no—
540C4×C7—42no—
541C4×C7C2×C22⋊Q812yes—
542C4×C7C23×Q811yescharacteristic
543C4×C7C22×#4111yescharacteristic
544Dic7—22no—
545Dic7—22no—
546Dic7—42no—
547Dic7—42no—
548Dic7—42no—
549Dic7C2×C22⋊Q814yes—
550C24—21no—
551C24—71no—
552C24—144no—
553C24—148no—
554C24—141no—
555C24—562no—
556C24—562no—
557C2×Q8—144no—
558C2×Q8—144no—
559C2×Q8—562no—
560C2×Q8—562no—
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—716no—
564C2×D4—74no—
565C2×D4—72no—
566C2×D4—1416no—
567C2×D4—148no—
568C2×D4—144no—
569C2×D4—148no—
570C2×D4—141no—
571C2×D4—142no—
572C2×D4Q8×D714yes—
573C2×D4C23×D712yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—71no—
579C22×C4—72no—
580C22×C4—74no—
581C22×C4—74no—
582C22×C4—72no—
583C22×C4—71no—
584C22×C4—71no—
585C22×C4—82no—
586C22×C4—144no—
587C22×C4—144no—
588C22×C4—144no—
589C22×C4—141no—
590C22×C4—141no—
591C22×C4—141no—
592C22×C4—144no—
593C22×C4—562no—
594C22×C4—562no—
595C22×C4—562no—
596C22×C4—562no—
597C22×C4D4×D711yescharacteristic
598C22×C4D4×D711yescharacteristic
599C22×C4C23×D711yescharacteristic
600M16—148no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—72no—
604C2×C8—72no—
605C2×C8—148no—
606C2×C8—142no—
607C2×C8—142no—
608C2×C8C23×D712yes—
609C2×C8C23×D712yes—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—74no—
616C4⋊C4—74no—
617C4⋊C4—72no—
618C4⋊C4—72no—
619C4⋊C4—72no—
620C4⋊C4—144no—
621C4⋊C4—144no—
622C4⋊C4—144no—
623C4⋊C4—144no—
624C4⋊C4—141no—
625C4⋊C4—141no—
626C4⋊C4—141no—
627C4⋊C4—144no—
628C4⋊C4C23×D712yes—
629C4⋊C4C23×D712yes—
630C4⋊C4C23×D712yes—
631C22⋊C4—24no—
632C22⋊C4—74no—
633C22⋊C4—74no—
634C22⋊C4—144no—
635C22⋊C4—144no—
636C22⋊C4—144no—
637C22⋊C4—144no—
638C22⋊C4—144no—
639C42—72no—
640C42—72no—
641C42—144no—
642C42—144no—
643C42D4×D712yes—
644C42C23×D712yes—
645C2×C7—44no—
646C2×C7#308114yescomplemented
647C2×C7C22×C22⋊Q811yescharacteristic
648C2×C7C2×#57611yescharacteristic
649C2×C7C2×#57711yescharacteristic
650D7—24no—
651D7—44no—
652C23—24no—
653C23—22no—
654C23—42no—
655C23—42no—
656C23—74no—
657C23—72no—
658C23—1416no—
659C23—142no—
660C23—142no—
661C23—144no—
662C23—142no—
663C23—282no—
664C23—282no—
665C23—564no—
666C23—5616no—
667C23—564no—
668C23C2×D4×D711yescharacteristic
669Q8—564no—
670Q8—564no—
671D4—24no—
672D4—22no—
673D4—74no—
674D4—1416no—
675D4—144no—
676D4—142no—
677D4C2×Q8×D714yes—
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—78no—
689C2×C4—74no—
690C2×C4—74no—
691C2×C4—72no—
692C2×C4—72no—
693C2×C4—84no—
694C2×C4—142no—
695C2×C4—142no—
696C2×C4—142no—
697C2×C4—142no—
698C2×C4—142no—
699C2×C4—282no—
700C2×C4—282no—
701C2×C4—282no—
702C2×C4—564no—
703C2×C4—564no—
704C2×C4—564no—
705C2×C4—564no—
706C2×C4C2×D4×D712yes—
707C2×C4C2×D4×D712yes—
708C2×C4C2×D4×D711yescharacteristic
709C2×C4C2×Q8×D712yes—
710C2×C4D7×#4112yes—
711C2×C4C24×D711yescharacteristic
712C8—22no—
713C8—22no—
714C8—142no—
715C8—142no—
716C7C2×#308111yescharacteristic, complemented, Sylow
717C22—24no—
718C22—42no—
719C22—48no—
720C22—42no—
721C22—74no—
722C22—142no—
723C22—148no—
724C22—142no—
725C22—144no—
726C22—282no—
727C22—288no—
728C22—282no—
729C22—5616no—
730C22D7×C22⋊Q812yes—
731C22#9046112yes—
732C22#9046512yes—
733C22C22×D4×D711yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—74no—
740C4—142no—
741C4—142no—
742C4—282no—
743C4—282no—
744C4—282no—
745C4D7×C22⋊Q812yes—
746C4C22×Q8×D711yescharacteristic
747C4C2×D7×#4111yescharacteristic
748C2—44no—
749C2—144no—
750C2—284no—
751C2#1173861314yesdirect product factor
752C2C2×D7×C22⋊Q811yescharacteristic
753C2C2×#9046111yescharacteristic
754C2C2×#9046511yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#478C2
socleC23×C7C22×D4
prime radicalC22×D4×D7C22
hypercenterC2×#478D7
hypocenterC7C2×#3081
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#90380C2semidirect
3. C2×C7×#478C2semidirect
4. C2×#89838C2semidirect
5. C2×#89779C2semidirect
6. #11738613C2direct (N × H)
7. C2×#89662C2semidirect
8. C2×#89653C2semidirect
9. C2×#89643C2semidirect
10. C2×#89632C2semidirect
11. C2×#89614C2semidirect
12. C2×#89611C2semidirect
15. C2×#89535C2semidirect
16. C2×#89533C2semidirect
18. C2×C7×#125C22semidirect
26. #90380C22semidirect
35. C2×#6453C22semidirect
38. C2×#6451C22semidirect
43. C2×#6432C22semidirect
44. C7×#478C22semidirect
45. C2×C7×#107C22semidirect
46. C2×C7×#106C22semidirect
47. C2×C7×C4⋊C8C22semidirect
54. C2×#6391C22semidirect
55. C2×#6391C22semidirect
56. C2×Dic7⋊C8C22semidirect
57. C2×Dic7⋊C8C22semidirect
58. #89838C22semidirect
59. #89779C22semidirect
62. C2×#6382C22semidirect
63. C2×#6381C22semidirect
64. C2×#6381C22semidirect
65. C2×#6381C22semidirect
66. C2×C4⋊(C7⋊C8)C22semidirect
67. #89662C22semidirect
68. #89653C22semidirect
69. #89643C22semidirect
70. #89632C22semidirect
71. #89614C22semidirect
72. #89611C22semidirect
75. #89535C22semidirect
76. #89533C22semidirect
85. C2×D4×D7Q8semidirect
97. C7×#125C23semidirect
148. #6453C23semidirect
152. #6451C23semidirect
160. #6432C23semidirect
161. C7×#107C23semidirect
162. C7×#106C23semidirect
163. C7×C4⋊C8C23semidirect
170. #6391C23semidirect
171. #6391C23semidirect
172. Dic7⋊C8C23semidirect
173. Dic7⋊C8C23semidirect
176. #6382C23semidirect
177. #6381C23semidirect
178. #6381C23semidirect
179. #6381C23semidirect
180. C4⋊(C7⋊C8)C23semidirect
187. C2×#478D7semidirect
228. D4×D7C2×Q8semidirect
302. C2×#125C2×D7semidirect
322. #478C2×D7semidirect
332. C2×#107C2×D7semidirect
336. C2×#106C2×D7semidirect
341. C2×C4⋊C8C2×D7semidirect
449. #125C22×D7semidirect
502. #107C22×D7semidirect
506. #106C22×D7semidirect
510. C4⋊C8C22×D7semidirect
646. C2×C7#3081semidirect
716. C7C2×#3081semidirect
751. C2#11738613direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903802
C2×#902362
C2×C7×#4782
C2×#898382
C2×#897792
#117386132
C2×#896622
C2×#896532
C2×#896432
C2×#896322
C2×#896142
C2×#896112
C2×#895422
C2×D7×#1022
C2×#895352
C2×#895332
C2×#30817