Finite Group Databasebeta

← C2×#11740912 #14222069

Subgroups — C2×#11740912 #14222069

Order 1792.

2058 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#542C211yesmaximal, characteristic
2C2×#90207C211yesmaximal, characteristic, complemented
3#11740912C2116yesmaximal, direct product factor
4C2×#89863C211yesmaximal, characteristic, complemented
5C2×#89866C211yesmaximal, characteristic, complemented
6C2×#89826C211yesmaximal, characteristic, complemented
7C2×#89826C211yesmaximal, characteristic, complemented
8C2×#89822C211yesmaximal, characteristic, complemented
9C2×#89817C211yesmaximal, characteristic, complemented
10C2×#89812C211yesmaximal, characteristic
11C2×#89807C211yesmaximal, characteristic
12C2×#89802C211yesmaximal, characteristic, complemented
13C2×C4×#1144C211yesmaximal, characteristic, complemented
14C2×C4×#1142C211yesmaximal, characteristic, complemented
15C2×#89790C211yesmaximal, characteristic, complemented
16C2×#89772C211yesmaximal, characteristic, complemented
17C23×Dic14C2211yescharacteristic
18C7×#542—24no—
19C7×#542C2218yes—
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×#1144C2211yescharacteristic
33C22×#1142C2211yescharacteristic
34C22×#1142C2211yescharacteristic
35C2×#6489C2211yescharacteristic
36#90207—24no—
37#90207C2218yescomplemented
38C2×#6450—21no—
39C2×#6450—21no—
40C2×#6440—21no—
41C2×#6440—21no—
42C2×C4×Dic14C2211yescharacteristic
43C2×C4×Dic14C2211yescharacteristic
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#89863C2218yescomplemented
54#89826C2218yescomplemented
55#89826C2218yescomplemented
56#89822C2218yescomplemented
57#89817C2218yescomplemented
58#89812C2218yes—
59#89807C2218yes—
60#89802C2218yescomplemented
61C4×#1144C2218yescomplemented
62#89790C2218yescomplemented
63C4×#1142C2218yescomplemented
64#89772C2218yescomplemented
65C2×#6384C2211yescharacteristic
66C2×#6384C2211yescharacteristic
67C2×#6384C2211yescharacteristic
68C2×#6384C2211yescharacteristic
69C2×#6382C2211yescharacteristic
70C2×#6382C2211yescharacteristic
71C2×#6381C2211yescharacteristic
72C2×#6381C2211yescharacteristic
73C2×C4⋊(C7⋊C8)C2211yescharacteristic
74C2×C4⋊(C7⋊C8)C2211yescharacteristic
75C2×#6377C2211yescharacteristic
76C2×C4×C7⋊C8C2211yescharacteristic
77C2×#3121—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8C2311yescharacteristic
80C22×C7×D4—21no—
81C22×C7×D4C2311yescharacteristic
82C23×C4×C7—21no—
83C23×C4×C7C2311yescharacteristic
84C23×Dic7—21no—
85C22×Dic14—21no—
86C22×Dic14—22no—
87C22×Dic14—24no—
88C22×Dic14—24no—
89C22×Dic14C2314yes—
90C22×Dic14C2311yescharacteristic
91C22×Dic14C2311yescharacteristic
92C7×C4⋊Q8—22no—
93C7×C4⋊Q8C2314yes—
94C7×#126—28no—
95C7×#124—28no—
96C7×#124—22no—
97C7×#124C2314yes—
98C7×#123—28no—
99C7×C22⋊Q8—22no—
100C7×C22⋊Q8—28no—
101C7×C22⋊Q8C2314yes—
102C7×#121—22no—
103C7×#121C2314yes—
104C4×C7×Q8—22no—
105C4×C7×Q8C2314yes—
106C4×C7×D4—22no—
107C4×C7×D4C2314yes—
108C7×#117D414yes—
109C7×#117C2314yes—
110C2×C7×C4⋊C4—21no—
111C2×C7×C4⋊C4—21no—
112C2×C7×C4⋊C4—21no—
113C2×C7×C4⋊C4D411yescharacteristic
114C2×C7×C4⋊C4D411yescharacteristic
115C2×C7×C4⋊C4C2311yescharacteristic
116C2×C7×C4⋊C4C2311yescharacteristic
117C2×C7×C22⋊C4—21no—
118C2×C7×C22⋊C4—21no—
119C2×C7×C22⋊C4—21no—
120C2×C7×C22⋊C4—21no—
121C2×C7×C22⋊C4—21no—
122C2×C7×C22⋊C4D411yescharacteristic
123C2×C7×C22⋊C4D411yescharacteristic
124C2×C42×C7—21no—
125C2×C42×C7C2311yescharacteristic
126C2×C42×C7C2311yescharacteristic
127C2×C22⋊Dic7—21no—
128C2×#1144—24no—
129C2×#1144—24no—
130C2×#1144C2314yes—
131C2×#1144C2314yes—
132C2×#1142—24no—
133C2×#1142—24no—
134C2×#1142C2314yes—
135C2×#1142C2314yes—
136#6489—22no—
137#6489C2314yes—
138C2×C4⋊Dic7C2311yescharacteristic
139C2×C4⋊Dic7C2311yescharacteristic
140C2×Dic7⋊C4—21no—
141C2×Dic7⋊C4—21no—
142C2×Dic7⋊C4—21no—
143C2×Dic7⋊C4—21no—
144C2×C4×Dic7—21no—
145C2×C4×Dic7—21no—
146C2×C4×Dic7—21no—
147C2×C4×Dic7—21no—
148C2×C4×Dic7—21no—
149C22×C7⋊C8C2311yescharacteristic
150C22×C7⋊C8C2311yescharacteristic
151C22×C7⋊C8C2311yescharacteristic
152C22×C7⋊C8C2311yescharacteristic
153#6450—28no—
154#6450—28no—
155#6440—28no—
156#6440—28no—
157C4×Dic14—22no—
158C4×Dic14—22no—
159C4×Dic14—22no—
160C4×Dic14—22no—
161C4×Dic14C2314yes—
162C4×Dic14C2314yes—
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#6384C2314yes—
174#6384C2314yes—
175#6382C2314yes—
176#6382C2314yes—
177#6381C2314yes—
178#6381C2314yes—
179C4⋊(C7⋊C8)C2314yes—
180C4⋊(C7⋊C8)C2314yes—
181#6377C2314yes—
182C4×C7⋊C8C2314yes—
183C2×#542D711yescharacteristic
184C2×#519—71no—
185#3121—716no—
186C2×#485—71no—
187C2×#482—71no—
188C2×#477—71no—
189C2×#475—71no—
190C2×#464—71no—
191C2×#464—71no—
192C2×#451—71no—
193C2×#448—71no—
194C2×#441—71no—
195C2×#440—71no—
196C2×C4×Q16—71no—
197C2×C4×SD16—71no—
198C2×#433—71no—
199C24×C7—21no—
200C24×C7C2×D411yescharacteristic
201C2×C7×Q8—21no—
202C2×C7×Q8—24no—
203C2×C7×Q8—22no—
204C2×C7×Q8—22no—
205C2×C7×Q8—82no—
206C2×C7×Q8C2412yes—
207C2×C7×D4—24no—
208C2×C7×D4—21no—
209C2×C7×D4—22no—
210C2×C7×D4—22no—
211C2×C7×D4—82no—
212C2×C7×D4C2412yes—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—24no—
219C22×C4×C7—82no—
220C22×C4×C7C2×D411yescharacteristic
221C22×C4×C7C2×D411yescharacteristic
222C22×C4×C7C2×D411yescharacteristic
223C22×C4×C7C2×D411yescharacteristic
224C22×C4×C7C2×D411yescharacteristic
225C22×C4×C7C2×D412yes—
226C22×C4×C7C2412yes—
227C22×C4×C7C2411yescharacteristic
228C22×Dic7—28no—
229C22×Dic7—24no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—21no—
234C2×Dic14—28no—
235C2×Dic14—216no—
236C2×Dic14—21no—
237C2×Dic14—21no—
238C2×Dic14—24no—
239C2×Dic14—22no—
240C2×Dic14—22no—
241C2×Dic14—28no—
242C2×Dic14—28no—
243C2×Dic14#4114yes—
244C2×Dic14#4114yes—
245C2×Dic14C2412yes—
246C2×Dic14C2412yes—
247C7×C4⋊C4—24no—
248C7×C4⋊C4—24no—
249C7×C4⋊C4—24no—
250C7×C4⋊C4—21no—
251C7×C4⋊C4—21no—
252C7×C4⋊C4C2×D414yes—
253C7×C4⋊C4C2×D414yes—
254C7×C4⋊C4C2412yes—
255C7×C4⋊C4C2412yes—
256C7×C22⋊C4—24no—
257C7×C22⋊C4—24no—
258C7×C22⋊C4—24no—
259C7×C22⋊C4—24no—
260C7×C22⋊C4—24no—
261C7×C22⋊C4C2×D414yes—
262C7×C22⋊C4C2×D414yes—
263C42×C7—24no—
264C42×C7C2×D412yes—
265C42×C7C2×D412yes—
266C42×C7C2412yes—
267C42×C7C2412yes—
268C22⋊Dic7—24no—
269#1144—28no—
270#1144—28no—
271#1142—28no—
272#1142—28no—
273C4⋊Dic7—21no—
274C4⋊Dic7—21no—
275C4⋊Dic7C2412yes—
276C4⋊Dic7C2412yes—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
281C4×Dic7—24no—
282C4×Dic7—24no—
283C4×Dic7—24no—
284C4×Dic7—24no—
285C4×Dic7—24no—
286C2×C7⋊C8—22no—
287C2×C7⋊C8—22no—
288C2×C7⋊C8—22no—
289C2×C7⋊C8—22no—
290C2×C7⋊C8C2412yes—
291C2×C7⋊C8C2412yes—
292C2×C7⋊C8C2412yes—
293C2×C7⋊C8C2412yes—
294C23×Q8—71no—
295C22×Q16—71no—
296C22×Q16—71no—
297C22×SD16—71no—
298C22×SD16—71no—
299#542—24no—
300#542C2×D718yes—
301C2×C4⋊Q8C2×D711yescharacteristic
302C2×#126—21no—
303C2×#124—21no—
304C2×#124C2×D711yescharacteristic
305C2×#123—21no—
306C2×C22⋊Q8—21no—
307C2×C22⋊Q8C2×D711yescharacteristic
308C2×#121C2×D711yescharacteristic
309#519—78no—
310#519—144no—
311C2×C4×Q8—71no—
312C2×C4×Q8—71no—
313C2×C4×Q8—71no—
314C2×C4×Q8—71no—
315C2×C4×Q8—141no—
316C2×C4×Q8—141no—
317C2×C4×Q8C2×D711yescharacteristic
318C2×C4×D4C2×D711yescharacteristic
319C2×#117—71no—
320C2×#117—141no—
321C2×#117—141no—
322C2×#117C2×D711yescharacteristic
323#485—78no—
324#482—78no—
325#477—78no—
326#475—78no—
327#464—78no—
328#464—78no—
329#451—78no—
330#448—78no—
331#441—78no—
332#440—78no—
333C4×Q16—78no—
334C4×SD16—78no—
335#433—78no—
336C2×#107—71no—
337C2×#107—71no—
338C2×#106—71no—
339C2×#106—71no—
340C2×C4⋊C8—71no—
341C2×C4⋊C8—71no—
342C2×#103—71no—
343C2×#103—71no—
344C2×#103—71no—
345C2×#103—71no—
346C2×#103—71no—
347C2×#103—71no—
348C2×#102—71no—
349C2×#102—71no—
350C2×C22⋊C8—71no—
351C2×C22⋊C8—71no—
352C2×#97—71no—
353C2×C4×C8—71no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—42no—
359C23×C7—42no—
360C23×C7—42no—
361C23×C7C22×D412yes—
362C23×C7C22×D411yescharacteristic
363C7×Q8—22no—
364C7×Q8—22no—
365C7×Q8—42no—
366C7×Q8—84no—
367C7×D4—22no—
368C7×D4—22no—
369C7×D4—42no—
370C7×D4—84no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—24no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—42no—
383C2×C4×C7—42no—
384C2×C4×C7—42no—
385C2×C4×C7—84no—
386C2×C4×C7C22×D412yes—
387C2×C4×C7C22×D412yes—
388C2×C4×C7C22×D412yes—
389C2×C4×C7C22×D412yes—
390C2×C4×C7C22×D412yes—
391C2×C4×C7C22×D411yescharacteristic
392C2×C4×C7C2×#4112yes—
393C2×C4×C7C2×#4112yes—
394C2×C4×C7C2511yescharacteristic
395C2×Dic7—216no—
396C2×Dic7—24no—
397C2×Dic7—24no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—42no—
403C2×Dic7—42no—
404Dic14—216no—
405Dic14—24no—
406Dic14—24no—
407Dic14—22no—
408Dic14—22no—
409Dic14C2×#4114yes—
410Dic14C2×#4114yes—
411C7⋊C8—22no—
412C7⋊C8—22no—
413C7⋊C8—22no—
414C7⋊C8—22no—
415C22×Q8—21no—
416C22×Q8—71no—
417C22×Q8—71no—
418C22×Q8—74no—
419C22×Q8—144no—
420C22×Q8—144no—
421C22×Q8—141no—
422C22×Q8—142no—
423C22×Q8C22×D711yescharacteristic
424C22×D4—21no—
425C22×D4C22×D711yescharacteristic
426C23×C4—21no—
427C23×C4—141no—
428C23×C4C22×D711yescharacteristic
429C2×Q16—74no—
430C2×Q16—74no—
431C2×Q16—144no—
432C2×Q16—144no—
433C2×SD16—74no—
434C2×SD16—74no—
435C2×SD16—144no—
436C2×SD16—144no—
437C22×C8—71no—
438C22×C8—71no—
439C22×C8—71no—
440C22×C8—71no—
441C4⋊Q8—22no—
442C4⋊Q8C22×D714yes—
443#126—28no—
444#124—28no—
445#124—22no—
446#124C22×D714yes—
447#123—28no—
448C22⋊Q8—22no—
449C22⋊Q8—28no—
450C22⋊Q8C22×D714yes—
451#121—22no—
452#121C22×D714yes—
453C4×Q8—22no—
454C4×Q8—74no—
455C4×Q8—74no—
456C4×Q8—74no—
457C4×Q8—74no—
458C4×Q8—148no—
459C4×Q8—148no—
460C4×Q8—142no—
461C4×Q8—142no—
462C4×Q8—142no—
463C4×Q8—142no—
464C4×Q8C22×D714yes—
465C4×D4—22no—
466C4×D4C22×D714yes—
467#117—74no—
468#117—142no—
469#117—148no—
470#117—148no—
471#117C22⋊D714yes—
472#117C22×D714yes—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—71no—
477C2×C4⋊C4—71no—
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×C4⋊C4C22×D711yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—141no—
492C2×C22⋊C4C22⋊D711yescharacteristic
493C2×C22⋊C4C22⋊D711yescharacteristic
494C2×C42—21no—
495C2×C42—141no—
496C2×C42—141no—
497C2×C42—141no—
498C2×C42—141no—
499C2×C42—141no—
500C2×C42C22×D711yescharacteristic
501C2×C42C22×D711yescharacteristic
502#107—74no—
503#107—74no—
504#106—74no—
505#106—74no—
506C4⋊C8—74no—
507C4⋊C8—74no—
508#103—74no—
509#103—74no—
510#103—74no—
511#103—74no—
512#103—74no—
513#103—74no—
514#102—74no—
515#102—74no—
516C22⋊C8—74no—
517C22⋊C8—74no—
518#97—74no—
519C4×C8—74no—
520C22×C7—22no—
521C22×C7—22no—
522C22×C7—22no—
523C22×C7—44no—
524C22×C7—42no—
525C22×C7—42no—
526C22×C7—42no—
527C22×C7—84no—
528C22×C7#52512yes—
529C22×C7#57712yes—
530C22×C7#57812yes—
531C22×C7C23×D411yescharacteristic
532C4×C7—22no—
533C4×C7—22no—
534C4×C7—22no—
535C4×C7—22no—
536C4×C7—22no—
537C4×C7—42no—
538C4×C7—42no—
539C4×C7—42no—
540C4×C7#52512yes—
541C4×C7C22×#4111yescharacteristic
542C4×C7C22×#4111yescharacteristic
543Dic7—24no—
544Dic7—24no—
545Dic7—42no—
546Dic7—42no—
547C24—21no—
548C24C2×C22⋊D711yescharacteristic
549C2×Q8—21no—
550C2×Q8—24no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—74no—
554C2×Q8—74no—
555C2×Q8—72no—
556C2×Q8—72no—
557C2×Q8—82no—
558C2×Q8—148no—
559C2×Q8—148no—
560C2×Q8—148no—
561C2×Q8—1416no—
562C2×Q8—142no—
563C2×Q8—142no—
564C2×Q8—144no—
565C2×Q8—141no—
566C2×Q8—141no—
567C2×Q8C23×D712yes—
568C2×D4—24no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—82no—
573C2×D4C23×D712yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—82no—
581C22×C4—148no—
582C22×C4—144no—
583C22×C4—141no—
584C22×C4—141no—
585C22×C4—141no—
586C22×C4—141no—
587C22×C4C2×C22⋊D712yes—
588C22×C4C2×C22⋊D711yescharacteristic
589C22×C4C2×C22⋊D711yescharacteristic
590C22×C4C2×C22⋊D711yescharacteristic
591C22×C4C2×C22⋊D711yescharacteristic
592C22×C4C2×C22⋊D711yescharacteristic
593C22×C4C23×D712yes—
594C22×C4C23×D711yescharacteristic
595Q16—148no—
596Q16—148no—
597SD16—148no—
598SD16—148no—
599C2×C8—72no—
600C2×C8—72no—
601C2×C8—72no—
602C2×C8—72no—
603C2×C8—142no—
604C2×C8—142no—
605C2×C8—142no—
606C2×C8—142no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—72no—
613C4⋊C4—72no—
614C4⋊C4—144no—
615C4⋊C4—144no—
616C4⋊C4—144no—
617C4⋊C4—144no—
618C4⋊C4—141no—
619C4⋊C4—141no—
620C4⋊C4C2×C22⋊D714yes—
621C4⋊C4C2×C22⋊D714yes—
622C4⋊C4C23×D712yes—
623C4⋊C4C23×D712yes—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—144no—
630C22⋊C4C2×C22⋊D714yes—
631C22⋊C4C2×C22⋊D714yes—
632C42—24no—
633C42—144no—
634C42—144no—
635C42—144no—
636C42—144no—
637C42—144no—
638C42C2×C22⋊D712yes—
639C42C2×C22⋊D712yes—
640C42C23×D712yes—
641C42C23×D712yes—
642C2×C7—42no—
643C2×C7—82no—
644C2×C7#312114yescomplemented
645C2×C7C2×#52511yescharacteristic
646C2×C7C2×#57711yescharacteristic
647C2×C7C2×#57811yescharacteristic
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23C22×C22⋊D712yes—
656C23C22×C22⋊D711yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—42no—
660Q8—74no—
661Q8—74no—
662Q8—84no—
663Q8—1416no—
664Q8—144no—
665Q8—144no—
666Q8—142no—
667Q8—142no—
668D4—22no—
669D4—22no—
670D4—42no—
671D4—84no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
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—84no—
687C2×C4—1416no—
688C2×C4—144no—
689C2×C4—144no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—142no—
693C2×C4—142no—
694C2×C4—282no—
695C2×C4—282no—
696C2×C4D7×#4112yes—
697C2×C4D7×#4112yes—
698C2×C4C22×C22⋊D712yes—
699C2×C4C22×C22⋊D712yes—
700C2×C4C22×C22⋊D712yes—
701C2×C4C22×C22⋊D712yes—
702C2×C4C22×C22⋊D712yes—
703C2×C4C22×C22⋊D711yescharacteristic
704C2×C4C24×D711yescharacteristic
705C8—142no—
706C8—142no—
707C8—142no—
708C8—142no—
709C7C2×#312111yescharacteristic, complemented, Sylow
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—84no—
718C22#9051912yes—
719C22#9052712yes—
720C22#9052912yes—
721C22C23×C22⋊D711yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—144no—
731C4—144no—
732C4—282no—
733C4—282no—
734C4#9051912yes—
735C4C2×D7×#4111yescharacteristic
736C4C2×D7×#4111yescharacteristic
737C2—42no—
738C2—82no—
739C2#1174091214yesdirect product factor
740C2C2×#9051911yescharacteristic
741C2C2×#9052711yescharacteristic
742C2C2×#9052911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#542C2
socleC23×C7C22×D4
prime radicalC2×C7×#121C22
hypercenterC2×#542D7
hypocenterC7C2×#3121
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
2. C2×#90207C2semidirect
3. #11740912C2direct (N × H)
4. C2×#89863C2semidirect
5. C2×#89866C2semidirect
6. C2×#89826C2semidirect
7. C2×#89826C2semidirect
8. C2×#89822C2semidirect
9. C2×#89817C2semidirect
12. C2×#89802C2semidirect
13. C2×C4×#1144C2semidirect
14. C2×C4×#1142C2semidirect
15. C2×#89790C2semidirect
16. C2×#89772C2semidirect
37. #90207C22semidirect
52. #89866C22semidirect
53. #89863C22semidirect
54. #89826C22semidirect
55. #89826C22semidirect
56. #89822C22semidirect
57. #89817C22semidirect
60. #89802C22semidirect
61. C4×#1144C22semidirect
62. #89790C22semidirect
63. C4×#1142C22semidirect
64. #89772C22semidirect
644. C2×C7#3121semidirect
709. C7C2×#3121semidirect
739. C2#11740912direct (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×#902072
#117409122
C2×#898632
C2×#898662
C2×#898262
C2×#898222
C2×#898172
C2×#898122
C2×#898072
C2×#898022
C2×C4×#11442
C2×C4×#11422
C2×#897902
C2×#897722
C2×#31217