Finite Group Databasebeta

← C2×#11740020 #14222059

Subgroups — C2×#11740020 #14222059

Order 1792.

2070 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×#520C211yesmaximal, characteristic
2C2×#90209C211yesmaximal, characteristic, complemented
3C2×#90011C211yesmaximal, characteristic
4C2×#90011C211yesmaximal, characteristic
5#11740020C2116yesmaximal, direct product factor
6C2×#89803C211yesmaximal, characteristic, complemented
7C2×#89794C211yesmaximal, characteristic, complemented
8C2×#89802C211yesmaximal, characteristic, complemented
9C2×C4×#1144C211yesmaximal, characteristic, complemented
10C2×#89791C211yesmaximal, characteristic, complemented
11C2×C4×#1142C211yesmaximal, characteristic, complemented
12C2×#89781C211yesmaximal, characteristic, complemented
13C2×#89790C211yesmaximal, characteristic, complemented
14C2×#89772C211yesmaximal, characteristic, complemented
15C2×#89742C211yesmaximal, characteristic, complemented
16C2×#89743C211yesmaximal, characteristic, complemented
17C22×C7×#41C2211yescharacteristic
18C7×#520—24no—
19C7×#520C2218yes—
20C2×C4×C7×Q8C2211yescharacteristic
21C2×C4×C7×Q8C2211yescharacteristic
22C2×C4×C7×D4—21no—
23C2×C4×C7×D4—21no—
24C2×C4×C7×D4C2211yescharacteristic
25C2×C4×C7×D4C2211yescharacteristic
26C2×C7×#117—21no—
27C2×C7×#117C2211yescharacteristic
28C22×C7×C4⋊C4—21no—
29C22×C7×C4⋊C4C2211yescharacteristic
30C22×#1144C2211yescharacteristic
31C22×#1144C2211yescharacteristic
32C22×#1142C2211yescharacteristic
33C22×#1142C2211yescharacteristic
34C2×#6487C2211yescharacteristic
35C2×#6487C2211yescharacteristic
36#90209—24no—
37#90209C2218yescomplemented
38C2×#6452—21no—
39C2×#6452—21no—
40C2×#6442—21no—
41C2×#6442—21no—
42C2×#6433C2211yescharacteristic
43C2×#6432C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C2×C4×Dic14C2211yescharacteristic
46#90011C2218yes—
47#90011C2218yes—
48C2×#6409C2211yescharacteristic
49C2×#6409C2211yescharacteristic
50C2×#6406C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52C2×C22⋊(C7⋊C8)C2211yescharacteristic
53C2×C22⋊(C7⋊C8)C2211yescharacteristic
54#89803C2218yescomplemented
55#89802C2218yescomplemented
56C4×#1144C2218yescomplemented
57#89794C2218yescomplemented
58#89791C2218yescomplemented
59#89790C2218yescomplemented
60C4×#1142C2218yescomplemented
61#89781C2218yescomplemented
62#89772C2218yescomplemented
63#89743C2218yescomplemented
64#89742C2218yescomplemented
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×#3120—71nomaximal, Sylow
78C2×C7×#41—24no—
79C2×C7×#41—24no—
80C2×C7×#41—22no—
81C2×C7×#41C2314yes—
82C22×C7×Q8C2311yescharacteristic
83C22×C7×D4—21no—
84C22×C7×D4C2311yescharacteristic
85C23×C4×C7—21no—
86C23×C4×C7—21no—
87C23×C4×C7—21no—
88C23×C4×C7—21no—
89C23×C4×C7C2311yescharacteristic
90C22×Dic14C2311yescharacteristic
91C22×Dic14C2311yescharacteristic
92C4×C7×Q8—22no—
93C4×C7×Q8—22no—
94C4×C7×Q8C2314yes—
95C4×C7×Q8C2314yes—
96C4×C7×D4—28no—
97C4×C7×D4—28no—
98C4×C7×D4—22no—
99C4×C7×D4—22no—
100C4×C7×D4C2314yes—
101C4×C7×D4C2314yes—
102C7×#117—28no—
103C7×#117D414yes—
104C7×#117C2314yes—
105C2×C7×C4⋊C4—21no—
106C2×C7×C4⋊C4—21no—
107C2×C7×C4⋊C4—21no—
108C2×C7×C4⋊C4—22no—
109C2×C7×C4⋊C4—28no—
110C2×C7×C4⋊C4D411yescharacteristic
111C2×C7×C4⋊C4D411yescharacteristic
112C2×C7×C4⋊C4C2311yescharacteristic
113C2×C7×C4⋊C4C2311yescharacteristic
114C2×C7×C4⋊C4C2314yes—
115C2×C7×C22⋊C4—21no—
116C2×C7×C22⋊C4—21no—
117C2×C7×C22⋊C4D411yescharacteristic
118C2×C7×C22⋊C4D411yescharacteristic
119C2×C42×C7—21no—
120C2×C42×C7—21no—
121C2×C42×C7C2311yescharacteristic
122C2×C42×C7C2311yescharacteristic
123C2×C22⋊Dic7—21no—
124C2×C22⋊Dic7—21no—
125C2×#1144—24no—
126C2×#1144—24no—
127C2×#1144C2314yes—
128C2×#1144C2314yes—
129C2×#1142—24no—
130C2×#1142—24no—
131C2×#1142C2314yes—
132C2×#1142C2314yes—
133C2×C4⋊Dic7—21no—
134C2×C4⋊Dic7—21no—
135C2×C4⋊Dic7C2311yescharacteristic
136C2×C4⋊Dic7C2311yescharacteristic
137#6487—22no—
138#6487—22no—
139#6487C2314yes—
140#6487C2314yes—
141C2×Dic7⋊C4—21no—
142C2×Dic7⋊C4—21no—
143C2×Dic7⋊C4—21no—
144C2×Dic7⋊C4—21no—
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#6452—28no—
154#6452—28no—
155#6442—28no—
156#6442—28no—
157#6433—22no—
158#6433C2314yes—
159#6432—22no—
160#6432C2314yes—
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#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×#541—71no—
184C2×#520D711yescharacteristic
185#3120—716no—
186C2×#484—71no—
187C2×#483—71no—
188C2×#479—71no—
189C2×#478—71no—
190C2×#462—71no—
191C2×#461—71no—
192C2×#452—71no—
193C2×#452—71no—
194C2×#441—71no—
195C2×#440—71no—
196C2×C4×Q16—71no—
197C2×C4×SD16—71no—
198C2×#433—71no—
199C24×C7—21no—
200C24×C7C2×D411yescharacteristic
201C7×#41—216no—
202C7×#41—28no—
203C7×#41—28no—
204C2×C7×Q8—21no—
205C2×C7×Q8—22no—
206C2×C7×Q8#4114yes—
207C2×C7×Q8C2412yes—
208C2×C7×D4—28no—
209C2×C7×D4—24no—
210C2×C7×D4—21no—
211C2×C7×D4—22no—
212C2×C7×D4#4114yes—
213C2×C7×D4C2412yes—
214C22×C4×C7—28no—
215C22×C4×C7—21no—
216C22×C4×C7—24no—
217C22×C4×C7—22no—
218C22×C4×C7—22no—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7—24no—
222C22×C4×C7—24no—
223C22×C4×C7—24no—
224C22×C4×C7—82no—
225C22×C4×C7—82no—
226C22×C4×C7—82no—
227C22×C4×C7C2×D411yescharacteristic
228C22×C4×C7C2×D411yescharacteristic
229C22×C4×C7C2×D411yescharacteristic
230C22×C4×C7C2×D411yescharacteristic
231C22×C4×C7C2×D411yescharacteristic
232C22×C4×C7C2×D412yes—
233C22×C4×C7C2412yes—
234C22×C4×C7C2411yescharacteristic
235C22×Dic7—21no—
236C22×Dic7—21no—
237C22×Dic7—21no—
238C22×Dic7—21no—
239C2×Dic14—22no—
240C2×Dic14—22no—
241C2×Dic14—22no—
242C2×Dic14—22no—
243C2×Dic14—21no—
244C2×Dic14—21no—
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⋊C4C2×D414yes—
259C7×C22⋊C4C2×D414yes—
260C42×C7—24no—
261C42×C7—24no—
262C42×C7C2×D412yes—
263C42×C7C2×D412yes—
264C42×C7C2412yes—
265C42×C7C2412yes—
266C22⋊Dic7—24no—
267C22⋊Dic7—24no—
268#1144—28no—
269#1144—28no—
270#1142—28no—
271#1142—28no—
272C4⋊Dic7—21no—
273C4⋊Dic7—21no—
274C4⋊Dic7—24no—
275C4⋊Dic7—24no—
276C4⋊Dic7C2412yes—
277C4⋊Dic7C2412yes—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282Dic7⋊C4—24no—
283Dic7⋊C4—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—
294C22×#41C2×D711yescharacteristic
295C22×Q16—71no—
296C22×Q16—71no—
297C22×SD16—71no—
298C22×SD16—71no—
299#541—78no—
300#541—144no—
301C2×C4⋊Q8—71no—
302C2×#126—141no—
303C2×#126—141no—
304C2×#125—71no—
305C2×#125—141no—
306C2×#125—141no—
307C2×C22⋊Q8—71no—
308C2×C22⋊Q8—71no—
309#520—24no—
310#520C2×D718yes—
311C2×C4×Q8—71no—
312C2×C4×Q8—71no—
313C2×C4×Q8C2×D711yescharacteristic
314C2×C4×Q8C2×D711yescharacteristic
315C2×C4×D4—21no—
316C2×C4×D4—21no—
317C2×C4×D4C2×D711yescharacteristic
318C2×C4×D4C2×D711yescharacteristic
319C2×#117—21no—
320C2×#117C2×D711yescharacteristic
321C22×C4⋊C4—21no—
322C22×C4⋊C4C2×D711yescharacteristic
323#484—78no—
324#483—78no—
325#479—78no—
326#478—78no—
327#462—78no—
328#461—78no—
329#452—78no—
330#452—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—24no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—42no—
360C23×C7—42no—
361C23×C7C22×D412yes—
362C23×C7C22×D411yescharacteristic
363C7×Q8—24no—
364C7×Q8—22no—
365C7×Q8C2×#4114yes—
366C7×D4—216no—
367C7×D4—24no—
368C7×D4—22no—
369C7×D4C2×#4114yes—
370C2×C4×C7—216no—
371C2×C4×C7—22no—
372C2×C4×C7—24no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—24no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—42no—
384C2×C4×C7—42no—
385C2×C4×C7—84no—
386C2×C4×C7—84no—
387C2×C4×C7—84no—
388C2×C4×C7C22×D412yes—
389C2×C4×C7C22×D412yes—
390C2×C4×C7C22×D412yes—
391C2×C4×C7C22×D412yes—
392C2×C4×C7C22×D412yes—
393C2×C4×C7C22×D411yescharacteristic
394C2×C4×C7C2×#4112yes—
395C2×C4×C7C2×#4112yes—
396C2×C4×C7C2511yescharacteristic
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—42no—
402C2×Dic7—42no—
403C2×Dic7—42no—
404C2×Dic7—42no—
405Dic14—22no—
406Dic14—22no—
407Dic14—22no—
408Dic14—22no—
409Dic14—42no—
410Dic14—42no—
411C7⋊C8—22no—
412C7⋊C8—22no—
413C7⋊C8—22no—
414C7⋊C8—22no—
415C2×#41—24no—
416C2×#41—24no—
417C2×#41—22no—
418C2×#41C22×D714yes—
419C22×Q8—71no—
420C22×Q8—71no—
421C22×Q8C22×D711yescharacteristic
422C22×D4—21no—
423C22×D4C22×D711yescharacteristic
424C23×C4—21no—
425C23×C4—21no—
426C23×C4—21no—
427C23×C4—21no—
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—74no—
442C4⋊Q8—142no—
443#126—148no—
444#126—148no—
445#125—74no—
446#125—148no—
447#125—148no—
448#125—142no—
449C22⋊Q8—74no—
450C22⋊Q8—74no—
451C22⋊Q8—142no—
452C22⋊Q8—142no—
453C4×Q8—22no—
454C4×Q8—22no—
455C4×Q8—74no—
456C4×Q8—74no—
457C4×Q8—142no—
458C4×Q8—142no—
459C4×Q8C22×D714yes—
460C4×Q8C22×D714yes—
461C4×D4—28no—
462C4×D4—28no—
463C4×D4—22no—
464C4×D4—22no—
465C4×D4C22×D714yes—
466C4×D4C22×D714yes—
467#117—28no—
468#117C22⋊D714yes—
469#117C22×D714yes—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—28no—
475C2×C4⋊C4—71no—
476C2×C4⋊C4—71no—
477C2×C4⋊C4—141no—
478C2×C4⋊C4—141no—
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⋊C4C22⋊D711yescharacteristic
486C2×C4⋊C4C22⋊D711yescharacteristic
487C2×C4⋊C4C22×D711yescharacteristic
488C2×C4⋊C4C22×D711yescharacteristic
489C2×C4⋊C4C22×D714yes—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—141no—
493C2×C22⋊C4—141no—
494C2×C22⋊C4C22⋊D711yescharacteristic
495C2×C22⋊C4C22⋊D711yescharacteristic
496C2×C42—21no—
497C2×C42—21no—
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—24no—
522C22×C7—22no—
523C22×C7—22no—
524C22×C7—44no—
525C22×C7—48no—
526C22×C7—42no—
527C22×C7—42no—
528C22×C7#52512yes—
529C22×C7#57712yes—
530C22×C7#57812yes—
531C22×C7C23×D411yescharacteristic
532C4×C7—22no—
533C4×C7—24no—
534C4×C7—22no—
535C4×C7—22no—
536C4×C7—22no—
537C4×C7—22no—
538C4×C7—42no—
539C4×C7—42no—
540C4×C7#52512yes—
541C4×C7C22×#4111yescharacteristic
542C4×C7C22×#4111yescharacteristic
543Dic7—42no—
544Dic7—42no—
545Dic7—42no—
546Dic7—42no—
547C24—21no—
548C24C2×C22⋊D711yescharacteristic
549#41—216no—
550#41—28no—
551#41—28no—
552C2×Q8—22no—
553C2×Q8—21no—
554C2×Q8—72no—
555C2×Q8—72no—
556C2×Q8—141no—
557C2×Q8—141no—
558C2×Q8—142no—
559C2×Q8—142no—
560C2×Q8—142no—
561C2×Q8—142no—
562C2×Q8#115714yes—
563C2×Q8C23×D712yes—
564C2×D4—28no—
565C2×D4—24no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4#115714yes—
569C2×D4C23×D712yes—
570C22×C4—28no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—82no—
581C22×C4—82no—
582C22×C4—82no—
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—144no—
619C4⋊C4—144no—
620C4⋊C4—141no—
621C4⋊C4—141no—
622C4⋊C4—144no—
623C4⋊C4—144no—
624C4⋊C4C2×C22⋊D714yes—
625C4⋊C4C2×C22⋊D714yes—
626C4⋊C4C23×D712yes—
627C4⋊C4C23×D712yes—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—144no—
631C22⋊C4—144no—
632C22⋊C4C2×C22⋊D714yes—
633C22⋊C4C2×C22⋊D714yes—
634C42—24no—
635C42—24no—
636C42—144no—
637C42—144no—
638C42C2×C22⋊D712yes—
639C42C2×C22⋊D712yes—
640C42C23×D712yes—
641C42C23×D712yes—
642C2×C7—42no—
643C2×C7—44no—
644C2×C7#312014yescomplemented
645C2×C7C2×#52511yescharacteristic
646C2×C7C2×#57711yescharacteristic
647C2×C7C2×#57811yescharacteristic
648C23—22no—
649C23—24no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—42no—
654C23—42no—
655C23C22×C22⋊D712yes—
656C23C22×C22⋊D711yescharacteristic
657Q8—24no—
658Q8—22no—
659Q8—142no—
660Q8—142no—
661Q8—142no—
662Q8—142no—
663Q8—282no—
664Q8—282no—
665Q8C2×#115714yes—
666D4—216no—
667D4—24no—
668D4—22no—
669D4C2×#115714yes—
670C2×C4—216no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—84no—
686C2×C4—84no—
687C2×C4—84no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—282no—
693C2×C4—282no—
694C2×C4—282no—
695C2×C4—282no—
696C2×C4C2×#115712yes—
697C2×C4C2×#115712yes—
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×#312011yescharacteristic, complemented, Sylow
710C22—22no—
711C22—24no—
712C22—22no—
713C22—22no—
714C22—42no—
715C22—42no—
716C22—44no—
717C22—48no—
718C22#9048212yes—
719C22#9052712yes—
720C22#9052912yes—
721C22C23×C22⋊D711yescharacteristic
722C4—22no—
723C4—24no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—282no—
731C4—282no—
732C4—282no—
733C4—282no—
734C4#9048212yes—
735C4C22×#115711yescharacteristic
736C4C22×#115711yescharacteristic
737C2—42no—
738C2—44no—
739C2#1174002014yesdirect product factor
740C2C2×#9048211yescharacteristic
741C2C2×#9052711yescharacteristic
742C2C2×#9052911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#520C2
socleC23×C7C22×D4
prime radicalC22×C7×#41C22
hypercenterC2×#520D7
hypocenterC7C2×#3120
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
2. C2×#90209C2semidirect
5. #11740020C2direct (N × H)
6. C2×#89803C2semidirect
7. C2×#89794C2semidirect
8. C2×#89802C2semidirect
9. C2×C4×#1144C2semidirect
10. C2×#89791C2semidirect
11. C2×C4×#1142C2semidirect
12. C2×#89781C2semidirect
13. C2×#89790C2semidirect
14. C2×#89772C2semidirect
15. C2×#89742C2semidirect
16. C2×#89743C2semidirect
37. #90209C22semidirect
54. #89803C22semidirect
55. #89802C22semidirect
56. C4×#1144C22semidirect
57. #89794C22semidirect
58. #89791C22semidirect
59. #89790C22semidirect
60. C4×#1142C22semidirect
61. #89781C22semidirect
62. #89772C22semidirect
63. #89743C22semidirect
64. #89742C22semidirect
644. C2×C7#3120semidirect
709. C7C2×#3120semidirect
739. C2#11740020direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5202
C2×#902092
C2×#900112
#117400202
C2×#898032
C2×#897942
C2×#898022
C2×C4×#11442
C2×#897912
C2×C4×#11422
C2×#897812
C2×#897902
C2×#897722
C2×#897422
C2×#897432
C2×#31207