Finite Group Databasebeta

← #13406902

Subgroups — #13406902

Order 1792.

1124 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#554C211yesmaximal, characteristic
2C2×#89824C211yesmaximal, characteristic, complemented
3#11739796C211yesmaximal, characteristic
4C2×#89743C211yesmaximal, characteristic, complemented
5#11729548C211yesmaximal, characteristic, complemented
6#11729537C211yesmaximal, characteristic, complemented
7#11729454C211yesmaximal, characteristic, complemented
8#11729448C211yesmaximal, characteristic, complemented
9#11729447C211yesmaximal, characteristic, complemented
10#11729386C211yesmaximal, characteristic, complemented
11#11729383C211yesmaximal, characteristic, complemented
12#11729365C211yesmaximal, characteristic
13#11729313C211yesmaximal, characteristic, complemented
14#11729312C211yesmaximal, characteristic, complemented
15#11729310C211yesmaximal, characteristic, complemented
16C7×#554—24no—
17C7×#554—24no—
18C2×C7×C4⋊Q8C2211yescharacteristic
19C2×C7×#125—21no—
20C2×C7×C22⋊Q8—21no—
21C2×C7×C22⋊Q8—21no—
22C2×C7×C22⋊Q8C2211yescharacteristic
23C2×C7×C22⋊Q8C2211yescharacteristic
24C2×C4×C7×Q8C2211yescharacteristic
25C2×C4×C7×D4—21no—
26C2×C4×C7×D4C2211yescharacteristic
27C22×C7×C4⋊C4C2211yescharacteristic
28C22×C7×C4⋊C4C2211yescharacteristic
29C22×#1144C2211yescharacteristic
30C2×#6489C2211yescharacteristic
31C2×#6487C2211yescharacteristic
32C2×#6487C2211yescharacteristic
33C22×#1136C2211yescharacteristic
34C2×#6409C2211yescharacteristic
35C2×#6409C2211yescharacteristic
36C2×#6409C2211yescharacteristic
37#89994—21no—
38#89984C2211yescharacteristic
39C2×C22⋊(C7⋊C8)C2211yescharacteristic
40C2×C22⋊(C7⋊C8)C2211yescharacteristic
41C2×C22⋊(C7⋊C8)C2211yescharacteristic
42#89824—24no—
43#89744—21no—
44#89743—24no—
45C2×#6384C2211yescharacteristic
46C2×#6384C2211yescharacteristic
47C2×#6384C2211yescharacteristic
48C2×#6382C2211yescharacteristic
49C2×#6382C2211yescharacteristic
50C2×#6382C2211yescharacteristic
51#89724—21no—
52#89717—21no—
53#89701C2211yescharacteristic
54#89700C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#89319C2211yescharacteristic
62#89319C2211yescharacteristic
63#25561—71nomaximal, Sylow
64C22×C7×Q8—21no—
65C22×C7×Q8C2311yescharacteristic
66C22×C7×D4D411yescharacteristic
67C23×C4×C7—21no—
68C23×C4×C7—21no—
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C22×Dic14C2311yescharacteristic
72C7×C4⋊Q8—22no—
73C7×C4⋊Q8—22no—
74C7×#125—28no—
75C7×C22⋊Q8—28no—
76C7×C22⋊Q8—28no—
77C7×C22⋊Q8—22no—
78C7×C22⋊Q8—22no—
79C7×C22⋊Q8—22no—
80C7×C22⋊Q8D414yes—
81C4×C7×Q8—22no—
82C4×C7×Q8—22no—
83C4×C7×D4—28no—
84C4×C7×D4—22no—
85C4×C7×D4—22no—
86C2×C7×C4⋊C4—21no—
87C2×C7×C4⋊C4—21no—
88C2×C7×C4⋊C4—22no—
89C2×C7×C4⋊C4—21no—
90C2×C7×C4⋊C4—21no—
91C2×C7×C4⋊C4—21no—
92C2×C7×C4⋊C4—21no—
93C2×C7×C4⋊C4—22no—
94C2×C7×C4⋊C4—22no—
95C2×C7×C4⋊C4D411yescharacteristic
96C2×C7×C4⋊C4D414yes—
97C2×C7×C4⋊C4C2311yescharacteristic
98C2×C7×C4⋊C4C2311yescharacteristic
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C7×C22⋊C4—21no—
101C2×C7×C22⋊C4—21no—
102C2×C7×C22⋊C4D411yescharacteristic
103C2×C7×C22⋊C4D411yescharacteristic
104C2×C42×C7—21no—
105C2×C42×C7C2311yescharacteristic
106C2×C22⋊Dic7—21no—
107C2×C22⋊Dic7—21no—
108C2×C22⋊Dic7—21no—
109C2×C22⋊Dic7—21no—
110C2×#1144—22no—
111C2×#1144—22no—
112C2×#1144—41no—
113#6489—22no—
114#6489—41no—
115C2×C4⋊Dic7C2311yescharacteristic
116C2×C4⋊Dic7C2311yescharacteristic
117C2×C4⋊Dic7C2311yescharacteristic
118#6487—22no—
119#6487—22no—
120#6487—22no—
121#6487—41no—
122C2×Dic7⋊C4—21no—
123C2×Dic7⋊C4—21no—
124C2×Dic7⋊C4—21no—
125C2×C4×Dic7—21no—
126C2×#1136—22no—
127C2×#1136—22no—
128C2×#1136—41no—
129C22×C7⋊C8C2311yescharacteristic
130C22×C7⋊C8C2311yescharacteristic
131C22×C7⋊C8C2311yescharacteristic
132C22×C7⋊C8C2311yescharacteristic
133#6409—22no—
134#6409—22no—
135#6409—41no—
136C7⋊#95—21no—
137C7⋊#95—21no—
138C7⋊#95—21no—
139C7⋊#95—21no—
140C22⋊(C7⋊C8)—22no—
141C22⋊(C7⋊C8)—22no—
142C22⋊(C7⋊C8)—41no—
143#6384—22no—
144#6384—22no—
145#6384—22no—
146#6382—22no—
147#6382—22no—
148#6382—22no—
149C2×#554D711yescharacteristic
150C2×#483—71no—
151C2×#470—71no—
152#2415—71no—
153#2058—71no—
154#2035—71no—
155#2024—71no—
156#2001—71no—
157#1878—71no—
158#1873—71no—
159#1872—71no—
160#1870—71no—
161#1865—71no—
162#1853—71no—
163#1736—71no—
164C24×C7C2×D411yescharacteristic
165C24×C7C2×D411yescharacteristic
166C2×C7×Q8—24no—
167C2×C7×Q8—21no—
168C2×C7×Q8—21no—
169C2×C7×Q8—21no—
170C2×C7×Q8—21no—
171C2×C7×Q8—21no—
172C2×C7×Q8—81no—
173C2×C7×Q8—81no—
174C2×C7×Q8C2×D412yes—
175C2×C7×D4—22no—
176C2×C7×D4—22no—
177C2×C7×D4—22no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—24no—
187C22×C4×C7—24no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—81no—
195C22×C4×C7—81no—
196C22×C4×C7—81no—
197C22×C4×C7—81no—
198C22×C4×C7C2×D411yescharacteristic
199C22×C4×C7C2×D411yescharacteristic
200C22×C4×C7C2×D411yescharacteristic
201C22×C4×C7C2×D412yes—
202C22×C4×C7C2×D412yes—
203C22×C4×C7C2×D411yescharacteristic
204C22×C4×C7C2411yescharacteristic
205C22×Dic7—21no—
206C22×Dic7—21no—
207C22×Dic7—21no—
208C22×Dic7—21no—
209C2×Dic14—21no—
210C2×Dic14—21no—
211C2×Dic14—21no—
212C2×Dic14—21no—
213C2×Dic14—21no—
214C2×Dic14—21no—
215C7×C4⋊C4—24no—
216C7×C4⋊C4—24no—
217C7×C4⋊C4—24no—
218C7×C4⋊C4—24no—
219C7×C4⋊C4—24no—
220C7×C4⋊C4—24no—
221C7×C4⋊C4—22no—
222C7×C4⋊C4—21no—
223C7×C4⋊C4—21no—
224C7×C4⋊C4—21no—
225C7×C4⋊C4C2×D412yes—
226C7×C4⋊C4C2×D412yes—
227C7×C4⋊C4C2×D412yes—
228C7×C22⋊C4—24no—
229C7×C22⋊C4—24no—
230C7×C22⋊C4—22no—
231C7×C22⋊C4—22no—
232C42×C7—24no—
233C42×C7—21no—
234C42×C7—21no—
235C22⋊Dic7—42no—
236C22⋊Dic7—42no—
237C22⋊Dic7—42no—
238C22⋊Dic7—42no—
239#1144—44no—
240C4⋊Dic7—21no—
241C4⋊Dic7—21no—
242C4⋊Dic7—21no—
243C4⋊Dic7—21no—
244C4⋊Dic7—21no—
245C4⋊Dic7#4112yes—
246Dic7⋊C4—42no—
247Dic7⋊C4—42no—
248Dic7⋊C4—42no—
249C4×Dic7—42no—
250#1136—44no—
251C2×C7⋊C8—21no—
252C2×C7⋊C8—21no—
253C2×C7⋊C8—21no—
254C2×C7⋊C8—21no—
255C2×C7⋊C8—21no—
256C2×C7⋊C8—21no—
257C2×C7⋊C8—21no—
258C2×C7⋊C8—21no—
259C2×C7⋊C8—21no—
260C2×C7⋊C8—21no—
261C2×C7⋊C8—21no—
262C2×C7⋊C8#4112yes—
263C22×Q16—71no—
264C22×M16—71no—
265#554—24no—
266#554—24no—
267C2×C4⋊Q8C2×D711yescharacteristic
268C2×#125—21no—
269C2×C22⋊Q8—21no—
270C2×C22⋊Q8—21no—
271C2×C22⋊Q8—71no—
272C2×C22⋊Q8—71no—
273C2×C22⋊Q8C2×D711yescharacteristic
274C2×C22⋊Q8C2×D711yescharacteristic
275C2×C4×Q8C2×D711yescharacteristic
276C2×C4×D4—21no—
277C2×C4×D4C2×D711yescharacteristic
278C2×#117—71no—
279C22×C4⋊C4C2×D711yescharacteristic
280C22×C4⋊C4C2×D711yescharacteristic
281#483—144no—
282#470—144no—
283C2×#106—71no—
284C2×#106—71no—
285C2×#106—71no—
286C2×#103—71no—
287C2×#103—71no—
288C2×#103—71no—
289C2×#103—71no—
290C2×#103—71no—
291C2×#103—71no—
292C2×C22⋊C8—71no—
293C2×C22⋊C8—71no—
294C2×C22⋊C8—71no—
295#397—141no—
296#394—141no—
297#391—71no—
298#389—71no—
299#389—141no—
300#388—141no—
301#380—71no—
302#340—71no—
303#340—71no—
304#340—71no—
305#340—71no—
306#340—71no—
307#340—71no—
308#336—71no—
309#336—71no—
310C23×C7—21no—
311C23×C7—21no—
312C23×C7—21no—
313C23×C7—21no—
314C23×C7—21no—
315C23×C7—21no—
316C23×C7—21no—
317C23×C7—21no—
318C23×C7—21no—
319C23×C7—21no—
320C23×C7—21no—
321C23×C7—21no—
322C23×C7#12012yes—
323C23×C7#13712yes—
324C23×C7C22×D411yescharacteristic
325C7×Q8—22no—
326C7×Q8—22no—
327C7×Q8—41no—
328C7×Q8—41no—
329C7×Q8—84no—
330C7×D4—28no—
331C2×C4×C7—21no—
332C2×C4×C7—21no—
333C2×C4×C7—21no—
334C2×C4×C7—21no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—21no—
341C2×C4×C7—22no—
342C2×C4×C7—21no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—21no—
346C2×C4×C7—21no—
347C2×C4×C7—21no—
348C2×C4×C7—21no—
349C2×C4×C7—41no—
350C2×C4×C7—41no—
351C2×C4×C7—41no—
352C2×C4×C7—41no—
353C2×C4×C7—41no—
354C2×C4×C7—41no—
355C2×C4×C7—41no—
356C2×C4×C7—41no—
357C2×C4×C7—41no—
358C2×C4×C7—41no—
359C2×C4×C7—41no—
360C2×C4×C7—41no—
361C2×C4×C7—84no—
362C2×C4×C7—84no—
363C2×C4×C7#12012yes—
364C2×C4×C7#13712yes—
365C2×C4×C7C22×D411yescharacteristic
366C2×C4×C7C22×D411yescharacteristic
367C2×C4×C7C2×#4111yescharacteristic
368C2×C4×C7C2×#4111yescharacteristic
369C2×C4×C7H(5,𝔽2)11yescharacteristic
370C2×C4×C72−1+411yescharacteristic
371C2×Dic7—22no—
372C2×Dic7—41no—
373C2×Dic7—41no—
374C2×Dic7—41no—
375C2×Dic7—41no—
376C2×Dic7—41no—
377C2×Dic7—41no—
378C2×Dic7—41no—
379C2×Dic7—41no—
380C2×Dic7—41no—
381C2×Dic7—41no—
382C2×Dic7—41no—
383Dic14—41no—
384Dic14—41no—
385Dic14—41no—
386Dic14—41no—
387C7⋊C8—22no—
388C7⋊C8—41no—
389C7⋊C8—41no—
390C7⋊C8—41no—
391C22×Q8—21no—
392C22×Q8—71no—
393C22×Q8C22×D711yescharacteristic
394C22×D4C22⋊D711yescharacteristic
395C23×C4—21no—
396C23×C4—21no—
397C23×C4C22×D711yescharacteristic
398C23×C4C22×D711yescharacteristic
399C2×Q16—142no—
400C2×Q16—142no—
401C2×Q16—281no—
402C2×M16—142no—
403C2×M16—142no—
404C2×M16—281no—
405C22×C8—71no—
406C22×C8—71no—
407C22×C8—71no—
408C22×C8—71no—
409C4⋊Q8—22no—
410C4⋊Q8—22no—
411#125—28no—
412C22⋊Q8—28no—
413C22⋊Q8—28no—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—22no—
417C22⋊Q8—142no—
418C22⋊Q8—142no—
419C22⋊Q8—142no—
420C22⋊Q8—281no—
421C22⋊Q8C22⋊D714yes—
422C4×Q8—22no—
423C4×Q8—22no—
424C4×D4—28no—
425C4×D4—22no—
426C4×D4—22no—
427#117—142no—
428#117—281no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—71no—
439C2×C4⋊C4—71no—
440C2×C4⋊C4—71no—
441C2×C4⋊C4—141no—
442C2×C4⋊C4—141no—
443C2×C4⋊C4—141no—
444C2×C4⋊C4C22⋊D711yescharacteristic
445C2×C4⋊C4C22⋊D714yes—
446C2×C4⋊C4C22×D711yescharacteristic
447C2×C4⋊C4C22×D711yescharacteristic
448C2×C4⋊C4C22×D711yescharacteristic
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—141no—
452C2×C22⋊C4—141no—
453C2×C22⋊C4—141no—
454C2×C22⋊C4—141no—
455C2×C22⋊C4C22⋊D711yescharacteristic
456C2×C22⋊C4C22⋊D711yescharacteristic
457C2×C42—21no—
458C2×C42—141no—
459C2×C42C22×D711yescharacteristic
460#106—142no—
461#106—142no—
462#106—142no—
463#103—142no—
464#103—142no—
465#103—142no—
466#103—142no—
467#103—142no—
468#103—281no—
469C22⋊C8—142no—
470C22⋊C8—142no—
471C22⋊C8—281no—
472#95—141no—
473#95—141no—
474#95—141no—
475#95—141no—
476C22×C7—22no—
477C22×C7—22no—
478C22×C7—22no—
479C22×C7—22no—
480C22×C7—22no—
481C22×C7—22no—
482C22×C7—41no—
483C22×C7—41no—
484C22×C7—41no—
485C22×C7—41no—
486C22×C7—41no—
487C22×C7—41no—
488C22×C7—41no—
489C22×C7—41no—
490C22×C7C2×#12011yescharacteristic
491C22×C7#54611yescharacteristic
492C22×C7#54711yescharacteristic
493C22×C7C2×#13711yescharacteristic
494C22×C7C2×#13711yescharacteristic
495C22×C7#57711yescharacteristic
496C22×C7#57711yescharacteristic
497C4×C7—22no—
498C4×C7—22no—
499C4×C7—41no—
500C4×C7—42no—
501C4×C7—41no—
502C4×C7—42no—
503C4×C7—42no—
504C4×C7—42no—
505C4×C7#53211yescharacteristic
506C4×C7#53711yescharacteristic
507C4×C7#54611yescharacteristic
508C4×C7#54711yescharacteristic
509Dic7—42no—
510Dic7—81no—
511Dic7—81no—
512Dic7—81no—
513C24C2×C22⋊D711yescharacteristic
514C24C2×C22⋊D711yescharacteristic
515C2×Q8—24no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—81no—
522C2×Q8—81no—
523C2×Q8—141no—
524C2×Q8—141no—
525C2×Q8—141no—
526C2×Q8—141no—
527C2×Q8—141no—
528C2×Q8—141no—
529C2×Q8C2×C22⋊D712yes—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—81no—
550C22×C4—81no—
551C22×C4—81no—
552C22×C4—81no—
553C22×C4—141no—
554C22×C4—141no—
555C22×C4—141no—
556C22×C4—141no—
557C22×C4C2×C22⋊D711yescharacteristic
558C22×C4C2×C22⋊D711yescharacteristic
559C22×C4C2×C22⋊D711yescharacteristic
560C22×C4C2×C22⋊D711yescharacteristic
561C22×C4C2×C22⋊D712yes—
562C22×C4C2×C22⋊D712yes—
563C22×C4C23×D711yescharacteristic
564Q16—284no—
565M16—284no—
566C2×C8—72no—
567C2×C8—141no—
568C2×C8—141no—
569C2×C8—141no—
570C2×C8—141no—
571C2×C8—141no—
572C2×C8—141no—
573C2×C8—141no—
574C2×C8—141no—
575C2×C8—141no—
576C2×C8—141no—
577C2×C8—141no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—22no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—72no—
589C4⋊C4—141no—
590C4⋊C4—141no—
591C4⋊C4—141no—
592C4⋊C4—141no—
593C4⋊C4—141no—
594C4⋊C4—282no—
595C4⋊C4—282no—
596C4⋊C4—282no—
597C4⋊C4C2×C22⋊D712yes—
598C4⋊C4C2×C22⋊D712yes—
599C4⋊C4C2×C22⋊D712yes—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—282no—
605C22⋊C4—282no—
606C22⋊C4—282no—
607C22⋊C4—282no—
608C42—24no—
609C42—21no—
610C42—21no—
611C42—282no—
612C2×C7—42no—
613C2×C7—42no—
614C2×C7#243011yescharacteristic
615C2×C7#300411yescharacteristic
616C2×C7#300911yescharacteristic
617C2×C7#331611yescharacteristic
618C2×C7#333111yescharacteristic
619C2×C7#334411yescharacteristic
620C2×C7#335611yescharacteristic
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23#650512yes—
634C23#651612yes—
635C23C22×C22⋊D711yescharacteristic
636Q8—22no—
637Q8—22no—
638Q8—41no—
639Q8—41no—
640Q8—84no—
641Q8—281no—
642Q8—281no—
643Q8—281no—
644Q8—281no—
645D4—28no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—84no—
677C2×C4—84no—
678C2×C4—142no—
679C2×C4—281no—
680C2×C4—281no—
681C2×C4—281no—
682C2×C4—281no—
683C2×C4—281no—
684C2×C4—281no—
685C2×C4—281no—
686C2×C4—281no—
687C2×C4—281no—
688C2×C4—281no—
689C2×C4—281no—
690C2×C4#650512yes—
691C2×C4#651612yes—
692C2×C4D7×#4111yescharacteristic
693C2×C4D7×#4111yescharacteristic
694C2×C4#655311yescharacteristic
695C2×C4#655411yescharacteristic
696C2×C4C22×C22⋊D711yescharacteristic
697C2×C4C22×C22⋊D711yescharacteristic
698C8—142no—
699C8—281no—
700C8—281no—
701C8—281no—
702C7#2556111yescharacteristic, complemented, Sylow
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22C2×#650511yescharacteristic
718C22C2×#650511yescharacteristic
719C22#9051511yescharacteristic
720C22#9052011yescharacteristic
721C22#9052711yescharacteristic
722C22#9052711yescharacteristic
723C22C2×#651611yescharacteristic
724C4—22no—
725C4—22no—
726C4—41no—
727C4—42no—
728C4—41no—
729C4—42no—
730C4—42no—
731C4—42no—
732C4—282no—
733C4—561no—
734C4—561no—
735C4—561no—
736C4#9051511yescharacteristic
737C4#9052011yescharacteristic
738C4#9052311yescharacteristic
739C4#9052411yescharacteristic
740C2—42no—
741C2—42no—
742C2#1174106911yescharacteristic
743C2#1174107111yescharacteristic
744C2#1174108111yescharacteristic
745C2#1174108611yescharacteristic
746C2#1174150411yescharacteristic
747C2#1174153611yescharacteristic
748C2#1174155011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×#554C2
socleC23×C7C22×D4
prime radicalC22×C7×D4D4
hypercenterC2×#554D7
hypocenterC7#25561
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. C2×#89824C2semidirect
4. C2×#89743C2semidirect
5. #11729548C2semidirect
6. #11729537C2semidirect
7. #11729454C2semidirect
8. #11729448C2semidirect
9. #11729447C2semidirect
10. #11729386C2semidirect
11. #11729383C2semidirect
13. #11729313C2semidirect
14. #11729312C2semidirect
15. #11729310C2semidirect
702. C7#25561semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5542
C2×#898242
#117397962
C2×#897432
#117295482
#117295372
#117294542
#117294482
#117294472
#117293862
#117293832
#117293652
#117293132
#117293122
#117293102
#255617