Finite Group Databasebeta

← #13370189

Subgroups — #13370189

Order 1792.

1186 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×#553C211yesmaximal, characteristic
2#11739782C211yesmaximal, characteristic, complemented
3C2×#89783C211yesmaximal, characteristic, complemented
4#11729495C211yesmaximal, characteristic, complemented
5#11729492C211yesmaximal, characteristic, complemented
6#11729436C211yesmaximal, characteristic, complemented
7#11729435C211yesmaximal, characteristic, complemented
8#11729432C211yesmaximal, characteristic, complemented
9#11729432C211yesmaximal, characteristic, complemented
10#11729363C211yesmaximal, characteristic, complemented
11#11729358C211yesmaximal, characteristic, complemented
12#11729334C211yesmaximal, characteristic, complemented
13#11729329C211yesmaximal, characteristic, complemented
14#11729312C211yesmaximal, characteristic, complemented
15#11729307C211yesmaximal, characteristic, complemented
16C7×#553—24no—
17C7×#553C418yescomplemented
18C2×C7×#126—21no—
19C2×C7×#125C2211yescharacteristic
20C2×C7×#123—21no—
21C2×C7×#121—21no—
22C2×C7×#121C2211yescharacteristic
23C2×C7×#121C2211yescharacteristic
24C2×C4×C7×D4—21no—
25C2×C4×C7×D4C2211yescharacteristic
26C2×C4×C7×D4C2211yescharacteristic
27C2×C7×#117C2211yescharacteristic
28C22×C7×C4⋊C4C2211yescharacteristic
29C2×#6489C2211yescharacteristic
30C2×#6489C2211yescharacteristic
31C22×#1136C2211yescharacteristic
32C23×C7⋊C8C2211yescharacteristic
33#89993—21no—
34C2×#6406C2211yescharacteristic
35C2×#6406C2211yescharacteristic
36C2×#6406C2211yescharacteristic
37C2×#6406C2211yescharacteristic
38#89984C2211yescharacteristic
39#89984C2211yescharacteristic
40C2×C22⋊(C7⋊C8)C2211yescharacteristic
41C2×C22⋊(C7⋊C8)C2211yescharacteristic
42#89783—24no—
43C4⋊C4×Dic7—21no—
44#89723—21no—
45#89723—21no—
46#89707C2211yescharacteristic
47C4×C4⋊Dic7C2211yescharacteristic
48C2×C4⋊(C7⋊C8)C2211yescharacteristic
49C2×#6377C2211yescharacteristic
50#89324C2211yescharacteristic
51#89324C2211yescharacteristic
52#89324C2211yescharacteristic
53#89324C2211yescharacteristic
54#89324C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#22498—71nomaximal, Sylow
63C22×C7×D4—21no—
64C22×C7×D4—21no—
65C22×C7×D4D411yescharacteristic
66C22×C7×D4C2311yescharacteristic
67C23×C4×C7—21no—
68C23×C4×C7—21no—
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C7×#126—28no—
72C7×#125—22no—
73C7×#125C2×C414yes—
74C7×#123—28no—
75C7×#121—28no—
76C7×#121—22no—
77C7×#121—22no—
78C7×#121C2×C414yes—
79C7×#121C2×C414yes—
80C4×C7×D4—28no—
81C4×C7×D4—22no—
82C4×C7×D4C2×C414yes—
83C4×C7×D4C2×C414yes—
84C4×C7×D4D414yes—
85C7×#117—22no—
86C7×#117C2×C414yes—
87C2×C7×C4⋊C4—21no—
88C2×C7×C4⋊C4—22no—
89C2×C7×C4⋊C4—21no—
90C2×C7×C4⋊C4—21no—
91C2×C7×C4⋊C4C2×C414yes—
92C2×C7×C4⋊C4D411yescharacteristic
93C2×C7×C4⋊C4C2311yescharacteristic
94C2×C7×C4⋊C4C2311yescharacteristic
95C2×C7×C4⋊C4C2311yescharacteristic
96C2×C7×C22⋊C4—21no—
97C2×C7×C22⋊C4—21no—
98C2×C7×C22⋊C4—21no—
99C2×C7×C22⋊C4—21no—
100C2×C7×C22⋊C4D411yescharacteristic
101C2×C7×C22⋊C4D411yescharacteristic
102C2×C42×C7—21no—
103C2×C42×C7C2311yescharacteristic
104C2×C22⋊Dic7—21no—
105C2×C22⋊Dic7—21no—
106C2×C22⋊Dic7—21no—
107C2×C22⋊Dic7—21no—
108#6489—22no—
109#6489—22no—
110#6489—41no—
111#6489—41no—
112C2×C4⋊Dic7—21no—
113C2×C4⋊Dic7—21no—
114C2×C4⋊Dic7C2311yescharacteristic
115C2×C4⋊Dic7C2311yescharacteristic
116C2×C4⋊Dic7C2311yescharacteristic
117C2×C4⋊Dic7C2311yescharacteristic
118C2×C4×Dic7—21no—
119C2×C4×Dic7—21no—
120C2×C4×Dic7—21no—
121C2×#1136—22no—
122C2×#1136—22no—
123C2×#1136—41no—
124C22×C7⋊C8—22no—
125C22×C7⋊C8—22no—
126C22×C7⋊C8—41no—
127C22×C7⋊C8C2311yescharacteristic
128C22×C7⋊C8C2311yescharacteristic
129C22×C7⋊C8C2311yescharacteristic
130C22×C7⋊C8C2311yescharacteristic
131#6406—22no—
132#6406—22no—
133#6406—41no—
134#6406—41no—
135C7⋊#95—21no—
136C7⋊#95—21no—
137C7⋊#95—21no—
138C22⋊(C7⋊C8)—22no—
139C22⋊(C7⋊C8)—22no—
140C4⋊(C7⋊C8)—22no—
141#6377—22no—
142C2×#553D711yescharacteristic
143C2×#435—71no—
144#2354—71no—
145#1992—71no—
146#1989—71no—
147#1895—71no—
148#1893—71no—
149#1875—71no—
150#1875—71no—
151#1825—71no—
152#1823—71no—
153#1802—71no—
154#1762—71no—
155#1736—71no—
156#1735—71no—
157C24×C7—21no—
158C24×C7C2×D411yescharacteristic
159C24×C7C2×D411yescharacteristic
160C2×C7×D4—24no—
161C2×C7×D4—24no—
162C2×C7×D4—21no—
163C2×C7×D4—21no—
164C2×C7×D4—21no—
165C2×C7×D4—21no—
166C2×C7×D4—21no—
167C2×C7×D4—41no—
168C2×C7×D4—41no—
169C2×C7×D4—42no—
170C2×C7×D4—42no—
171C2×C7×D4—81no—
172C2×C7×D4—81no—
173C2×C7×D4C22⋊C414yes—
174C2×C7×D4C22×C412yes—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
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—81no—
189C22×C4×C7—81no—
190C22×C4×C7—81no—
191C22×C4×C7—81no—
192C22×C4×C7C22×C412yes—
193C22×C4×C7C22×C412yes—
194C22×C4×C7C2×D411yescharacteristic
195C22×C4×C7C2×D411yescharacteristic
196C22×C4×C7C2×D411yescharacteristic
197C22×C4×C7C2×D411yescharacteristic
198C22×C4×C7C2×D412yes—
199C22×C4×C7C2×D412yes—
200C22×C4×C7C2411yescharacteristic
201C22×Dic7—21no—
202C22×Dic7—21no—
203C22×Dic7—21no—
204C22×Dic7—21no—
205C7×C4⋊C4—24no—
206C7×C4⋊C4—24no—
207C7×C4⋊C4—24no—
208C7×C4⋊C4—21no—
209C7×C4⋊C4—21no—
210C7×C4⋊C4—21no—
211C7×C4⋊C4C22⋊C414yes—
212C7×C4⋊C4C22×C412yes—
213C7×C4⋊C4C22×C412yes—
214C7×C4⋊C4C22×C412yes—
215C7×C22⋊C4—24no—
216C7×C22⋊C4—24no—
217C7×C22⋊C4—24no—
218C7×C22⋊C4—24no—
219C7×C22⋊C4C22⋊C414yes—
220C7×C22⋊C4C22⋊C414yes—
221C42×C7—24no—
222C42×C7C22×C412yes—
223C42×C7C2×D412yes—
224C22⋊Dic7—42no—
225C22⋊Dic7—42no—
226C22⋊Dic7—81no—
227C22⋊Dic7—81no—
228C4⋊Dic7—21no—
229C4⋊Dic7—21no—
230C4⋊Dic7—21no—
231C4⋊Dic7—21no—
232C4⋊Dic7—21no—
233C4⋊Dic7—21no—
234C4⋊Dic7—21no—
235C4⋊Dic7—42no—
236C4⋊Dic7—81no—
237C4⋊Dic7#4112yes—
238C4×Dic7—42no—
239C4×Dic7—42no—
240C4×Dic7—42no—
241#1136—44no—
242C2×C7⋊C8—21no—
243C2×C7⋊C8—21no—
244C2×C7⋊C8—21no—
245C2×C7⋊C8—21no—
246C2×C7⋊C8—21no—
247C2×C7⋊C8—21no—
248C2×C7⋊C8—21no—
249C2×C7⋊C8—21no—
250C2×C7⋊C8—21no—
251C2×C7⋊C8—21no—
252C2×C7⋊C8—21no—
253C2×C7⋊C8—44no—
254C2×C7⋊C8#4112yes—
255C22×M16—71no—
256C23×C8—71no—
257#553—24no—
258#553Dic718yescomplemented
259C2×#126—21no—
260C2×#125C2×D711yescharacteristic
261C2×#123—21no—
262C2×#121—21no—
263C2×#121C2×D711yescharacteristic
264C2×#121C2×D711yescharacteristic
265C2×C4×D4—21no—
266C2×C4×D4C2×D711yescharacteristic
267C2×C4×D4C2×D711yescharacteristic
268C2×#117—71no—
269C2×#117—71no—
270C2×#117C2×D711yescharacteristic
271C22×C4⋊C4C2×D711yescharacteristic
272#435—144no—
273C2×C4⋊C8—71no—
274C2×#102—71no—
275C2×#102—71no—
276C2×#102—71no—
277C2×#102—71no—
278C2×C22⋊C8—71no—
279C2×C22⋊C8—71no—
280C2×#97—71no—
281#390—141no—
282#388—141no—
283#388—141no—
284#384—71no—
285#380—71no—
286#380—71no—
287C4×C4⋊C4—71no—
288C4×C4⋊C4—141no—
289#340—71no—
290#340—71no—
291#340—71no—
292#340—71no—
293#340—71no—
294#340—71no—
295#340—71no—
296#340—71no—
297#340—71no—
298#340—71no—
299#340—71no—
300#340—71no—
301C23×C7—21no—
302C23×C7—21no—
303C23×C7—21no—
304C23×C7—21no—
305C23×C7—21no—
306C23×C7—21no—
307C23×C7—21no—
308C23×C7—21no—
309C23×C7—21no—
310C23×C7—21no—
311C23×C7—21no—
312C23×C7—21no—
313C23×C7—22no—
314C23×C7—41no—
315C23×C7—41no—
316C23×C7—41no—
317C23×C7—41no—
318C23×C7—41no—
319C23×C7—41no—
320C23×C7C2×C22⋊C412yes—
321C23×C7C2×C22⋊C412yes—
322C23×C7C22×D411yescharacteristic
323C7×D4—22no—
324C7×D4—22no—
325C7×D4—44no—
326C7×D4—48no—
327C7×D4—41no—
328C7×D4—41no—
329C7×D4—84no—
330C2×C4×C7—21no—
331C2×C4×C7—21no—
332C2×C4×C7—21no—
333C2×C4×C7—21no—
334C2×C4×C7—21no—
335C2×C4×C7—21no—
336C2×C4×C7—21no—
337C2×C4×C7—21no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—22no—
342C2×C4×C7—22no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—22no—
348C2×C4×C7—22no—
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—84no—
356C2×C4×C7—84no—
357C2×C4×C7C2×C22⋊C412yes—
358C2×C4×C7C2×C22⋊C412yes—
359C2×C4×C7C2×C22⋊C412yes—
360C2×C4×C7C2×C22⋊C412yes—
361C2×C4×C7C23×C411yescharacteristic
362C2×C4×C7C22×D411yescharacteristic
363C2×C4×C7C2×#4111yescharacteristic
364C2×C4×C7C2×#4111yescharacteristic
365C2×C4×C7H(5,𝔽2)11yescharacteristic
366C2×C4×C72−1+411yescharacteristic
367C2×Dic7—22no—
368C2×Dic7—41no—
369C2×Dic7—41no—
370C2×Dic7—41no—
371C2×Dic7—41no—
372C2×Dic7—41no—
373C2×Dic7—41no—
374C2×Dic7—41no—
375C2×Dic7—41no—
376C2×Dic7—41no—
377C2×Dic7—41no—
378C2×Dic7—41no—
379C7⋊C8—22no—
380C7⋊C8—41no—
381C7⋊C8—41no—
382C7⋊C8—41no—
383C22×D4—21no—
384C22×D4—21no—
385C22×D4C22⋊D711yescharacteristic
386C22×D4C22×D711yescharacteristic
387C23×C4—21no—
388C23×C4—21no—
389C23×C4C22×D711yescharacteristic
390C23×C4C22×D711yescharacteristic
391C2×M16—142no—
392C2×M16—142no—
393C2×M16—281no—
394C22×C8—71no—
395C22×C8—71no—
396C22×C8—71no—
397C22×C8—71no—
398C22×C8—142no—
399C22×C8—142no—
400C22×C8—281no—
401#126—28no—
402#125—22no—
403#125C2×Dic714yes—
404#123—28no—
405#121—28no—
406#121—22no—
407#121—22no—
408#121C2×Dic714yes—
409#121C2×Dic714yes—
410C4×D4—28no—
411C4×D4—22no—
412C4×D4C2×Dic714yes—
413C4×D4C2×Dic714yes—
414C4×D4C22⋊D714yes—
415#117—22no—
416#117—142no—
417#117—142no—
418#117—281no—
419#117—281no—
420#117C2×Dic714yes—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—71no—
426C2×C4⋊C4—71no—
427C2×C4⋊C4—71no—
428C2×C4⋊C4—71no—
429C2×C4⋊C4—141no—
430C2×C4⋊C4—141no—
431C2×C4⋊C4C2×Dic714yes—
432C2×C4⋊C4C22⋊D711yescharacteristic
433C2×C4⋊C4C22×D711yescharacteristic
434C2×C4⋊C4C22×D711yescharacteristic
435C2×C4⋊C4C22×D711yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—141no—
441C2×C22⋊C4—141no—
442C2×C22⋊C4—141no—
443C2×C22⋊C4—141no—
444C2×C22⋊C4C22⋊D711yescharacteristic
445C2×C22⋊C4C22⋊D711yescharacteristic
446C2×C42—21no—
447C2×C42—141no—
448C2×C42—141no—
449C2×C42—141no—
450C2×C42C22×D711yescharacteristic
451C4⋊C8—142no—
452#102—142no—
453#102—142no—
454#102—281no—
455#102—281no—
456C22⋊C8—142no—
457C22⋊C8—142no—
458#97—142no—
459#95—141no—
460#95—141no—
461#95—141no—
462C22×C7—22no—
463C22×C7—22no—
464C22×C7—22no—
465C22×C7—22no—
466C22×C7—22no—
467C22×C7—22no—
468C22×C7—41no—
469C22×C7—41no—
470C22×C7—41no—
471C22×C7—41no—
472C22×C7—41no—
473C22×C7—41no—
474C22×C7—41no—
475C22×C7—41no—
476C22×C7—42no—
477C22×C7—42no—
478C22×C7—42no—
479C22×C7—81no—
480C22×C7—81no—
481C22×C7—81no—
482C22×C7—81no—
483C22×C7C22×C22⋊C411yescharacteristic
484C22×C7#54611yescharacteristic
485C22×C7#54711yescharacteristic
486C22×C7#57511yescharacteristic
487C22×C7#57511yescharacteristic
488C22×C7#57611yescharacteristic
489C22×C7#57711yescharacteristic
490C4×C7—22no—
491C4×C7—22no—
492C4×C7—22no—
493C4×C7—22no—
494C4×C7—42no—
495C4×C7—42no—
496C4×C7—42no—
497C4×C7C4×#4111yescharacteristic
498C4×C7#52011yescharacteristic
499C4×C7#54611yescharacteristic
500C4×C7#54711yescharacteristic
501Dic7—42no—
502Dic7—81no—
503Dic7—81no—
504Dic7—81no—
505C24—21no—
506C24C2×C22⋊D711yescharacteristic
507C24C2×C22⋊D711yescharacteristic
508C2×D4—24no—
509C2×D4—24no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—41no—
516C2×D4—41no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—81no—
520C2×D4—81no—
521C2×D4C22⋊Dic714yes—
522C2×D4C22×Dic712yes—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—81no—
537C22×C4—81no—
538C22×C4—81no—
539C22×C4—81no—
540C22×C4—141no—
541C22×C4—141no—
542C22×C4—141no—
543C22×C4—141no—
544C22×C4C22×Dic712yes—
545C22×C4C22×Dic712yes—
546C22×C4C2×C22⋊D711yescharacteristic
547C22×C4C2×C22⋊D711yescharacteristic
548C22×C4C2×C22⋊D711yescharacteristic
549C22×C4C2×C22⋊D711yescharacteristic
550C22×C4C2×C22⋊D712yes—
551C22×C4C2×C22⋊D712yes—
552C22×C4C23×D711yescharacteristic
553M16—284no—
554C2×C8—72no—
555C2×C8—141no—
556C2×C8—141no—
557C2×C8—141no—
558C2×C8—141no—
559C2×C8—141no—
560C2×C8—141no—
561C2×C8—141no—
562C2×C8—141no—
563C2×C8—141no—
564C2×C8—141no—
565C2×C8—141no—
566C2×C8—284no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—72no—
574C4⋊C4—141no—
575C4⋊C4—141no—
576C4⋊C4—141no—
577C4⋊C4—141no—
578C4⋊C4—141no—
579C4⋊C4—141no—
580C4⋊C4—141no—
581C4⋊C4—282no—
582C4⋊C4—561no—
583C4⋊C4C22⋊Dic714yes—
584C4⋊C4C22×Dic712yes—
585C4⋊C4C22×Dic712yes—
586C4⋊C4C22×Dic712yes—
587C22⋊C4—24no—
588C22⋊C4—24no—
589C22⋊C4—24no—
590C22⋊C4—24no—
591C22⋊C4—282no—
592C22⋊C4—282no—
593C22⋊C4—561no—
594C22⋊C4—561no—
595C22⋊C4C22⋊Dic714yes—
596C22⋊C4C22⋊Dic714yes—
597C42—24no—
598C42—282no—
599C42—282no—
600C42—282no—
601C42C22×Dic712yes—
602C42C2×C22⋊D712yes—
603C2×C7—42no—
604C2×C7—42no—
605C2×C7—82no—
606C2×C7#233911yescharacteristic
607C2×C7#289611yescharacteristic
608C2×C7#289711yescharacteristic
609C2×C7#330711yescharacteristic
610C2×C7#330911yescharacteristic
611C2×C7#334711yescharacteristic
612C2×C7#335011yescharacteristic
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—22no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23C2×C22⋊Dic712yes—
633C23C2×C22⋊Dic712yes—
634C23C22×C22⋊D711yescharacteristic
635D4—22no—
636D4—22no—
637D4—44no—
638D4—48no—
639D4—41no—
640D4—41no—
641D4—84no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
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—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—84no—
668C2×C4—84no—
669C2×C4—142no—
670C2×C4—281no—
671C2×C4—281no—
672C2×C4—281no—
673C2×C4—281no—
674C2×C4—281no—
675C2×C4—281no—
676C2×C4—281no—
677C2×C4—281no—
678C2×C4—281no—
679C2×C4—281no—
680C2×C4—281no—
681C2×C4C2×C22⋊Dic712yes—
682C2×C4C2×C22⋊Dic712yes—
683C2×C4C2×C22⋊Dic712yes—
684C2×C4C2×C22⋊Dic712yes—
685C2×C4D7×#4111yescharacteristic
686C2×C4D7×#4111yescharacteristic
687C2×C4#655311yescharacteristic
688C2×C4#655411yescharacteristic
689C2×C4C23×Dic711yescharacteristic
690C2×C4C22×C22⋊D711yescharacteristic
691C8—142no—
692C8—281no—
693C8—281no—
694C8—281no—
695C7#2249811yescharacteristic, complemented, Sylow
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22#9051311yescharacteristic
718C22#9051311yescharacteristic
719C22#9051511yescharacteristic
720C22#9052011yescharacteristic
721C22#9052611yescharacteristic
722C22#9052711yescharacteristic
723C22C22×C22⋊Dic711yescharacteristic
724C4—22no—
725C4—22no—
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—282no—
732C4—561no—
733C4—561no—
734C4—561no—
735C4#9051511yescharacteristic
736C4#41×Dic711yescharacteristic
737C4#9051811yescharacteristic
738C4#9052011yescharacteristic
739C2—42no—
740C2—42no—
741C2—82no—
742C2#1174105511yescharacteristic
743C2#1174105611yescharacteristic
744C2#1174106011yescharacteristic
745C2#1174106411yescharacteristic
746C2#1174151711yescharacteristic
747C2#1174153311yescharacteristic
748C2#1174154411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
Fitting, prime radicalC2×C7×#553C2
socleC23×C7C22×D4
cosocleC22×C4×C7C24
hypercenterC2×#553D7
hypocenterC7#22498
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
2. #11739782C2semidirect
3. C2×#89783C2semidirect
4. #11729495C2semidirect
5. #11729492C2semidirect
6. #11729436C2semidirect
7. #11729435C2semidirect
8. #11729432C2semidirect
9. #11729432C2semidirect
10. #11729363C2semidirect
11. #11729358C2semidirect
12. #11729334C2semidirect
13. #11729329C2semidirect
14. #11729312C2semidirect
15. #11729307C2semidirect
17. C7×#553C4semidirect
258. #553Dic7semidirect
695. C7#22498semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5532
#117397822
C2×#897832
#117294952
#117294922
#117294362
#117294352
#117294322
#117293632
#117293582
#117293342
#117293292
#117293122
#117293072
#224987