Finite Group Databasebeta

← #13369321

Subgroups — #13369321

Order 1792.

1530 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#550C211yesmaximal, characteristic
2C2×#90004C211yesmaximal, characteristic, complemented
3C2×#90005C211yesmaximal, characteristic, complemented
4#11739780C211yesmaximal, characteristic, complemented
5C2×#89783C211yesmaximal, characteristic, complemented
6#11729889C211yesmaximal, characteristic, complemented
7#11729889C211yesmaximal, characteristic, complemented
8#11729519C211yesmaximal, characteristic, complemented
9#11729515C211yesmaximal, characteristic, complemented
10#11729436C211yesmaximal, characteristic, complemented
11#11729435C211yesmaximal, characteristic, complemented
12#11729432C211yesmaximal, characteristic, complemented
13#11729431C211yesmaximal, characteristic, complemented
14#11729385C211yesmaximal, characteristic, complemented
15#11729381C211yesmaximal, characteristic, complemented
16C22×C7×#41C2211yescharacteristic
17C22×C7×#41C2211yescharacteristic
18C7×#550—24no—
19C7×#550C418yescomplemented
20C2×C7×#127—21no—
21C2×C7×#127C2211yescharacteristic
22C2×C7×#121—21no—
23C2×C7×#121—21no—
24C2×C7×#121C2211yescharacteristic
25C2×C7×#121C2211yescharacteristic
26C2×C4×C7×Q8C2211yescharacteristic
27C2×C4×C7×D4—21no—
28C2×C4×C7×D4C2211yescharacteristic
29C2×#6489C2211yescharacteristic
30C22×C4⋊Dic7C2211yescharacteristic
31C22×#1136C2211yescharacteristic
32C23×C7⋊C8C2211yescharacteristic
33#90005—24no—
34#90004—24no—
35C2×#6409C2211yescharacteristic
36C2×#6409C2211yescharacteristic
37C2×#6409C2211yescharacteristic
38C2×#6409C2211yescharacteristic
39#89992—21no—
40C2×#6406C2211yescharacteristic
41C2×#6406C2211yescharacteristic
42C2×#6406C2211yescharacteristic
43C2×#6406C2211yescharacteristic
44C2×#6406C2211yescharacteristic
45C2×#6406C2211yescharacteristic
46C2×#6406C2211yescharacteristic
47C2×#6406C2211yescharacteristic
48#89984C2211yescharacteristic
49#89984C2211yescharacteristic
50C2×C22⋊(C7⋊C8)C2211yescharacteristic
51C2×C22⋊(C7⋊C8)C2211yescharacteristic
52#89783—24no—
53#89753—21no—
54#89723—21no—
55C22⋊C4×Dic7—21no—
56#89708C2211yescharacteristic
57C4×C4⋊Dic7C2211yescharacteristic
58C2×C4⋊(C7⋊C8)C2211yescharacteristic
59C2×#6377C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#89324C2211yescharacteristic
63#89324C2211yescharacteristic
64#22422—71nomaximal, Sylow
65C2×C7×#41—22no—
66C2×C7×#41—22no—
67C2×C7×#41—22no—
68C2×C7×#41—22no—
69C2×C7×#41—22no—
70C2×C7×#41—22no—
71C2×C7×#41—41no—
72C2×C7×#41—41no—
73C2×C7×#41—41no—
74C2×C7×#41—41no—
75C2×C7×#41C2×C414yes—
76C2×C7×#41C2×C414yescomplemented
77C22×C7×Q8C2311yescharacteristic
78C22×C7×D4—21no—
79C22×C7×D4—21no—
80C22×C7×D4—21no—
81C22×C7×D4—21no—
82C22×C7×D4—21no—
83C22×C7×D4—21no—
84C22×C7×D4D411yescharacteristic
85C22×C7×D4C2311yescharacteristic
86C22×C7×D4C2311yescharacteristic
87C23×C4×C7—21no—
88C23×C4×C7—21no—
89C23×C4×C7C2311yescharacteristic
90C23×C4×C7C2311yescharacteristic
91C23×Dic7—21no—
92C7×#127—28no—
93C7×#127—22no—
94C7×#127C2×C414yescomplemented
95C7×#121—22no—
96C7×#121—22no—
97C7×#121—28no—
98C7×#121—28no—
99C7×#121C2×C414yes—
100C7×#121C2×C414yescomplemented
101C4×C7×Q8—22no—
102C4×C7×Q8C2×C414yescomplemented
103C4×C7×D4—28no—
104C4×C7×D4C2×C414yes—
105C4×C7×D4D414yes—
106C2×C7×C4⋊C4—21no—
107C2×C7×C4⋊C4D411yescharacteristic
108C2×C7×C4⋊C4C2311yescharacteristic
109C2×C7×C22⋊C4—21no—
110C2×C7×C22⋊C4—21no—
111C2×C7×C22⋊C4D411yescharacteristic
112C2×C7×C22⋊C4D411yescharacteristic
113C2×C42×C7—21no—
114C2×C42×C7C2311yescharacteristic
115C2×C22⋊Dic7—21no—
116C2×C22⋊Dic7—21no—
117C2×C22⋊Dic7—21no—
118#6489—22no—
119#6489—41no—
120C2×C4⋊Dic7—22no—
121C2×C4⋊Dic7—21no—
122C2×C4⋊Dic7—41no—
123C2×C4⋊Dic7C2311yescharacteristic
124C2×C4⋊Dic7C2311yescharacteristic
125C2×C4⋊Dic7C2311yescharacteristic
126C2×C4⋊Dic7C2311yescharacteristic
127C2×C4×Dic7—21no—
128C2×C4×Dic7—21no—
129C2×#1136—22no—
130C2×#1136—22no—
131C2×#1136—41no—
132C22×C7⋊C8—22no—
133C22×C7⋊C8—22no—
134C22×C7⋊C8—41no—
135C22×C7⋊C8C2311yescharacteristic
136C22×C7⋊C8C2311yescharacteristic
137C22×C7⋊C8C2311yescharacteristic
138C22×C7⋊C8C2311yescharacteristic
139#6409—22no—
140#6409—22no—
141#6409—22no—
142#6409D414yescomplemented
143#6406—22no—
144#6406—22no—
145#6406—22no—
146#6406—22no—
147#6406—41no—
148#6406—41no—
149#6406—41no—
150#6406—41no—
151C7⋊#95—21no—
152C7⋊#95—21no—
153C7⋊#95—21no—
154C7⋊#95—21no—
155C7⋊#95—21no—
156C22⋊(C7⋊C8)—22no—
157C22⋊(C7⋊C8)—22no—
158C4⋊(C7⋊C8)—22no—
159#6377—22no—
160C2×#550D711yescharacteristic
161C2×#435—71no—
162C2×#417—71no—
163C2×#416—71no—
164#2352—71no—
165#1982—71no—
166#1961—71no—
167#1895—71no—
168#1893—71no—
169#1875—71no—
170#1874—71no—
171#1805—71no—
172#1788—71no—
173#1788—71no—
174#1763—71no—
175C24×C7—21no—
176C24×C7—21no—
177C24×C7C2×D411yescharacteristic
178C24×C7C2×D411yescharacteristic
179C7×#41—28no—
180C7×#41—28no—
181C7×#41—44no—
182C7×#41—44no—
183C7×#41—44no—
184C7×#41—44no—
185C7×#41—44no—
186C7×#41—44no—
187C2×C7×Q8—21no—
188C2×C7×Q8—21no—
189C2×C7×Q8—21no—
190C2×C7×Q8C22×C412yes—
191C2×C7×Q8C2×D412yes—
192C2×C7×Q8#4112yes—
193C2×C7×D4—24no—
194C2×C7×D4—24no—
195C2×C7×D4—24no—
196C2×C7×D4—24no—
197C2×C7×D4—24no—
198C2×C7×D4—24no—
199C2×C7×D4—21no—
200C2×C7×D4—21no—
201C2×C7×D4—21no—
202C2×C7×D4—21no—
203C2×C7×D4—21no—
204C2×C7×D4—21no—
205C2×C7×D4—21no—
206C2×C7×D4—21no—
207C2×C7×D4—21no—
208C2×C7×D4—21no—
209C2×C7×D4—41no—
210C2×C7×D4—41no—
211C2×C7×D4—42no—
212C2×C7×D4—42no—
213C2×C7×D4—42no—
214C2×C7×D4—42no—
215C2×C7×D4—42no—
216C2×C7×D4—42no—
217C2×C7×D4—81no—
218C2×C7×D4—81no—
219C2×C7×D4—81no—
220C2×C7×D4—81no—
221C2×C7×D4—81no—
222C2×C7×D4—81no—
223C2×C7×D4C22⋊C414yes—
224C2×C7×D4C22×C412yes—
225C2×C7×D4C22×C412yes—
226C22×C4×C7—21no—
227C22×C4×C7—21no—
228C22×C4×C7—21no—
229C22×C4×C7—21no—
230C22×C4×C7—21no—
231C22×C4×C7—21no—
232C22×C4×C7—21no—
233C22×C4×C7—21no—
234C22×C4×C7—21no—
235C22×C4×C7—21no—
236C22×C4×C7—24no—
237C22×C4×C7—24no—
238C22×C4×C7—42no—
239C22×C4×C7—42no—
240C22×C4×C7—42no—
241C22×C4×C7—42no—
242C22×C4×C7C22×C412yes—
243C22×C4×C7C22×C412yes—
244C22×C4×C7C2×D411yescharacteristic
245C22×C4×C7C2×D411yescharacteristic
246C22×C4×C7C2×D411yescharacteristic
247C22×C4×C7C2×D411yescharacteristic
248C22×C4×C7C2×D412yes—
249C22×C4×C7C2×D412yes—
250C22×C4×C7C2411yescharacteristic
251C22×Dic7—21no—
252C22×Dic7—21no—
253C22×Dic7—21no—
254C22×Dic7—21no—
255C22×Dic7—42no—
256C22×Dic7—42no—
257C22×Dic7—81no—
258C7×C4⋊C4—24no—
259C7×C4⋊C4—21no—
260C7×C4⋊C4C22⋊C414yes—
261C7×C4⋊C4C22×C412yes—
262C7×C22⋊C4—24no—
263C7×C22⋊C4—24no—
264C7×C22⋊C4C22⋊C414yes—
265C7×C22⋊C4C22⋊C414yes—
266C42×C7—24no—
267C42×C7C22×C412yes—
268C42×C7C2×D412yes—
269C22⋊Dic7—42no—
270C22⋊Dic7—42no—
271C22⋊Dic7—81no—
272C4⋊Dic7—21no—
273C4⋊Dic7—21no—
274C4⋊Dic7—21no—
275C4⋊Dic7—21no—
276C4⋊Dic7—21no—
277C4⋊Dic7—21no—
278C4⋊Dic7—21no—
279C4⋊Dic7—42no—
280C4⋊Dic7C2×D412yes—
281C4×Dic7—42no—
282C4×Dic7—81no—
283#1136—44no—
284C2×C7⋊C8—21no—
285C2×C7⋊C8—21no—
286C2×C7⋊C8—21no—
287C2×C7⋊C8—21no—
288C2×C7⋊C8—21no—
289C2×C7⋊C8—21no—
290C2×C7⋊C8—21no—
291C2×C7⋊C8—21no—
292C2×C7⋊C8—21no—
293C2×C7⋊C8—21no—
294C2×C7⋊C8—21no—
295C2×C7⋊C8—44no—
296C2×C7⋊C8C2×D412yes—
297C22×#41C2×D711yescharacteristic
298C22×#41C2×D711yescharacteristic
299C22×M16—71no—
300C23×C8—71no—
301#550—24no—
302#550Dic718yescomplemented
303C2×#127—21no—
304C2×#127C2×D711yescharacteristic
305C2×#121—21no—
306C2×#121—21no—
307C2×#121C2×D711yescharacteristic
308C2×#121C2×D711yescharacteristic
309C2×C4×Q8C2×D711yescharacteristic
310C2×C4×D4—21no—
311C2×C4×D4C2×D711yescharacteristic
312C2×#117—71no—
313C22×C4⋊C4—71no—
314#435—144no—
315C2×C4⋊C8—71no—
316#417—144no—
317#416—144no—
318C2×#103—71no—
319C2×#103—71no—
320C2×#103—71no—
321C2×#103—71no—
322C2×#102—71no—
323C2×#102—71no—
324C2×#102—71no—
325C2×#102—71no—
326C2×#102—71no—
327C2×#102—71no—
328C2×#102—71no—
329C2×#102—71no—
330C2×C22⋊C8—71no—
331C2×C22⋊C8—71no—
332C2×#97—71no—
333#388—141no—
334#387—141no—
335#386—141no—
336#382—71no—
337#380—71no—
338#380—71no—
339C4×C4⋊C4—71no—
340C4×C22⋊C4—141no—
341#340—71no—
342#340—71no—
343#340—71no—
344#340—71no—
345C23×C7—21no—
346C23×C7—21no—
347C23×C7—21no—
348C23×C7—21no—
349C23×C7—21no—
350C23×C7—21no—
351C23×C7—21no—
352C23×C7—21no—
353C23×C7—21no—
354C23×C7—21no—
355C23×C7—21no—
356C23×C7—21no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—41no—
360C23×C7—41no—
361C23×C7—41no—
362C23×C7—41no—
363C23×C7—41no—
364C23×C7—41no—
365C23×C7—41no—
366C23×C7—41no—
367C23×C7—41no—
368C23×C7—41no—
369C23×C7—41no—
370C23×C7—41no—
371C23×C7C2×C22⋊C412yes—
372C23×C7C2×C22⋊C412yes—
373C23×C7C22×D411yescharacteristic
374C7×Q8—22no—
375C7×Q8—22no—
376C7×Q8—22no—
377C7×Q8C4×D414yes—
378C7×D4—22no—
379C7×D4—22no—
380C7×D4—22no—
381C7×D4—22no—
382C7×D4—44no—
383C7×D4—48no—
384C7×D4—48no—
385C7×D4—48no—
386C7×D4—41no—
387C7×D4—41no—
388C7×D4—41no—
389C7×D4—41no—
390C7×D4—84no—
391C7×D4—84no—
392C7×D4—84no—
393C2×C4×C7—22no—
394C2×C4×C7—21no—
395C2×C4×C7—21no—
396C2×C4×C7—22no—
397C2×C4×C7—21no—
398C2×C4×C7—21no—
399C2×C4×C7—22no—
400C2×C4×C7—21no—
401C2×C4×C7—21no—
402C2×C4×C7—21no—
403C2×C4×C7—21no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—48no—
414C2×C4×C7—48no—
415C2×C4×C7—41no—
416C2×C4×C7—41no—
417C2×C4×C7C2×C22⋊C412yes—
418C2×C4×C7C2×C22⋊C412yes—
419C2×C4×C7C2×C22⋊C412yes—
420C2×C4×C7C2×C22⋊C412yes—
421C2×C4×C7C23×C411yescharacteristic
422C2×C4×C7C22×D411yescharacteristic
423C2×C4×C7C22×D411yescharacteristic
424C2×C4×C7C2×#4111yescharacteristic
425C2×C4×C7H(5,𝔽2)11yescharacteristic
426C2×C4×C7H(5,𝔽2)11yescharacteristic
427C2×Dic7—22no—
428C2×Dic7—41no—
429C2×Dic7—41no—
430C2×Dic7—41no—
431C2×Dic7—41no—
432C2×Dic7—41no—
433C2×Dic7—41no—
434C2×Dic7—41no—
435C2×Dic7—41no—
436C2×Dic7—41no—
437C2×Dic7—41no—
438C2×Dic7—41no—
439C2×Dic7—84no—
440C7⋊C8—22no—
441C7⋊C8—41no—
442C7⋊C8—41no—
443C7⋊C8—41no—
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—22no—
447C2×#41—22no—
448C2×#41—22no—
449C2×#41—22no—
450C2×#41—41no—
451C2×#41—41no—
452C2×#41—41no—
453C2×#41—41no—
454C2×#41C2×Dic714yes—
455C2×#41C2×Dic714yescomplemented
456C22×Q8C22×D711yescharacteristic
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4C22⋊D711yescharacteristic
464C22×D4C22×D711yescharacteristic
465C22×D4C22×D711yescharacteristic
466C23×C4—21no—
467C23×C4—21no—
468C23×C4—141no—
469C23×C4C22×D711yescharacteristic
470C23×C4C22×D711yescharacteristic
471C2×M16—142no—
472C2×M16—142no—
473C2×M16—281no—
474C22×C8—71no—
475C22×C8—71no—
476C22×C8—71no—
477C22×C8—71no—
478C22×C8—142no—
479C22×C8—142no—
480C22×C8—281no—
481#127—28no—
482#127—22no—
483#127C2×Dic714yescomplemented
484#121—22no—
485#121—22no—
486#121—28no—
487#121—28no—
488#121C2×Dic714yes—
489#121C2×Dic714yescomplemented
490C4×Q8—22no—
491C4×Q8C2×Dic714yescomplemented
492C4×D4—28no—
493C4×D4C2×Dic714yes—
494C4×D4C22⋊D714yes—
495#117—142no—
496#117—281no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—71no—
499C2×C4⋊C4—71no—
500C2×C4⋊C4—71no—
501C2×C4⋊C4—71no—
502C2×C4⋊C4—142no—
503C2×C4⋊C4—141no—
504C2×C4⋊C4—281no—
505C2×C4⋊C4C22⋊D711yescharacteristic
506C2×C4⋊C4C22×D711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—141no—
510C2×C22⋊C4—141no—
511C2×C22⋊C4—141no—
512C2×C22⋊C4C22⋊D711yescharacteristic
513C2×C22⋊C4C22⋊D711yescharacteristic
514C2×C42—21no—
515C2×C42—141no—
516C2×C42—141no—
517C2×C42C22×D711yescharacteristic
518C4⋊C8—142no—
519#103—74no—
520#103—142no—
521#103—142no—
522#103—142no—
523#102—142no—
524#102—142no—
525#102—142no—
526#102—142no—
527#102—281no—
528#102—281no—
529#102—281no—
530#102—281no—
531C22⋊C8—142no—
532C22⋊C8—142no—
533#97—142no—
534#95—141no—
535#95—141no—
536#95—141no—
537#95—141no—
538#95—141no—
539C22×C7—22no—
540C22×C7—22no—
541C22×C7—22no—
542C22×C7—22no—
543C22×C7—22no—
544C22×C7—22no—
545C22×C7—41no—
546C22×C7—41no—
547C22×C7—41no—
548C22×C7—41no—
549C22×C7—41no—
550C22×C7—41no—
551C22×C7—41no—
552C22×C7—41no—
553C22×C7—42no—
554C22×C7—42no—
555C22×C7—42no—
556C22×C7—42no—
557C22×C7—42no—
558C22×C7—42no—
559C22×C7—81no—
560C22×C7—81no—
561C22×C7—81no—
562C22×C7—81no—
563C22×C7—81no—
564C22×C7—81no—
565C22×C7—81no—
566C22×C7—81no—
567C22×C7C22×C22⋊C411yescharacteristic
568C22×C7D4211yescharacteristic
569C22×C7#54611yescharacteristic
570C22×C7#57511yescharacteristic
571C22×C7#57511yescharacteristic
572C22×C7#57611yescharacteristic
573C22×C7#57711yescharacteristic
574C4×C7—22no—
575C4×C7—22no—
576C4×C7—24no—
577C4×C7—22no—
578C4×C7—22no—
579C4×C7—42no—
580C4×C7C2×C4×D411yescharacteristic
581C4×C7#51811yescharacteristic
582C4×C7D4211yescharacteristic
583C4×C7#54611yescharacteristic
584Dic7—42no—
585Dic7—81no—
586Dic7—81no—
587Dic7—81no—
588C24—21no—
589C24—21no—
590C24C2×C22⋊D711yescharacteristic
591C24C2×C22⋊D711yescharacteristic
592#41—28no—
593#41—28no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8D4×D712yes—
604C2×Q8#115912yes—
605C2×Q8C22×Dic712yes—
606C2×D4—24no—
607C2×D4—24no—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4—81no—
636C2×D4C22⋊Dic714yes—
637C2×D4C22×Dic712yes—
638C2×D4C22×Dic712yes—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—141no—
656C22×C4—141no—
657C22×C4—141no—
658C22×C4—141no—
659C22×C4—282no—
660C22×C4—282no—
661C22×C4—561no—
662C22×C4C22×Dic712yes—
663C22×C4C22×Dic712yes—
664C22×C4C2×C22⋊D711yescharacteristic
665C22×C4C2×C22⋊D711yescharacteristic
666C22×C4C2×C22⋊D711yescharacteristic
667C22×C4C2×C22⋊D711yescharacteristic
668C22×C4C2×C22⋊D712yes—
669C22×C4C2×C22⋊D712yes—
670C22×C4C23×D711yescharacteristic
671M16—284no—
672C2×C8—72no—
673C2×C8—141no—
674C2×C8—141no—
675C2×C8—141no—
676C2×C8—141no—
677C2×C8—141no—
678C2×C8—141no—
679C2×C8—141no—
680C2×C8—141no—
681C2×C8—141no—
682C2×C8—141no—
683C2×C8—141no—
684C2×C8—284no—
685C4⋊C4—24no—
686C4⋊C4—21no—
687C4⋊C4—72no—
688C4⋊C4—141no—
689C4⋊C4—141no—
690C4⋊C4—141no—
691C4⋊C4—141no—
692C4⋊C4—141no—
693C4⋊C4—141no—
694C4⋊C4—141no—
695C4⋊C4—282no—
696C4⋊C4C22⋊Dic714yes—
697C4⋊C4C22×Dic712yes—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—282no—
701C22⋊C4—282no—
702C22⋊C4—561no—
703C22⋊C4C22⋊Dic714yes—
704C22⋊C4C22⋊Dic714yes—
705C42—24no—
706C42—282no—
707C42—561no—
708C42C22×Dic712yes—
709C42C2×C22⋊D712yes—
710C2×C7—42no—
711C2×C7—42no—
712C2×C7—82no—
713C2×C7—82no—
714C2×C7D4×C22⋊C411yescharacteristic
715C2×C7#289611yescharacteristic
716C2×C7#289711yescharacteristic
717C2×C7#326811yescharacteristic
718C2×C7#327111yescharacteristic
719C2×C7#330911yescharacteristic
720C2×C7#331711yescharacteristic
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—22no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23C2×C22⋊Dic712yes—
748C23C2×C22⋊Dic712yes—
749C23C22×C22⋊D711yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—22no—
753Q8D4×Dic714yes—
754D4—22no—
755D4—22no—
756D4—22no—
757D4—22no—
758D4—44no—
759D4—48no—
760D4—48no—
761D4—48no—
762D4—41no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—84no—
767D4—84no—
768D4—84no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—48no—
790C2×C4—48no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—142no—
794C2×C4—281no—
795C2×C4—281no—
796C2×C4—281no—
797C2×C4—281no—
798C2×C4—281no—
799C2×C4—281no—
800C2×C4—281no—
801C2×C4—281no—
802C2×C4—281no—
803C2×C4—281no—
804C2×C4—281no—
805C2×C4—564no—
806C2×C4C2×C22⋊Dic712yes—
807C2×C4C2×C22⋊Dic712yes—
808C2×C4C2×C22⋊Dic712yes—
809C2×C4C2×C22⋊Dic712yes—
810C2×C4C2×D4×D711yescharacteristic
811C2×C4C2×#115911yescharacteristic
812C2×C4#654811yescharacteristic
813C2×C4#654811yescharacteristic
814C2×C4C23×Dic711yescharacteristic
815C2×C4C22×C22⋊D711yescharacteristic
816C8—142no—
817C8—281no—
818C8—281no—
819C8—281no—
820C7#2242211yescharacteristic, complemented, Sylow
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22D4×C22⋊D711yescharacteristic
850C22#9049711yescharacteristic
851C22#9051311yescharacteristic
852C22#9051311yescharacteristic
853C22#9052611yescharacteristic
854C22#9052711yescharacteristic
855C22C22×C22⋊Dic711yescharacteristic
856C4—22no—
857C4—22no—
858C4—24no—
859C4—22no—
860C4—22no—
861C4—42no—
862C4—282no—
863C4—561no—
864C4—561no—
865C4—561no—
866C4C2×D4×Dic711yescharacteristic
867C4#9048911yescharacteristic
868C4D4×C22⋊D711yescharacteristic
869C4#9049711yescharacteristic
870C2—42no—
871C2—42no—
872C2—82no—
873C2—82no—
874C2#1174101711yescharacteristic
875C2#1174101811yescharacteristic
876C2#1174102211yescharacteristic
877C2#1174102811yescharacteristic
878C2D4×C22⋊Dic711yescharacteristic
879C2#1174151711yescharacteristic
880C2#1174154411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
Fitting, prime radicalC2×C7×#550C2
socleC23×C7C22×D4
cosocleC22×C4×C7C24
hypercenterC2×#550D7
hypocenterC7#22422
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
2. C2×#90004C2semidirect
3. C2×#90005C2semidirect
4. #11739780C2semidirect
5. C2×#89783C2semidirect
6. #11729889C2semidirect
7. #11729889C2semidirect
8. #11729519C2semidirect
9. #11729515C2semidirect
10. #11729436C2semidirect
11. #11729435C2semidirect
12. #11729432C2semidirect
13. #11729431C2semidirect
14. #11729385C2semidirect
15. #11729381C2semidirect
19. C7×#550C4semidirect
76. C2×C7×#41C2×C4semidirect
94. C7×#127C2×C4semidirect
100. C7×#121C2×C4semidirect
102. C4×C7×Q8C2×C4semidirect
142. #6409D4semidirect
302. #550Dic7semidirect
455. C2×#41C2×Dic7semidirect
483. #127C2×Dic7semidirect
489. #121C2×Dic7semidirect
491. C4×Q8C2×Dic7semidirect
820. C7#22422semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5502
C2×#900042
C2×#900052
#117397802
C2×#897832
#117298892
#117295192
#117295152
#117294362
#117294352
#117294322
#117294312
#117293852
#117293812
#224227