Finite Group Databasebeta

← #13370169

Subgroups — #13370169

Order 1792.

1174 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90326C211yesmaximal, characteristic
2C2×#89899C211yesmaximal, characteristic
3#11731457C211yesmaximal, characteristic
4C7×#1894C211yesmaximal, characteristic, complemented
5#11729739C211yesmaximal, characteristic, complemented
6#11729447C211yesmaximal, characteristic, complemented
7#11728024C211yesmaximal, characteristic, complemented
8#11728022C211yesmaximal, characteristic, complemented
9#11727976C211yesmaximal, characteristic, complemented
10#11727974C211yesmaximal, characteristic, complemented
11#11727255C211yesmaximal, characteristic, complemented
12#11726626C211yesmaximal, characteristic, complemented
13D7×#340C211yesmaximal, characteristic, complemented
14#11726560C211yesmaximal, characteristic, complemented
15#11726554C211yesmaximal, characteristic, complemented
16C22×C7×M16C2211yescharacteristic
17C2×C7×C22⋊Q8C2211yescharacteristic
18C2×#6509C2211yescharacteristic
19C2×Q8×Dic7C2211yescharacteristic
20C2×C4×C22⋊D7C2211yescharacteristic
21C2×#6489C2211yescharacteristic
22C22×C4⋊Dic7C2211yescharacteristic
23C22×C8×D7C2211yescharacteristic
24#90326—24no—
25#90326C418yescomplemented
26C2×#6460—21no—
27C2×D7×C4⋊C4C2211yescharacteristic
28C2×D7×C4⋊C4C2211yescharacteristic
29C2×#6452—21no—
30C2×#6451C2211yescharacteristic
31C2×(C22⋊D7)⋊C4—21no—
32C2×#6441—21no—
33C2×C7×#103C2211yescharacteristic
34C2×C7×#103C2211yescharacteristic
35C7×#380C2211yescharacteristic
36C2×#6409C2211yescharacteristic
37C2×#6409C2211yescharacteristic
38C2×C22⋊(C7⋊C8)C2211yescharacteristic
39#89899—24no—
40C2×(C2×D7)⋊C8C2211yescharacteristic
41C2×#6389C2211yescharacteristic
42C2×Dic7⋊C8C2211yescharacteristic
43#89759C2211yescharacteristic
44#89749C2211yescharacteristic
45C4⋊C4×Dic7C2211yescharacteristic
46#89728—21no—
47#89716—21no—
48#89438—21no—
49#89424—21no—
50C7×#340C2211yescharacteristic
51C7×#340C2211yescharacteristic
52#89346C2211yescharacteristic
53#89346C2211yescharacteristic
54#89346C2211yescharacteristic
55#89346C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#22497—71nomaximal, Sylow
63C22×C7×Q8C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C22×C22⋊D7D411yescharacteristic
66C23×Dic7—21no—
67C22×C4×D7—21no—
68C22×C4×D7—21no—
69C22×C4×D7C2311yescharacteristic
70C22×Dic14—21no—
71C2×C7×M16—22no—
72C2×C7×M16—22no—
73C2×C7×M16—41no—
74C22×C7×C8C2311yescharacteristic
75C22×C7×C8C2311yescharacteristic
76C7×C22⋊Q8—22no—
77C7×C22⋊Q8C2×C414yescomplemented
78C2×C7×C4⋊C4—21no—
79C2×C7×C4⋊C4C2311yescharacteristic
80C2×C7×C4⋊C4C2311yescharacteristic
81C2×C7×C4⋊C4C2311yescharacteristic
82C2×C7×C22⋊C4—21no—
83C2×C7×C22⋊C4—21no—
84C2×C22⋊Dic7—21no—
85C2×C22⋊Dic7D411yescharacteristic
86#6509—22no—
87#6509C2×C414yes—
88Q8×Dic7—22no—
89Q8×Dic7C2×C414yescomplemented
90C4×C22⋊D7C2×C414yes—
91C4×C22⋊D7D414yes—
92C2×(C2×D7)⋊C4—21no—
93C2×(C2×D7)⋊C4—21no—
94C2×(C2×D7)⋊C4D411yescharacteristic
95#6489—22no—
96#6489—41no—
97C2×C4⋊Dic7—21no—
98C2×C4⋊Dic7—22no—
99C2×C4⋊Dic7—21no—
100C2×C4⋊Dic7C2×C414yescomplemented
101C2×C4⋊Dic7C2311yescharacteristic
102C2×C4⋊Dic7C2311yescharacteristic
103C2×C4⋊Dic7C2311yescharacteristic
104C2×C4⋊Dic7C2311yescharacteristic
105C2×Dic7⋊C4—21no—
106C2×Dic7⋊C4—21no—
107C2×Dic7⋊C4—21no—
108C2×Dic7⋊C4—21no—
109C2×Dic7⋊C4D411yescharacteristic
110C2×C4×Dic7—21no—
111C2×C4×Dic7—21no—
112C2×C4×Dic7—21no—
113C2×C4×Dic7C2311yescharacteristic
114C22×C7⋊C8C2311yescharacteristic
115C22×C7⋊C8C2311yescharacteristic
116C2×C8×D7—22no—
117C2×C8×D7—22no—
118C2×C8×D7—41no—
119#6460—28no—
120D7×C4⋊C4—22no—
121D7×C4⋊C4—22no—
122D7×C4⋊C4—41no—
123D7×C4⋊C4C2×C414yes—
124#6452—28no—
125#6451—22no—
126#6451C2×C414yescomplemented
127(C22⋊D7)⋊C4—28no—
128#6441—28no—
129C7×#103—22no—
130C7×#103—41no—
131C7×#95—21no—
132#6409—22no—
133#6409—41no—
134C7⋊#95—21no—
135C7⋊#95—21no—
136C7⋊#95—21no—
137C7⋊#95—21no—
138C22⋊(C7⋊C8)—22no—
139(C2×D7)⋊C8—22no—
140#6389—22no—
141Dic7⋊C8—22no—
142C2×#554—71no—
143C2×#435—71no—
144#2352—71no—
145#1993—71no—
146#1988—71no—
147#1894D711yescharacteristic, complemented
148#1892—71no—
149#1873—71no—
150#1872—71no—
151#1824—71no—
152#1823—71no—
153#1805—71no—
154#1763—71no—
155#1736—71no—
156C2×#340—71no—
157C24×C7C2×D411yescharacteristic
158C23×D7C2×D411yescharacteristic
159C2×C7×Q8—21no—
160C2×C7×Q8—21no—
161C2×C7×Q8—21no—
162C2×C7×Q8—21no—
163C2×C7×Q8—21no—
164C2×C7×Q8C22×C412yes—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7C22×C412yes—
174C22×C4×C7C2×D411yescharacteristic
175C22×C4×C7C2×D412yes—
176C22×C4×C7C2411yescharacteristic
177C2×C22⋊D7—22no—
178C2×C22⋊D7—22no—
179C2×C22⋊D7C22⋊C414yes—
180C22×Dic7—21no—
181C22×Dic7—21no—
182C22×Dic7—21no—
183C22×Dic7—24no—
184C22×Dic7—21no—
185C22×Dic7—81no—
186C22×Dic7—81no—
187C22×Dic7C2×D411yescharacteristic
188C22×Dic7C2×D411yescharacteristic
189C22×Dic7C2×D411yescharacteristic
190C2×C4×D7—21no—
191C2×C4×D7—21no—
192C2×C4×D7—21no—
193C2×C4×D7—21no—
194C2×C4×D7—24no—
195C2×C4×D7—42no—
196C2×C4×D7—42no—
197C2×C4×D7—81no—
198C2×C4×D7—81no—
199C2×C4×D7—81no—
200C2×C4×D7C22×C412yes—
201C2×C4×D7C2×D412yes—
202C2×Dic14—24no—
203C2×Dic14—81no—
204C2×Dic14—81no—
205C7×M16—44no—
206C2×C7×C8—21no—
207C2×C7×C8—21no—
208C2×C7×C8—21no—
209C2×C7×C8—21no—
210C2×C7×C8—21no—
211C2×C7×C8#4112yes—
212C7×C4⋊C4—24no—
213C7×C4⋊C4—21no—
214C7×C4⋊C4—21no—
215C7×C4⋊C4—21no—
216C7×C4⋊C4—21no—
217C7×C4⋊C4—21no—
218C7×C4⋊C4C22×C412yes—
219C7×C22⋊C4—24no—
220C7×C22⋊C4—81no—
221C22⋊Dic7—42no—
222C22⋊Dic7C22⋊C414yes—
223(C2×D7)⋊C4—24no—
224(C2×D7)⋊C4—42no—
225(C2×D7)⋊C4C22⋊C414yes—
226C4⋊Dic7—24no—
227C4⋊Dic7—21no—
228C4⋊Dic7—21no—
229C4⋊Dic7—21no—
230C4⋊Dic7—24no—
231C4⋊Dic7—21no—
232C4⋊Dic7—21no—
233C4⋊Dic7C22×C412yes—
234C4⋊Dic7C22×C412yes—
235C4⋊Dic7#4112yes—
236Dic7⋊C4—24no—
237Dic7⋊C4—24no—
238Dic7⋊C4—24no—
239Dic7⋊C4—42no—
240Dic7⋊C4C22⋊C414yes—
241C4×Dic7—24no—
242C4×Dic7—42no—
243C4×Dic7—81no—
244C4×Dic7C22×C412yes—
245C4×Dic7C2×D412yes—
246C2×C7⋊C8—21no—
247C2×C7⋊C8—21no—
248C2×C7⋊C8—21no—
249C2×C7⋊C8—21no—
250C2×C7⋊C8—21no—
251C2×C7⋊C8—21no—
252C8×D7—44no—
253C22×M16C2×D711yescharacteristic
254C23×C8—71no—
255#554—78no—
256#554—144no—
257C2×C4⋊Q8—71no—
258C2×#125—141no—
259C2×C22⋊Q8—71no—
260C2×C22⋊Q8—141no—
261C2×C22⋊Q8—141no—
262C2×C22⋊Q8C2×D711yescharacteristic
263C2×C4×Q8—71no—
264C2×C4×D4—71no—
265C2×C4×D4—141no—
266C2×#117—71no—
267C22×C4⋊C4—71no—
268C22×C4⋊C4—71no—
269C22×C4⋊C4—71no—
270#435—144no—
271C2×C4⋊C8—71no—
272C2×#103—71no—
273C2×#103—71no—
274C2×#103C2×D711yescharacteristic
275C2×#103C2×D711yescharacteristic
276C2×C22⋊C8—71no—
277C2×C22⋊C8—71no—
278C2×#97—71no—
279#388—141no—
280#387—141no—
281#386—141no—
282#382—71no—
283#380—71no—
284#380C2×D711yescharacteristic
285C4×C4⋊C4—71no—
286C4×C22⋊C4—141no—
287#340—71no—
288#340—71no—
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#340C2×D711yescharacteristic
298#340C2×D711yescharacteristic
299C23×C7—21no—
300C23×C7—21no—
301C23×C7—21no—
302C23×C7—21no—
303C23×C7—21no—
304C23×C7—21no—
305C23×C7C2×C22⋊C412yes—
306C23×C7C22×D411yescharacteristic
307C22×D7—21no—
308C22×D7—21no—
309C22×D7—21no—
310C22×D7—21no—
311C22×D7C2×C22⋊C412yes—
312C22×D7#13712yes—
313C22×D7#13712yes—
314C7×Q8—22no—
315C7×Q8—22no—
316C7×Q8—41no—
317C7×Q8—41no—
318C2×C4×C7—21no—
319C2×C4×C7—21no—
320C2×C4×C7—22no—
321C2×C4×C7—22no—
322C2×C4×C7—22no—
323C2×C4×C7—22no—
324C2×C4×C7—22no—
325C2×C4×C7—22no—
326C2×C4×C7—41no—
327C2×C4×C7—41no—
328C2×C4×C7—41no—
329C2×C4×C7—41no—
330C2×C4×C7—41no—
331C2×C4×C7—41no—
332C2×C4×C7—41no—
333C2×C4×C7—41no—
334C2×C4×C7—41no—
335C2×C4×C7—41no—
336C2×C4×C7C2×C22⋊C412yes—
337C2×C4×C7C23×C411yescharacteristic
338C2×C4×C7C22×D411yescharacteristic
339C2×C4×C7C2×#4111yescharacteristic
340C2×C4×C7C2×#4111yescharacteristic
341C2×C4×C7H(5,𝔽2)11yescharacteristic
342C2×C4×C72−1+411yescharacteristic
343C22⋊D7—28no—
344C2×Dic7—21no—
345C2×Dic7—21no—
346C2×Dic7—21no—
347C2×Dic7—21no—
348C2×Dic7—21no—
349C2×Dic7—21no—
350C2×Dic7—22no—
351C2×Dic7—22no—
352C2×Dic7—22no—
353C2×Dic7—41no—
354C2×Dic7—41no—
355C2×Dic7—41no—
356C2×Dic7—41no—
357C2×Dic7—41no—
358C2×Dic7—41no—
359C2×Dic7—41no—
360C2×Dic7—41no—
361C2×Dic7—41no—
362C2×Dic7—84no—
363C2×Dic7C2×C22⋊C412yes—
364C2×Dic7C2×C22⋊C412yes—
365C2×Dic7C2×C22⋊C412yes—
366C4×D7—22no—
367C4×D7—22no—
368C4×D7—22no—
369C4×D7—22no—
370C4×D7—84no—
371C4×D7—84no—
372Dic14—84no—
373C7×C8—22no—
374C7×C8—41no—
375C7⋊C8—41no—
376C7⋊C8—41no—
377C22×Q8—141no—
378C22×Q8C22×D711yescharacteristic
379C22×D4—71no—
380C23×C4—71no—
381C23×C4—141no—
382C23×C4—141no—
383C23×C4—141no—
384C23×C4C22×D711yescharacteristic
385C2×M16—22no—
386C2×M16—22no—
387C2×M16—41no—
388C22×C8—71no—
389C22×C8—71no—
390C22×C8—142no—
391C22×C8—142no—
392C22×C8—281no—
393C22×C8C22×D711yescharacteristic
394C22×C8C22×D711yescharacteristic
395C4⋊Q8—74no—
396C4⋊Q8—142no—
397#125—148no—
398C22⋊Q8—22no—
399C22⋊Q8—74no—
400C22⋊Q8—148no—
401C22⋊Q8—148no—
402C22⋊Q8—142no—
403C22⋊Q8C4×D714yescomplemented
404C4×Q8—74no—
405C4×Q8—142no—
406C4×D4—74no—
407C4×D4—74no—
408C4×D4—148no—
409#117—142no—
410#117—281no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—71no—
413C2×C4⋊C4—74no—
414C2×C4⋊C4—71no—
415C2×C4⋊C4—71no—
416C2×C4⋊C4—71no—
417C2×C4⋊C4—74no—
418C2×C4⋊C4—71no—
419C2×C4⋊C4—142no—
420C2×C4⋊C4—142no—
421C2×C4⋊C4—141no—
422C2×C4⋊C4—141no—
423C2×C4⋊C4—141no—
424C2×C4⋊C4—141no—
425C2×C4⋊C4—141no—
426C2×C4⋊C4—142no—
427C2×C4⋊C4—141no—
428C2×C4⋊C4—281no—
429C2×C4⋊C4C22×D711yescharacteristic
430C2×C4⋊C4C22×D711yescharacteristic
431C2×C4⋊C4C22×D711yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—71no—
435C2×C22⋊C4—71no—
436C2×C22⋊C4—141no—
437C2×C22⋊C4—141no—
438C2×C22⋊C4—141no—
439C2×C42—71no—
440C2×C42—141no—
441C2×C42—141no—
442C2×C42—141no—
443C4⋊C8—142no—
444#103—22no—
445#103—41no—
446#103—142no—
447#103—281no—
448C22⋊C8—142no—
449C22⋊C8—142no—
450#97—142no—
451#95—21no—
452#95—141no—
453#95—141no—
454#95—141no—
455#95—141no—
456C22×C7—22no—
457C22×C7—22no—
458C22×C7—22no—
459C22×C7—41no—
460C22×C7—41no—
461C22×C7—41no—
462C22×C7—41no—
463C22×C7C22×C22⋊C411yescharacteristic
464C22×C7#54611yescharacteristic
465C22×C7#54711yescharacteristic
466C22×C7C2×#13711yescharacteristic
467C22×C7C2×#13711yescharacteristic
468C22×C7#57611yescharacteristic
469C22×C7#57711yescharacteristic
470C2×D7—22no—
471C2×D7—22no—
472C2×D7—22no—
473C2×D7—22no—
474C2×D7—22no—
475C2×D7—22no—
476C2×D7#41914yes—
477C4×C7—22no—
478C4×C7—42no—
479C4×C7—42no—
480C4×C7—81no—
481C4×C7—81no—
482C4×C7C4×#4111yescharacteristic
483C4×C7#52011yescharacteristic
484C4×C7#54611yescharacteristic
485C4×C7#54711yescharacteristic
486Dic7—22no—
487Dic7—22no—
488Dic7—22no—
489Dic7—42no—
490Dic7—42no—
491Dic7—42no—
492Dic7—81no—
493C24—71no—
494C24D4×D711yescharacteristic
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—144no—
501C2×Q8—561no—
502C2×Q8—561no—
503C2×Q8C2×C4×D712yes—
504C2×D4—74no—
505C2×D4—142no—
506C2×D4—142no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—71no—
516C22×C4—71no—
517C22×C4—71no—
518C22×C4—72no—
519C22×C4—72no—
520C22×C4—144no—
521C22×C4—141no—
522C22×C4—141no—
523C22×C4—141no—
524C22×C4—141no—
525C22×C4—141no—
526C22×C4—141no—
527C22×C4—141no—
528C22×C4—144no—
529C22×C4—141no—
530C22×C4—282no—
531C22×C4—282no—
532C22×C4—561no—
533C22×C4—561no—
534C22×C4—561no—
535C22×C4—561no—
536C22×C4—561no—
537C22×C4C2×C4×D712yes—
538C22×C4D4×D711yescharacteristic
539C22×C4D4×D712yes—
540C22×C4C23×D711yescharacteristic
541M16—44no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—141no—
548C2×C8—141no—
549C2×C8—141no—
550C2×C8—141no—
551C2×C8—141no—
552C2×C8—141no—
553C2×C8—284no—
554C2×C8#115912yes—
555C4⋊C4—24no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—74no—
562C4⋊C4—72no—
563C4⋊C4—72no—
564C4⋊C4—72no—
565C4⋊C4—144no—
566C4⋊C4—144no—
567C4⋊C4—144no—
568C4⋊C4—144no—
569C4⋊C4—144no—
570C4⋊C4—141no—
571C4⋊C4—141no—
572C4⋊C4—141no—
573C4⋊C4—141no—
574C4⋊C4—141no—
575C4⋊C4—282no—
576C4⋊C4C2×C4×D712yes—
577C22⋊C4—24no—
578C22⋊C4—74no—
579C22⋊C4—74no—
580C22⋊C4—81no—
581C22⋊C4—144no—
582C22⋊C4—282no—
583C22⋊C4—282no—
584C42—72no—
585C42—72no—
586C42—144no—
587C42—282no—
588C42—561no—
589C2×C7—42no—
590C2×C7#233911yescharacteristic
591C2×C7C2×#41911yescharacteristic
592C2×C7#289711yescharacteristic
593C2×C7#331411yescharacteristic
594C2×C7#331611yescharacteristic
595C2×C7#334411yescharacteristic
596C2×C7#334611yescharacteristic
597D7—24no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—72no—
605C23—72no—
606C23—72no—
607C23—141no—
608C23—141no—
609C23—141no—
610C23—141no—
611C23D7×C22⋊C412yes—
612C23C2×D4×D711yescharacteristic
613Q8—22no—
614Q8—22no—
615Q8—41no—
616Q8—41no—
617Q8—564no—
618D4—148no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—72no—
638C2×C4—72no—
639C2×C4—72no—
640C2×C4—141no—
641C2×C4—141no—
642C2×C4—141no—
643C2×C4—141no—
644C2×C4—141no—
645C2×C4—141no—
646C2×C4—142no—
647C2×C4—142no—
648C2×C4—142no—
649C2×C4—142no—
650C2×C4—142no—
651C2×C4—142no—
652C2×C4—142no—
653C2×C4—281no—
654C2×C4—281no—
655C2×C4—281no—
656C2×C4—281no—
657C2×C4—281no—
658C2×C4—281no—
659C2×C4—281no—
660C2×C4—281no—
661C2×C4—281no—
662C2×C4—564no—
663C2×C4—564no—
664C2×C4—564no—
665C2×C4D7×C22⋊C412yes—
666C2×C4C22×C4×D711yescharacteristic
667C2×C4C2×D4×D711yescharacteristic
668C2×C4C2×#115911yescharacteristic
669C2×C4#654811yescharacteristic
670C2×C4D7×#4111yescharacteristic
671C2×C4#655411yescharacteristic
672C8—22no—
673C8—41no—
674C8—281no—
675C8—281no—
676C7#2249711yescharacteristic, complemented, Sylow
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—74no—
685C22—142no—
686C22—142no—
687C22—142no—
688C22—142no—
689C22—142no—
690C22—142no—
691C22C2×D7×C22⋊C411yescharacteristic
692C22#9030111yescharacteristic
693C22#9030211yescharacteristic
694C22#9046511yescharacteristic
695C22D7×#13711yescharacteristic
696C22D7×#13711yescharacteristic
697C22#9046911yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—81no—
702C4—81no—
703C4—142no—
704C4—142no—
705C4—142no—
706C4—282no—
707C4—282no—
708C4—282no—
709C4—561no—
710C4C4×#115911yescharacteristic
711C4#9023711yescharacteristic
712C4#9028211yescharacteristic
713C4#9034611yescharacteristic
714C2—42no—
715C2—144no—
716C2#1173211711yescharacteristic
717C2#1173632711yescharacteristic
718C2D7×#41911yescharacteristic
719C2#1173826811yescharacteristic
720C2#1173827511yescharacteristic
721C2#1173836211yescharacteristic
722C2#1173836411yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1894C2
socleC23×C7C22×D4
prime radicalC22×C22⋊D7D4
cosocleC22×C4×C7C24
hypercenter#1894D7
hypocenterC7#22497
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
4. C7×#1894C2semidirect
5. #11729739C2semidirect
6. #11729447C2semidirect
7. #11728024C2semidirect
8. #11728022C2semidirect
9. #11727976C2semidirect
10. #11727974C2semidirect
11. #11727255C2semidirect
12. #11726626C2semidirect
13. D7×#340C2semidirect
14. #11726560C2semidirect
15. #11726554C2semidirect
25. #90326C4semidirect
77. C7×C22⋊Q8C2×C4semidirect
89. Q8×Dic7C2×C4semidirect
100. C2×C4⋊Dic7C2×C4semidirect
126. #6451C2×C4semidirect
147. #1894D7semidirect
403. C22⋊Q8C4×D7semidirect
676. C7#22497semidirect

Maximal subgroups

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

subgroupindex
C2×#903262
C2×#898992
#117314572
C7×#18942
#117297392
#117294472
#117280242
#117280222
#117279762
#117279742
#117272552
#117266262
D7×#3402
#117265602
#117265542
#224977