Finite Group Databasebeta

← #13370175

Subgroups — #13370175

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×#90202C211yesmaximal, characteristic
2C2×#89899C211yesmaximal, characteristic
3#11739717C211yesmaximal, characteristic
4C7×#1736C211yesmaximal, characteristic, complemented
5#11729743C211yesmaximal, characteristic, complemented
6#11729339C211yesmaximal, characteristic, complemented
7#11729307C211yesmaximal, characteristic, complemented
8#11726659C211yesmaximal, characteristic, complemented
9#11726636C211yesmaximal, characteristic, complemented
10#11726632C211yesmaximal, characteristic, complemented
11#11726626C211yesmaximal, characteristic, complemented
12D7×#340C211yesmaximal, characteristic, complemented
13#11726560C211yesmaximal, characteristic, complemented
14#11726554C211yesmaximal, characteristic, complemented
15#11726537C211yesmaximal, characteristic, complemented
16C22×C7×M16C2211yescharacteristic
17C2×C7×#117C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C2×C4×C22⋊D7—21no—
20C2×C4×C22⋊D7C2211yescharacteristic
21C2×#6487—21no—
22C2×#6487C2211yescharacteristic
23C22×C8×D7C2211yescharacteristic
24#90202—24no—
25#90202C418yescomplemented
26C2×#6460C2211yescharacteristic
27C2×#6459—21no—
28C2×D7×C4⋊C4C2211yescharacteristic
29C2×D7×C4⋊C4C2211yescharacteristic
30C2×#6452—21no—
31C2×#6451C2211yescharacteristic
32C2×#6450C2211yescharacteristic
33#89984C2211yescharacteristic
34C2×C22⋊(C7⋊C8)C2211yescharacteristic
35#89899—24no—
36C2×(C2×D7)⋊C8C2211yescharacteristic
37C2×#6390C2211yescharacteristic
38C2×#6390C2211yescharacteristic
39C2×#6389C2211yescharacteristic
40C2×Dic7⋊C8C2211yescharacteristic
41#89759C2211yescharacteristic
42#89749C2211yescharacteristic
43C4⋊C4×Dic7C2211yescharacteristic
44C2×#6384C2211yescharacteristic
45C2×#6384C2211yescharacteristic
46#89728—21no—
47#89717—21no—
48C4×(C2×D7)⋊C4—21no—
49#89705—21no—
50C7×#340C2211yescharacteristic
51C7×#340C2211yescharacteristic
52C7×#340C2211yescharacteristic
53C7×#340C2211yescharacteristic
54#89346C2211yescharacteristic
55#89346C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#22497—71nomaximal, Sylow
63C23×C4×C7—21no—
64C23×C4×C7C2311yescharacteristic
65C22×C22⋊D7D411yescharacteristic
66C22×C4×D7—21no—
67C22×C4×D7—21no—
68C22×C4×D7C2311yescharacteristic
69C22×Dic14—21no—
70C22×Dic14C2311yescharacteristic
71C2×C7×M16—22no—
72C2×C7×M16—22no—
73C2×C7×M16—41no—
74C22×C7×C8C2311yescharacteristic
75C22×C7×C8C2311yescharacteristic
76C7×#117—22no—
77C7×#117—41no—
78C2×C7×C4⋊C4—21no—
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4C2×C414yescomplemented
81C2×C7×C4⋊C4C2311yescharacteristic
82C2×C7×C4⋊C4C2311yescharacteristic
83C2×C7×C4⋊C4C2311yescharacteristic
84C2×C7×C4⋊C4C2311yescharacteristic
85C2×C7×C22⋊C4—21no—
86C2×C42×C7—21no—
87C2×C22⋊Dic7—21no—
88C2×C22⋊Dic7—21no—
89C2×C22⋊Dic7D411yescharacteristic
90C4×C22⋊D7—28no—
91C4×C22⋊D7C2×C414yes—
92C4×C22⋊D7D414yes—
93C2×(C2×D7)⋊C4—21no—
94C2×(C2×D7)⋊C4—21no—
95C2×(C2×D7)⋊C4D411yescharacteristic
96C2×C4⋊Dic7—21no—
97C2×C4⋊Dic7C2311yescharacteristic
98C2×C4⋊Dic7C2311yescharacteristic
99C2×C4⋊Dic7C2311yescharacteristic
100#6487—22no—
101#6487—28no—
102#6487C2×C414yescomplemented
103C2×Dic7⋊C4—21no—
104C2×Dic7⋊C4—21no—
105C2×Dic7⋊C4—21no—
106C2×Dic7⋊C4—21no—
107C2×Dic7⋊C4—21no—
108C2×Dic7⋊C4D411yescharacteristic
109C2×C4×Dic7—21no—
110C2×C4×Dic7—21no—
111C2×C4×Dic7C2311yescharacteristic
112C22×C7⋊C8C2311yescharacteristic
113C22×C7⋊C8C2311yescharacteristic
114C2×C8×D7—22no—
115C2×C8×D7—22no—
116C2×C8×D7—41no—
117#6460—22no—
118#6460C2×C414yes—
119#6459—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#6450—22no—
128#6450C2×C414yescomplemented
129C7⋊#95—21no—
130C7⋊#95—21no—
131C7⋊#95—21no—
132C7⋊#95—21no—
133C7⋊#95—21no—
134C22⋊(C7⋊C8)—22no—
135(C2×D7)⋊C8—22no—
136#6390—22no—
137#6390—41no—
138#6389—22no—
139Dic7⋊C8—22no—
140#6384—22no—
141#6384—41no—
142C2×#554—71no—
143C2×#435—71no—
144#2352—71no—
145#1993—71no—
146#1988—71no—
147#1894—71no—
148#1892—71no—
149#1873—71no—
150#1872—71no—
151#1824—71no—
152#1823—71no—
153#1805—71no—
154#1763—71no—
155#1736D711yescharacteristic, complemented
156C2×#340—71no—
157C24×C7C2×D411yescharacteristic
158C23×D7C2×D411yescharacteristic
159C22×C4×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—24no—
167C22×C4×C7—21no—
168C22×C4×C7—81no—
169C22×C4×C7—81no—
170C22×C4×C7C22×C412yes—
171C22×C4×C7C2×D411yescharacteristic
172C22×C4×C7C2×D412yes—
173C22×C4×C7C2411yescharacteristic
174C2×C22⋊D7—22no—
175C2×C22⋊D7—22no—
176C2×C22⋊D7C22⋊C414yes—
177C22×Dic7—21no—
178C22×Dic7—21no—
179C22×Dic7—21no—
180C22×Dic7—21no—
181C22×Dic7C2×D411yescharacteristic
182C22×Dic7C2×D411yescharacteristic
183C22×Dic7C2×D411yescharacteristic
184C2×C4×D7—21no—
185C2×C4×D7—21no—
186C2×C4×D7—21no—
187C2×C4×D7—21no—
188C2×C4×D7—24no—
189C2×C4×D7—42no—
190C2×C4×D7—42no—
191C2×C4×D7—81no—
192C2×C4×D7—81no—
193C2×C4×D7—81no—
194C2×C4×D7C22×C412yes—
195C2×C4×D7C2×D412yes—
196C2×Dic14—21no—
197C2×Dic14—21no—
198C2×Dic14—21no—
199C2×Dic14—21no—
200C2×Dic14—21no—
201C2×Dic14—24no—
202C2×Dic14—81no—
203C2×Dic14—81no—
204C2×Dic14C22×C412yes—
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×C4⋊C4C22×C412yes—
220C7×C4⋊C4#4112yes—
221C7×C22⋊C4—42no—
222C42×C7—42no—
223C22⋊Dic7—24no—
224C22⋊Dic7—81no—
225C22⋊Dic7C22⋊C414yes—
226(C2×D7)⋊C4—24no—
227(C2×D7)⋊C4—42no—
228(C2×D7)⋊C4C22⋊C414yes—
229C4⋊Dic7—21no—
230C4⋊Dic7—24no—
231C4⋊Dic7—21no—
232C4⋊Dic7—21no—
233C4⋊Dic7—21no—
234C4⋊Dic7—21no—
235C4⋊Dic7C22×C412yes—
236Dic7⋊C4—24no—
237Dic7⋊C4—24no—
238Dic7⋊C4—24no—
239Dic7⋊C4—24no—
240Dic7⋊C4—42no—
241Dic7⋊C4C22⋊C414yes—
242C4×Dic7—24no—
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—71no—
261C2×C22⋊Q8—141no—
262C2×C22⋊Q8—141no—
263C2×C4×Q8—71no—
264C2×C4×D4—71no—
265C2×C4×D4—141no—
266C2×#117C2×D711yescharacteristic
267C22×C4⋊C4—71no—
268C22×C4⋊C4—71no—
269C22×C4⋊C4C2×D711yescharacteristic
270#435—144no—
271C2×C4⋊C8—71no—
272C2×#103—71no—
273C2×#103—71no—
274C2×#103—71no—
275C2×#103—71no—
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#380—71no—
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#340C2×D711yescharacteristic
296#340C2×D711yescharacteristic
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—
314C2×C4×C7—21no—
315C2×C4×C7—21no—
316C2×C4×C7—22no—
317C2×C4×C7—22no—
318C2×C4×C7—22no—
319C2×C4×C7—22no—
320C2×C4×C7—22no—
321C2×C4×C7—22no—
322C2×C4×C7—22no—
323C2×C4×C7—41no—
324C2×C4×C7—41no—
325C2×C4×C7—41no—
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—84no—
333C2×C4×C7C2×C22⋊C412yes—
334C2×C4×C7C23×C411yescharacteristic
335C2×C4×C7C22×D411yescharacteristic
336C2×C4×C7C2×#4111yescharacteristic
337C2×C4×C7C2×#4111yescharacteristic
338C2×C4×C7H(5,𝔽2)11yescharacteristic
339C2×C4×C72−1+411yescharacteristic
340C22⋊D7—28no—
341C2×Dic7—21no—
342C2×Dic7—21no—
343C2×Dic7—21no—
344C2×Dic7—21no—
345C2×Dic7—21no—
346C2×Dic7—21no—
347C2×Dic7—22no—
348C2×Dic7—22no—
349C2×Dic7—41no—
350C2×Dic7—41no—
351C2×Dic7—41no—
352C2×Dic7—41no—
353C2×Dic7—41no—
354C2×Dic7—41no—
355C2×Dic7—41no—
356C2×Dic7—41no—
357C2×Dic7—41no—
358C2×Dic7—41no—
359C2×Dic7C2×C22⋊C412yes—
360C2×Dic7C2×C22⋊C412yes—
361C2×Dic7C2×C22⋊C412yes—
362C4×D7—22no—
363C4×D7—22no—
364C4×D7—22no—
365C4×D7—22no—
366C4×D7—84no—
367C4×D7—84no—
368Dic14—22no—
369Dic14—22no—
370Dic14—41no—
371Dic14—41no—
372Dic14—84no—
373C7×C8—22no—
374C7×C8—41no—
375C7⋊C8—41no—
376C7⋊C8—41no—
377C22×Q8—71no—
378C22×Q8—141no—
379C22×D4—71no—
380C23×C4—21no—
381C23×C4—71no—
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—74no—
399C22⋊Q8—74no—
400C22⋊Q8—148no—
401C22⋊Q8—148no—
402C22⋊Q8—142no—
403C22⋊Q8—142no—
404C4×Q8—74no—
405C4×Q8—142no—
406C4×D4—74no—
407C4×D4—74no—
408C4×D4—148no—
409#117—22no—
410#117—41no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—71no—
414C2×C4⋊C4—71no—
415C2×C4⋊C4—74no—
416C2×C4⋊C4—71no—
417C2×C4⋊C4—71no—
418C2×C4⋊C4—142no—
419C2×C4⋊C4—141no—
420C2×C4⋊C4—141no—
421C2×C4⋊C4—141no—
422C2×C4⋊C4—141no—
423C2×C4⋊C4—141no—
424C2×C4⋊C4—142no—
425C2×C4⋊C4—141no—
426C2×C4⋊C4—281no—
427C2×C4⋊C4C4×D714yescomplemented
428C2×C4⋊C4C22×D711yescharacteristic
429C2×C4⋊C4C22×D711yescharacteristic
430C2×C4⋊C4C22×D711yescharacteristic
431C2×C4⋊C4C22×D711yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—71no—
434C2×C22⋊C4—71no—
435C2×C22⋊C4—141no—
436C2×C22⋊C4—141no—
437C2×C22⋊C4—141no—
438C2×C22⋊C4—141no—
439C2×C42—21no—
440C2×C42—71no—
441C2×C42—141no—
442C2×C42—141no—
443C4⋊C8—142no—
444#103—142no—
445#103—142no—
446#103—281no—
447#103—281no—
448C22⋊C8—142no—
449C22⋊C8—142no—
450#97—142no—
451#95—141no—
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—42no—
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—81no—
492Dic7—81no—
493C24—71no—
494C24D4×D711yescharacteristic
495C2×Q8—72no—
496C2×Q8—144no—
497C2×Q8—141no—
498C2×Q8—141no—
499C2×Q8—141no—
500C2×Q8—141no—
501C2×Q8—141no—
502C2×Q8—561no—
503C2×Q8—561no—
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—24no—
515C22×C4—21no—
516C22×C4—71no—
517C22×C4—71no—
518C22×C4—71no—
519C22×C4—72no—
520C22×C4—72no—
521C22×C4—81no—
522C22×C4—81no—
523C22×C4—144no—
524C22×C4—141no—
525C22×C4—141no—
526C22×C4—141no—
527C22×C4—141no—
528C22×C4—141no—
529C22×C4—141no—
530C22×C4—141no—
531C22×C4—141no—
532C22×C4—282no—
533C22×C4—282no—
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#115712yes—
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—144no—
564C4⋊C4—144no—
565C4⋊C4—144no—
566C4⋊C4—144no—
567C4⋊C4—144no—
568C4⋊C4—141no—
569C4⋊C4—141no—
570C4⋊C4—141no—
571C4⋊C4—141no—
572C4⋊C4—141no—
573C4⋊C4—282no—
574C4⋊C4C2×C4×D712yes—
575C4⋊C4C2×C4×D712yes—
576C4⋊C4#115712yes—
577C22⋊C4—42no—
578C22⋊C4—74no—
579C22⋊C4—74no—
580C22⋊C4—144no—
581C22⋊C4—144no—
582C22⋊C4—282no—
583C22⋊C4—561no—
584C42—42no—
585C42—72no—
586C42—72no—
587C42—144no—
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—142no—
614Q8—142no—
615Q8—281no—
616Q8—281no—
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—22no—
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—84no—
641C2×C4—141no—
642C2×C4—141no—
643C2×C4—141no—
644C2×C4—141no—
645C2×C4—141no—
646C2×C4—141no—
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—281no—
663C2×C4—564no—
664C2×C4—564no—
665C2×C4D7×C22⋊C412yes—
666C2×C4C22×C4×D711yescharacteristic
667C2×C4C2×#115711yescharacteristic
668C2×C4C2×#115711yescharacteristic
669C2×C4C2×D4×D711yescharacteristic
670C2×C4#654811yescharacteristic
671C2×C4#655111yescharacteristic
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#9018111yescharacteristic
693C22#9019811yescharacteristic
694C22#9046511yescharacteristic
695C22#9046611yescharacteristic
696C22D7×#13711yescharacteristic
697C22D7×#13711yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—81no—
703C4—142no—
704C4—142no—
705C4—142no—
706C4—282no—
707C4—282no—
708C4—561no—
709C4—561no—
710C4C4×#115711yescharacteristic
711C4#9018111yescharacteristic
712C4#9019511yescharacteristic
713C4#9019811yescharacteristic
714C2—42no—
715C2—144no—
716C2#1173081311yescharacteristic
717C2#1173634311yescharacteristic
718C2#1173634511yescharacteristic
719C2#1173637011yescharacteristic
720C2D7×#41911yescharacteristic
721C2#1173666911yescharacteristic
722C2#1173667111yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1736C2
socleC23×C7C22×D4
prime radicalC22×C22⋊D7D4
cosocleC22×C4×C7C24
hypercenter#1736D7
hypocenterC7#22497
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
4. C7×#1736C2semidirect
5. #11729743C2semidirect
6. #11729339C2semidirect
7. #11729307C2semidirect
8. #11726659C2semidirect
9. #11726636C2semidirect
10. #11726632C2semidirect
11. #11726626C2semidirect
12. D7×#340C2semidirect
13. #11726560C2semidirect
14. #11726554C2semidirect
15. #11726537C2semidirect
25. #90202C4semidirect
80. C2×C7×C4⋊C4C2×C4semidirect
102. #6487C2×C4semidirect
126. #6451C2×C4semidirect
128. #6450C2×C4semidirect
155. #1736D7semidirect
427. C2×C4⋊C4C4×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×#902022
C2×#898992
#117397172
C7×#17362
#117297432
#117293392
#117293072
#117266592
#117266362
#117266322
#117266262
D7×#3402
#117265602
#117265542
#117265372
#224977