Finite Group Databasebeta

← #13370159

Subgroups — #13370159

Order 1792.

1122 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#552C211yesmaximal, characteristic
2#11739782C211yesmaximal, characteristic
3C2×#89783C211yesmaximal, characteristic
4#11729495C211yesmaximal, characteristic, complemented
5#11729492C211yesmaximal, characteristic, complemented
6#11729451C211yesmaximal, characteristic, complemented
7#11729450C211yesmaximal, characteristic, complemented
8#11729447C211yesmaximal, characteristic, complemented
9#11729447C211yesmaximal, characteristic, complemented
10#11729385C211yesmaximal, characteristic, complemented
11#11729380C211yesmaximal, characteristic, complemented
12#11729334C211yesmaximal, characteristic, complemented
13#11729329C211yesmaximal, characteristic, complemented
14#11729312C211yesmaximal, characteristic, complemented
15#11729308C211yesmaximal, characteristic, complemented
16C7×#552—24no—
17C7×#552C418yescomplemented
18C2×C7×#126—21no—
19C2×C7×#125—21no—
20C2×C7×#125C2211yescharacteristic
21C2×C7×#123—21no—
22C2×C7×C22⋊Q8C2211yescharacteristic
23C2×C7×C22⋊Q8C2211yescharacteristic
24C2×C4×C7×Q8C2211yescharacteristic
25C2×C4×C7×D4C2211yescharacteristic
26C2×C7×#117—21no—
27C2×C7×#117C2211yescharacteristic
28C22×C7×C4⋊C4C2211yescharacteristic
29C2×#6489C2211yescharacteristic
30C2×#6489C2211yescharacteristic
31C22×#1136C2211yescharacteristic
32C23×C7⋊C8C2211yescharacteristic
33C2×#6409C2211yescharacteristic
34C2×#6409C2211yescharacteristic
35C2×#6409C2211yescharacteristic
36C2×#6409C2211yescharacteristic
37#89993—21no—
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#22496—71nomaximal, Sylow
63C22×C7×Q8C2311yescharacteristic
64C22×C7×D4D411yescharacteristic
65C23×C4×C7—21no—
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C7×#126—28no—
69C7×#125—28no—
70C7×#125—22no—
71C7×#125C2×C414yes—
72C7×#123—28no—
73C7×C22⋊Q8—22no—
74C7×C22⋊Q8—22no—
75C7×C22⋊Q8C2×C414yes—
76C7×C22⋊Q8C2×C414yes—
77C4×C7×Q8—22no—
78C4×C7×Q8C2×C414yes—
79C4×C7×D4C2×C414yes—
80C4×C7×D4D414yes—
81C7×#117—22no—
82C7×#117—28no—
83C7×#117C2×C414yes—
84C2×C7×C4⋊C4—21no—
85C2×C7×C4⋊C4—22no—
86C2×C7×C4⋊C4—21no—
87C2×C7×C4⋊C4—21no—
88C2×C7×C4⋊C4—21no—
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⋊C4D411yescharacteristic
100C2×C7×C22⋊C4D411yescharacteristic
101C2×C42×C7—21no—
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#6409—22no—
132#6409—22no—
133#6409—41no—
134#6409—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×#552D711yescharacteristic
143C2×#435—71no—
144#2354—71no—
145#1992—71no—
146#1989—71no—
147#1894—71no—
148#1892—71no—
149#1873—71no—
150#1873—71no—
151#1825—71no—
152#1824—71no—
153#1803—71no—
154#1763—71no—
155#1736—71no—
156#1735—71no—
157C24×C7C2×D411yescharacteristic
158C24×C7C2×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—
165C2×C7×D4—41no—
166C2×C7×D4—41no—
167C2×C7×D4C22⋊C414yes—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—24no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—42no—
182C22×C4×C7—42no—
183C22×C4×C7C22×C412yes—
184C22×C4×C7C22×C412yes—
185C22×C4×C7C2×D411yescharacteristic
186C22×C4×C7C2×D411yescharacteristic
187C22×C4×C7C2×D411yescharacteristic
188C22×C4×C7C2×D411yescharacteristic
189C22×C4×C7C2×D412yes—
190C22×C4×C7C2×D412yes—
191C22×C4×C7C2411yescharacteristic
192C22×Dic7—21no—
193C22×Dic7—21no—
194C22×Dic7—21no—
195C22×Dic7—21no—
196C7×C4⋊C4—24no—
197C7×C4⋊C4—24no—
198C7×C4⋊C4—24no—
199C7×C4⋊C4—24no—
200C7×C4⋊C4—24no—
201C7×C4⋊C4—24no—
202C7×C4⋊C4—21no—
203C7×C4⋊C4—21no—
204C7×C4⋊C4—21no—
205C7×C4⋊C4C22⋊C414yes—
206C7×C4⋊C4C22×C412yes—
207C7×C4⋊C4C22×C412yes—
208C7×C4⋊C4C22×C412yes—
209C7×C22⋊C4—24no—
210C7×C22⋊C4—24no—
211C7×C22⋊C4—24no—
212C7×C22⋊C4C22⋊C414yes—
213C7×C22⋊C4C22⋊C414yes—
214C42×C7—24no—
215C42×C7—24no—
216C42×C7C22×C412yes—
217C42×C7C2×D412yes—
218C22⋊Dic7—42no—
219C22⋊Dic7—42no—
220C22⋊Dic7—81no—
221C22⋊Dic7—81no—
222C4⋊Dic7—21no—
223C4⋊Dic7—21no—
224C4⋊Dic7—21no—
225C4⋊Dic7—21no—
226C4⋊Dic7—21no—
227C4⋊Dic7—21no—
228C4⋊Dic7—21no—
229C4⋊Dic7—42no—
230C4⋊Dic7—81no—
231C4⋊Dic7#4112yes—
232C4×Dic7—42no—
233C4×Dic7—42no—
234C4×Dic7—42no—
235#1136—44no—
236C2×C7⋊C8—21no—
237C2×C7⋊C8—21no—
238C2×C7⋊C8—21no—
239C2×C7⋊C8—21no—
240C2×C7⋊C8—21no—
241C2×C7⋊C8—21no—
242C2×C7⋊C8—21no—
243C2×C7⋊C8—21no—
244C2×C7⋊C8—21no—
245C2×C7⋊C8—21no—
246C2×C7⋊C8—21no—
247C2×C7⋊C8—44no—
248C2×C7⋊C8#4112yes—
249C22×M16—71no—
250C23×C8—71no—
251#552—24no—
252#552Dic718yescomplemented
253C2×#126—21no—
254C2×#125—21no—
255C2×#125C2×D711yescharacteristic
256C2×#123—21no—
257C2×C22⋊Q8C2×D711yescharacteristic
258C2×C22⋊Q8C2×D711yescharacteristic
259C2×C4×Q8C2×D711yescharacteristic
260C2×C4×D4C2×D711yescharacteristic
261C2×#117—21no—
262C2×#117—71no—
263C2×#117—71no—
264C2×#117C2×D711yescharacteristic
265C22×C4⋊C4C2×D711yescharacteristic
266#435—144no—
267C2×C4⋊C8—71no—
268C2×#103—71no—
269C2×#103—71no—
270C2×#103—71no—
271C2×#103—71no—
272C2×C22⋊C8—71no—
273C2×C22⋊C8—71no—
274C2×#97—71no—
275#390—141no—
276#388—141no—
277#388—141no—
278#384—71no—
279#380—71no—
280#380—71no—
281C4×C4⋊C4—71no—
282C4×C4⋊C4—141no—
283#340—71no—
284#340—71no—
285#340—71no—
286#340—71no—
287#340—71no—
288#340—71no—
289#340—71no—
290#340—71no—
291#340—71no—
292#340—71no—
293#340—71no—
294#340—71no—
295C23×C7—21no—
296C23×C7—21no—
297C23×C7—21no—
298C23×C7—21no—
299C23×C7—21no—
300C23×C7—21no—
301C23×C7—21no—
302C23×C7—21no—
303C23×C7—21no—
304C23×C7—21no—
305C23×C7—21no—
306C23×C7—21no—
307C23×C7C2×C22⋊C412yes—
308C23×C7C2×C22⋊C412yes—
309C23×C7C22×D411yescharacteristic
310C7×Q8—22no—
311C7×Q8—22no—
312C7×Q8—41no—
313C7×Q8—41no—
314C7×D4—44no—
315C2×C4×C7—21no—
316C2×C4×C7—21no—
317C2×C4×C7—21no—
318C2×C4×C7—21no—
319C2×C4×C7—21no—
320C2×C4×C7—21no—
321C2×C4×C7—21no—
322C2×C4×C7—21no—
323C2×C4×C7—22no—
324C2×C4×C7—22no—
325C2×C4×C7—22no—
326C2×C4×C7—22no—
327C2×C4×C7—22no—
328C2×C4×C7—22no—
329C2×C4×C7—22no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—48no—
336C2×C4×C7—41no—
337C2×C4×C7—41no—
338C2×C4×C7—41no—
339C2×C4×C7—41no—
340C2×C4×C7—41no—
341C2×C4×C7—41no—
342C2×C4×C7—41no—
343C2×C4×C7—41no—
344C2×C4×C7C2×C22⋊C412yes—
345C2×C4×C7C2×C22⋊C412yes—
346C2×C4×C7C2×C22⋊C412yes—
347C2×C4×C7C2×C22⋊C412yes—
348C2×C4×C7C23×C411yescharacteristic
349C2×C4×C7C22×D411yescharacteristic
350C2×C4×C7C2×#4111yescharacteristic
351C2×C4×C7C2×#4111yescharacteristic
352C2×C4×C7H(5,𝔽2)11yescharacteristic
353C2×C4×C72−1+411yescharacteristic
354C2×Dic7—22no—
355C2×Dic7—41no—
356C2×Dic7—41no—
357C2×Dic7—41no—
358C2×Dic7—41no—
359C2×Dic7—41no—
360C2×Dic7—41no—
361C2×Dic7—41no—
362C2×Dic7—41no—
363C2×Dic7—41no—
364C2×Dic7—41no—
365C2×Dic7—41no—
366C7⋊C8—22no—
367C7⋊C8—41no—
368C7⋊C8—41no—
369C7⋊C8—41no—
370C22×Q8C22×D711yescharacteristic
371C22×D4C22⋊D711yescharacteristic
372C23×C4—21no—
373C23×C4C22×D711yescharacteristic
374C23×C4C22×D711yescharacteristic
375C2×M16—142no—
376C2×M16—142no—
377C2×M16—281no—
378C22×C8—71no—
379C22×C8—71no—
380C22×C8—71no—
381C22×C8—71no—
382C22×C8—142no—
383C22×C8—142no—
384C22×C8—281no—
385#126—28no—
386#125—28no—
387#125—22no—
388#125C2×Dic714yes—
389#123—28no—
390C22⋊Q8—22no—
391C22⋊Q8—22no—
392C22⋊Q8C2×Dic714yes—
393C22⋊Q8C2×Dic714yes—
394C4×Q8—22no—
395C4×Q8C2×Dic714yes—
396C4×D4C2×Dic714yes—
397C4×D4C22⋊D714yes—
398#117—22no—
399#117—28no—
400#117—142no—
401#117—142no—
402#117—281no—
403#117—281no—
404#117C2×Dic714yes—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—71no—
413C2×C4⋊C4—71no—
414C2×C4⋊C4—71no—
415C2×C4⋊C4—71no—
416C2×C4⋊C4—141no—
417C2×C4⋊C4—141no—
418C2×C4⋊C4C2×Dic714yes—
419C2×C4⋊C4C22⋊D711yescharacteristic
420C2×C4⋊C4C22×D711yescharacteristic
421C2×C4⋊C4C22×D711yescharacteristic
422C2×C4⋊C4C22×D711yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—141no—
427C2×C22⋊C4—141no—
428C2×C22⋊C4—141no—
429C2×C22⋊C4—141no—
430C2×C22⋊C4C22⋊D711yescharacteristic
431C2×C22⋊C4C22⋊D711yescharacteristic
432C2×C42—21no—
433C2×C42—21no—
434C2×C42—141no—
435C2×C42—141no—
436C2×C42—141no—
437C2×C42C22×D711yescharacteristic
438C4⋊C8—142no—
439#103—142no—
440#103—142no—
441#103—281no—
442#103—281no—
443C22⋊C8—142no—
444C22⋊C8—142no—
445#97—142no—
446#95—141no—
447#95—141no—
448#95—141no—
449C22×C7—22no—
450C22×C7—22no—
451C22×C7—22no—
452C22×C7—22no—
453C22×C7—22no—
454C22×C7—22no—
455C22×C7—41no—
456C22×C7—41no—
457C22×C7—41no—
458C22×C7—41no—
459C22×C7—41no—
460C22×C7—41no—
461C22×C7—41no—
462C22×C7—41no—
463C22×C7C22×C22⋊C411yescharacteristic
464C22×C7#54611yescharacteristic
465C22×C7#54711yescharacteristic
466C22×C7#57511yescharacteristic
467C22×C7#57511yescharacteristic
468C22×C7#57711yescharacteristic
469C22×C7#57811yescharacteristic
470C4×C7—22no—
471C4×C7—22no—
472C4×C7—22no—
473C4×C7—22no—
474C4×C7—42no—
475C4×C7—42no—
476C4×C7—42no—
477C4×C7—42no—
478C4×C7C4×#4111yescharacteristic
479C4×C7#52011yescharacteristic
480C4×C7#54611yescharacteristic
481C4×C7#54711yescharacteristic
482Dic7—42no—
483Dic7—81no—
484Dic7—81no—
485Dic7—81no—
486C24C2×C22⋊D711yescharacteristic
487C24C2×C22⋊D711yescharacteristic
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8C22×Dic712yes—
494C2×D4—41no—
495C2×D4—41no—
496C2×D4C22⋊Dic714yes—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—24no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—141no—
513C22×C4—141no—
514C22×C4—141no—
515C22×C4—141no—
516C22×C4C22×Dic712yes—
517C22×C4C22×Dic712yes—
518C22×C4C2×C22⋊D711yescharacteristic
519C22×C4C2×C22⋊D711yescharacteristic
520C22×C4C2×C22⋊D711yescharacteristic
521C22×C4C2×C22⋊D711yescharacteristic
522C22×C4C2×C22⋊D712yes—
523C22×C4C2×C22⋊D712yes—
524C22×C4C23×D711yescharacteristic
525M16—284no—
526C2×C8—72no—
527C2×C8—141no—
528C2×C8—141no—
529C2×C8—141no—
530C2×C8—141no—
531C2×C8—141no—
532C2×C8—141no—
533C2×C8—141no—
534C2×C8—141no—
535C2×C8—141no—
536C2×C8—141no—
537C2×C8—141no—
538C2×C8—284no—
539C4⋊C4—24no—
540C4⋊C4—24no—
541C4⋊C4—24no—
542C4⋊C4—24no—
543C4⋊C4—24no—
544C4⋊C4—24no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—72no—
549C4⋊C4—141no—
550C4⋊C4—141no—
551C4⋊C4—141no—
552C4⋊C4—141no—
553C4⋊C4—141no—
554C4⋊C4—141no—
555C4⋊C4—141no—
556C4⋊C4—282no—
557C4⋊C4—561no—
558C4⋊C4C22⋊Dic714yes—
559C4⋊C4C22×Dic712yes—
560C4⋊C4C22×Dic712yes—
561C4⋊C4C22×Dic712yes—
562C22⋊C4—24no—
563C22⋊C4—24no—
564C22⋊C4—24no—
565C22⋊C4—282no—
566C22⋊C4—282no—
567C22⋊C4—561no—
568C22⋊C4—561no—
569C22⋊C4C22⋊Dic714yes—
570C22⋊C4C22⋊Dic714yes—
571C42—24no—
572C42—24no—
573C42—282no—
574C42—282no—
575C42—282no—
576C42C22×Dic712yes—
577C42C2×C22⋊D712yes—
578C2×C7—42no—
579C2×C7—42no—
580C2×C7#233911yescharacteristic
581C2×C7#289611yescharacteristic
582C2×C7#289811yescharacteristic
583C2×C7#331511yescharacteristic
584C2×C7#331711yescharacteristic
585C2×C7#334811yescharacteristic
586C2×C7#334911yescharacteristic
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23C2×C22⋊Dic712yes—
600C23C2×C22⋊Dic712yes—
601C23C22×C22⋊D711yescharacteristic
602Q8—22no—
603Q8—22no—
604Q8—41no—
605Q8—41no—
606D4—44no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—48no—
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—142no—
637C2×C4—281no—
638C2×C4—281no—
639C2×C4—281no—
640C2×C4—281no—
641C2×C4—281no—
642C2×C4—281no—
643C2×C4—281no—
644C2×C4—281no—
645C2×C4—281no—
646C2×C4—281no—
647C2×C4—281no—
648C2×C4C2×C22⋊Dic712yes—
649C2×C4C2×C22⋊Dic712yes—
650C2×C4C2×C22⋊Dic712yes—
651C2×C4C2×C22⋊Dic712yes—
652C2×C4D7×#4111yescharacteristic
653C2×C4D7×#4111yescharacteristic
654C2×C4#655311yescharacteristic
655C2×C4#655411yescharacteristic
656C2×C4C23×Dic711yescharacteristic
657C2×C4C22×C22⋊D711yescharacteristic
658C8—142no—
659C8—281no—
660C8—281no—
661C8—281no—
662C7#2249611yescharacteristic, complemented, Sylow
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22#9051311yescharacteristic
678C22#9051311yescharacteristic
679C22#9051511yescharacteristic
680C22#9052011yescharacteristic
681C22#9052811yescharacteristic
682C22#9052911yescharacteristic
683C22C22×C22⋊Dic711yescharacteristic
684C4—22no—
685C4—22no—
686C4—22no—
687C4—22no—
688C4—42no—
689C4—42no—
690C4—42no—
691C4—42no—
692C4—282no—
693C4—561no—
694C4—561no—
695C4—561no—
696C4#9051511yescharacteristic
697C4#41×Dic711yescharacteristic
698C4#9051811yescharacteristic
699C4#9052011yescharacteristic
700C2—42no—
701C2—42no—
702C2#1174103911yescharacteristic
703C2#1174104011yescharacteristic
704C2#1174104511yescharacteristic
705C2#1174104911yescharacteristic
706C2#1174151711yescharacteristic
707C2#1174153311yescharacteristic
708C2#1174155611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#552C2
socleC23×C7C22×D4
prime radicalC22×C7×D4D4
cosocleC22×C4×C7C24
hypercenterC2×#552D7
hypocenterC7#22496
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
4. #11729495C2semidirect
5. #11729492C2semidirect
6. #11729451C2semidirect
7. #11729450C2semidirect
8. #11729447C2semidirect
9. #11729447C2semidirect
10. #11729385C2semidirect
11. #11729380C2semidirect
12. #11729334C2semidirect
13. #11729329C2semidirect
14. #11729312C2semidirect
15. #11729308C2semidirect
17. C7×#552C4semidirect
252. #552Dic7semidirect
662. C7#22496semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5522
#117397822
C2×#897832
#117294952
#117294922
#117294512
#117294502
#117294472
#117293852
#117293802
#117293342
#117293292
#117293122
#117293082
#224967