Finite Group Databasebeta

← C2×#11735232 #13525613

Subgroups — C2×#11735232 #13525613

Order 1792.

2446 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6452C211yesmaximal, characteristic
2C22×#6452C211yesmaximal, characteristic
3C2×C7×#398C211yesmaximal, characteristic
4C2×#89756C211yesmaximal, characteristic
5C2×#89744C211yesmaximal, characteristic
6C2×#89744C211yesmaximal, characteristic
7C2×#89748C211yesmaximal, characteristic
8C2×#89748C211yesmaximal, characteristic
9C2×#89748C211yesmaximal, characteristic
10#11735232C2116yesmaximal, direct product factor
11C2×#89433C211yesmaximal, characteristic
12C2×#89429C211yesmaximal, characteristic
13C2×#89419C211yesmaximal, characteristic
14C2×#89419C211yesmaximal, characteristic
15C2×#89421C211yesmaximal, characteristic
16C2×#89421C211yesmaximal, characteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C4⋊Dic7C2211yescharacteristic
22C22×C4⋊Dic7C2211yescharacteristic
23C22×C4⋊Dic7C2211yescharacteristic
24C22×C4⋊Dic7C2211yescharacteristic
25C22×Dic7⋊C4C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C22×C4×Dic7C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C22×C4×Dic7C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C2×#6452—28no—
45C2×#6452—28no—
46C2×#6452C2218yes—
47C2×#6452C2218yes—
48C7×#398C2218yes—
49C2×C7×#95C2211yescharacteristic
50C2×C7×#95C2211yescharacteristic
51C2×C7×#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57#89756C2218yes—
58#89748C2218yes—
59#89748C2218yes—
60#89748C2218yes—
61#89744C2218yes—
62#89744C2218yes—
63#89433C2218yes—
64#89429C2218yes—
65#89421C2218yes—
66#89421C2218yes—
67#89419C2218yes—
68#89419C2218yes—
69C2×#2552—71nomaximal, Sylow
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C2×C7×C4⋊C4—24no—
86C2×C7×C4⋊C4—24no—
87C2×C7×C4⋊C4—42no—
88C2×C7×C4⋊C4—42no—
89C2×C7×C4⋊C4C2314yes—
90C2×C7×C4⋊C4C2314yes—
91C2×C7×C4⋊C4C2314yes—
92C2×C7×C4⋊C4C2314yes—
93C2×C4⋊Dic7—24no—
94C2×C4⋊Dic7—24no—
95C2×C4⋊Dic7—42no—
96C2×C4⋊Dic7—42no—
97C2×C4⋊Dic7C2314yes—
98C2×C4⋊Dic7C2314yes—
99C2×C4⋊Dic7C2314yes—
100C2×C4⋊Dic7C2314yes—
101C2×Dic7⋊C4—24no—
102C2×Dic7⋊C4—24no—
103C2×Dic7⋊C4—24no—
104C2×Dic7⋊C4—24no—
105C2×Dic7⋊C4—24no—
106C2×Dic7⋊C4—24no—
107C2×Dic7⋊C4—24no—
108C2×Dic7⋊C4—24no—
109C2×Dic7⋊C4—24no—
110C2×Dic7⋊C4—24no—
111C2×Dic7⋊C4—42no—
112C2×Dic7⋊C4—42no—
113C2×Dic7⋊C4D418yes—
114C2×Dic7⋊C4Q818yes—
115C2×Dic7⋊C4C2314yes—
116C2×Dic7⋊C4C2314yes—
117C2×Dic7⋊C4C2314yes—
118C2×Dic7⋊C4C2314yes—
119C2×Dic7⋊C4C2314yes—
120C2×Dic7⋊C4C2314yes—
121C2×Dic7⋊C4C2314yes—
122C2×Dic7⋊C4C2314yes—
123C2×Dic7⋊C4C2314yes—
124C2×Dic7⋊C4C2314yes—
125C2×Dic7⋊C4C2314yes—
126C2×Dic7⋊C4C2314yes—
127C2×Dic7⋊C4C2314yes—
128C2×Dic7⋊C4C2314yes—
129C2×C4×Dic7—24no—
130C2×C4×Dic7—24no—
131C2×C4×Dic7—24no—
132C2×C4×Dic7—24no—
133C2×C4×Dic7Q818yes—
134C2×C4×Dic7C2314yes—
135C2×C4×Dic7C2314yes—
136C2×C4×Dic7C2314yes—
137C2×C4×Dic7C2314yes—
138C2×C4×Dic7C2314yes—
139#6452—232no—
140#6452—232no—
141C7×#95C2314yes—
142C7×#95C2314yes—
143C7×#95C2314yes—
144C7⋊#95C2314yes—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C22×#125—71no—
150C22×#125—71no—
151#2552—716no—
152C2×#398—71no—
153C2×#398—71no—
154C2×#398—71no—
155C2×#398D711yescharacteristic
156C2×#389—71no—
157C2×#389—71no—
158C2×#389—71no—
159C2×#389—71no—
160C2×#384—71no—
161C2×#384—71no—
162C2×#384—71no—
163C2×C4×C4⋊C4—71no—
164C2×C4×C4⋊C4—71no—
165C24×C7C2411yescharacteristic
166C22×C4×C7—22no—
167C22×C4×C7—22no—
168C22×C4×C7—22no—
169C22×C4×C7—22no—
170C22×C4×C7—22no—
171C22×C4×C7—22no—
172C22×C4×C7—22no—
173C22×C4×C7—22no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
184C22×C4×C7C2×D414yes—
185C22×C4×C7C2×Q814yes—
186C22×C4×C7C2×Q814yes—
187C22×C4×C7C2412yes—
188C22×C4×C7C2412yes—
189C22×C4×C7C2412yes—
190C22×C4×C7C2412yes—
191C22×C4×C7C2412yes—
192C22×C4×C7C2412yes—
193C22×C4×C7C2412yes—
194C22×Dic7—22no—
195C22×Dic7—22no—
196C22×Dic7—22no—
197C22×Dic7—22no—
198C22×Dic7—22no—
199C22×Dic7—22no—
200C22×Dic7—22no—
201C22×Dic7—22no—
202C22×Dic7—22no—
203C22×Dic7—22no—
204C22×Dic7—22no—
205C22×Dic7—22no—
206C22×Dic7—22no—
207C22×Dic7—22no—
208C22×Dic7—22no—
209C22×Dic7—22no—
210C22×Dic7C2×D414yes—
211C22×Dic7C2×D414yes—
212C22×Dic7C2×Q814yes—
213C22×Dic7C2×Q814yes—
214C22×Dic7C2×Q814yes—
215C22×Dic7C2×Q814yes—
216C22×Dic7#4114yes—
217C22×Dic7#4114yes—
218C22×Dic7C2412yes—
219C22×Dic7C2412yes—
220C22×Dic7C2412yes—
221C22×Dic7C2412yes—
222C22×Dic7C2412yes—
223C22×Dic7C2412yes—
224C22×Dic7C2412yes—
225C22×Dic7C2412yes—
226C7×C4⋊C4—28no—
227C7×C4⋊C4—28no—
228C7×C4⋊C4—44no—
229C7×C4⋊C4—44no—
230C4⋊Dic7—28no—
231C4⋊Dic7—28no—
232C4⋊Dic7—44no—
233C4⋊Dic7—44no—
234Dic7⋊C4—28no—
235Dic7⋊C4—28no—
236Dic7⋊C4—28no—
237Dic7⋊C4—28no—
238Dic7⋊C4—28no—
239Dic7⋊C4—28no—
240Dic7⋊C4—28no—
241Dic7⋊C4—28no—
242Dic7⋊C4—28no—
243Dic7⋊C4—28no—
244Dic7⋊C4—44no—
245Dic7⋊C4—44no—
246Dic7⋊C4C2×D4116yes—
247Dic7⋊C4C2×Q8116yes—
248C4×Dic7—28no—
249C4×Dic7—28no—
250C4×Dic7—28no—
251C4×Dic7—28no—
252C4×Dic7C2×Q8116yes—
253C2×#125—78no—
254C2×#125—78no—
255C2×#125—148no—
256C2×#125—148no—
257C22×C4⋊C4—71no—
258C22×C4⋊C4—71no—
259C22×C4⋊C4—71no—
260C22×C4⋊C4—71no—
261C22×C4⋊C4—71no—
262C22×C4⋊C4—71no—
263C22×C4⋊C4—71no—
264C22×C4⋊C4—71no—
265C22×C4⋊C4—71no—
266C22×C4⋊C4—71no—
267C22×C4⋊C4—71no—
268C22×C4⋊C4—71no—
269C22×C4⋊C4—71no—
270C22×C4⋊C4—71no—
271C22×C4⋊C4—71no—
272C22×C4⋊C4—71no—
273C22×C4⋊C4—71no—
274C22×C4⋊C4—71no—
275C22×C4⋊C4C2×D711yescharacteristic
276C22×C4⋊C4C2×D711yescharacteristic
277C22×C4⋊C4C2×D711yescharacteristic
278C22×C4⋊C4C2×D711yescharacteristic
279C22×C42—71no—
280C22×C42—71no—
281C22×C42—71no—
282C22×C42—71no—
283C22×C42—71no—
284#398—78no—
285#398—78no—
286#398—78no—
287#398C2×D718yes—
288#389—78no—
289#389—78no—
290#389—78no—
291#389—78no—
292#384—78no—
293#384—78no—
294#384—78no—
295C4×C4⋊C4—78no—
296C4×C4⋊C4—78no—
297C2×#95—71no—
298C2×#95—71no—
299C2×#95—71no—
300C2×#95—71no—
301C2×#95—71no—
302C2×#95C2×D711yescharacteristic
303C2×#95C2×D711yescharacteristic
304C2×#95C2×D711yescharacteristic
305C23×C7C22×D412yes—
306C23×C7C22×Q812yes—
307C23×C7C22×Q812yes—
308C23×C7C2×#4112yes—
309C23×C7C2×#4112yes—
310C23×C7H(5,𝔽2)12yes—
311C23×C72−1+412yes—
312C23×C7C2511yescharacteristic
313C2×C4×C7—28no—
314C2×C4×C7—28no—
315C2×C4×C7—28no—
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—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—44no—
335C2×C4×C7—44no—
336C2×C4×C7—44no—
337C2×C4×C7—44no—
338C2×C4×C7C22×D414yes—
339C2×C4×C7C22×Q814yes—
340C2×C4×C7C22×Q814yes—
341C2×Dic7—28no—
342C2×Dic7—28no—
343C2×Dic7—22no—
344C2×Dic7—22no—
345C2×Dic7—22no—
346C2×Dic7—22no—
347C2×Dic7—22no—
348C2×Dic7—22no—
349C2×Dic7—22no—
350C2×Dic7—22no—
351C2×Dic7—22no—
352C2×Dic7—22no—
353C2×Dic7—22no—
354C2×Dic7—22no—
355C2×Dic7—22no—
356C2×Dic7—22no—
357C2×Dic7—22no—
358C2×Dic7—22no—
359C2×Dic7—44no—
360C2×Dic7—44no—
361C2×Dic7—44no—
362C2×Dic7—44no—
363C2×Dic7#125116yescomplemented
364C2×Dic7C4⋊Q8116yes—
365C2×Dic7C22×D414yes—
366C2×Dic7C22×D414yes—
367C2×Dic7C22×Q814yes—
368C2×Dic7C22×Q814yes—
369C2×Dic7C22×Q814yes—
370C2×Dic7C22×Q814yes—
371C2×Dic7C2×#4114yes—
372C2×Dic7C2×#4114yes—
373C23×C4—71no—
374C23×C4—71no—
375C23×C4—71no—
376C23×C4—71no—
377C23×C4—71no—
378C23×C4—71no—
379C23×C4—71no—
380C23×C4—71no—
381C23×C4C22×D711yescharacteristic
382C23×C4C22×D711yescharacteristic
383C23×C4C22×D711yescharacteristic
384C23×C4C22×D711yescharacteristic
385C23×C4C22×D711yescharacteristic
386C23×C4C22×D711yescharacteristic
387C23×C4C22×D711yescharacteristic
388#125—1432no—
389#125—1432no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4—42no—
394C2×C4⋊C4—78no—
395C2×C4⋊C4—78no—
396C2×C4⋊C4—74no—
397C2×C4⋊C4—74no—
398C2×C4⋊C4—74no—
399C2×C4⋊C4—74no—
400C2×C4⋊C4—74no—
401C2×C4⋊C4—74no—
402C2×C4⋊C4—74no—
403C2×C4⋊C4—74no—
404C2×C4⋊C4—74no—
405C2×C4⋊C4—74no—
406C2×C4⋊C4—74no—
407C2×C4⋊C4—74no—
408C2×C4⋊C4—74no—
409C2×C4⋊C4—74no—
410C2×C4⋊C4—74no—
411C2×C4⋊C4—74no—
412C2×C4⋊C4—74no—
413C2×C4⋊C4—74no—
414C2×C4⋊C4—144no—
415C2×C4⋊C4—144no—
416C2×C4⋊C4—144no—
417C2×C4⋊C4—144no—
418C2×C4⋊C4—144no—
419C2×C4⋊C4—144no—
420C2×C4⋊C4—144no—
421C2×C4⋊C4—144no—
422C2×C4⋊C4—144no—
423C2×C4⋊C4—144no—
424C2×C4⋊C4—144no—
425C2×C4⋊C4—144no—
426C2×C4⋊C4—282no—
427C2×C4⋊C4—282no—
428C2×C4⋊C4—282no—
429C2×C4⋊C4—282no—
430C2×C4⋊C4C22×D714yes—
431C2×C4⋊C4C22×D714yes—
432C2×C4⋊C4C22×D714yes—
433C2×C4⋊C4C22×D714yes—
434C2×C42—78no—
435C2×C42—74no—
436C2×C42—74no—
437C2×C42—74no—
438C2×C42—74no—
439C2×C42—74no—
440C2×C42—144no—
441C2×C42—144no—
442C2×C42—144no—
443C2×C42—144no—
444#95—74no—
445#95—74no—
446#95—74no—
447#95—74no—
448#95—74no—
449#95C22×D714yes—
450#95C22×D714yes—
451#95C22×D714yes—
452C22×C7C2×#12514yes—
453C22×C7C2×C4⋊Q814yes—
454C22×C7#54414yes—
455C22×C7#54714yes—
456C22×C7#55014yes—
457C22×C7#55414yes—
458C22×C7#55714yes—
459C22×C7C23×D411yescharacteristic
460C22×C7C23×Q811yescharacteristic
461C22×C7C23×Q811yescharacteristic
462C22×C7C22×#4111yescharacteristic
463C22×C7C22×#4111yescharacteristic
464C22×C7C2×H(5,𝔽2)11yescharacteristic
465C22×C7C2×2−1+411yescharacteristic
466C4×C7—24no—
467C4×C7—24no—
468C4×C7—24no—
469C4×C7—42no—
470C4×C7—42no—
471C4×C7—42no—
472C4×C7—42no—
473Dic7—24no—
474Dic7—24no—
475Dic7—42no—
476Dic7—42no—
477Dic7—42no—
478Dic7—42no—
479Dic7C2×#12518yescomplemented
480Dic7C2×C4⋊Q818yes—
481C24C23×D711yescharacteristic
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—74no—
501C22×C4—74no—
502C22×C4—74no—
503C22×C4—74no—
504C22×C4—74no—
505C22×C4—74no—
506C22×C4—72no—
507C22×C4—72no—
508C22×C4—74no—
509C22×C4—74no—
510C22×C4—72no—
511C22×C4—72no—
512C22×C4—72no—
513C22×C4—72no—
514C22×C4—72no—
515C22×C4—72no—
516C22×C4—142no—
517C22×C4—142no—
518C22×C4—142no—
519C22×C4—142no—
520C22×C4—142no—
521C22×C4—142no—
522C22×C4—142no—
523C22×C4—142no—
524C22×C4—142no—
525C22×C4—142no—
526C22×C4—142no—
527C22×C4—142no—
528C22×C4—142no—
529C22×C4—142no—
530C22×C4—142no—
531C22×C4—142no—
532C22×C4D4×D714yes—
533C22×C4Q8×D714yes—
534C22×C4Q8×D714yes—
535C22×C4C23×D712yes—
536C22×C4C23×D712yes—
537C22×C4C23×D712yes—
538C22×C4C23×D712yes—
539C22×C4C23×D712yes—
540C22×C4C23×D712yes—
541C22×C4C23×D712yes—
542C4⋊C4—28no—
543C4⋊C4—28no—
544C4⋊C4—44no—
545C4⋊C4—44no—
546C4⋊C4—716no—
547C4⋊C4—716no—
548C4⋊C4—148no—
549C4⋊C4—148no—
550C4⋊C4—148no—
551C4⋊C4—148no—
552C4⋊C4—148no—
553C4⋊C4—148no—
554C4⋊C4—148no—
555C4⋊C4—148no—
556C4⋊C4—148no—
557C4⋊C4—148no—
558C4⋊C4—148no—
559C4⋊C4—148no—
560C4⋊C4—284no—
561C4⋊C4—284no—
562C4⋊C4—284no—
563C4⋊C4—284no—
564C42—716no—
565C42—148no—
566C42—148no—
567C42—148no—
568C42—148no—
569C2×C7#255218yescomplemented
570C2×C7C22×#12511yescharacteristic
571C2×C7C22×C4⋊Q811yescharacteristic
572C2×C7C2×#54411yescharacteristic
573C2×C7C2×#54711yescharacteristic
574C2×C7C2×#55011yescharacteristic
575C2×C7C2×#55411yescharacteristic
576C2×C7C2×#55711yescharacteristic
577C23C2×D4×D712yes—
578C23#654812yes—
579C23C2×Q8×D712yes—
580C23C2×Q8×D712yes—
581C23D7×#4112yes—
582C23D7×#4112yes—
583C23#655412yes—
584C23C24×D711yescharacteristic
585C2×C4—28no—
586C2×C4—28no—
587C2×C4—28no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—44no—
607C2×C4—44no—
608C2×C4—44no—
609C2×C4—44no—
610C2×C4—716no—
611C2×C4—716no—
612C2×C4—74no—
613C2×C4—74no—
614C2×C4—74no—
615C2×C4—74no—
616C2×C4—74no—
617C2×C4—74no—
618C2×C4—74no—
619C2×C4—74no—
620C2×C4—148no—
621C2×C4—148no—
622C2×C4—142no—
623C2×C4—142no—
624C2×C4—142no—
625C2×C4—142no—
626C2×C4—142no—
627C2×C4—142no—
628C2×C4—142no—
629C2×C4—142no—
630C2×C4—142no—
631C2×C4—142no—
632C2×C4—142no—
633C2×C4—142no—
634C2×C4—142no—
635C2×C4—142no—
636C2×C4—142no—
637C2×C4—142no—
638C2×C4—284no—
639C2×C4—284no—
640C2×C4—284no—
641C2×C4—284no—
642C2×C4C2×D4×D714yes—
643C2×C4C2×Q8×D714yes—
644C2×C4C2×Q8×D714yes—
645C7C2×#255211yescharacteristic, complemented, Sylow
646C22#9029014yes—
647C22#9031414yes—
648C22#9032714yes—
649C22#9034614yes—
650C22#9037614yes—
651C22D7×#12514yes—
652C22D7×C4⋊Q814yes—
653C22C22×D4×D711yescharacteristic
654C22C2×#654811yescharacteristic
655C22C22×Q8×D711yescharacteristic
656C22C22×Q8×D711yescharacteristic
657C22C2×D7×#4111yescharacteristic
658C22C2×D7×#4111yescharacteristic
659C22C2×#655411yescharacteristic
660C4—24no—
661C4—24no—
662C4—24no—
663C4—42no—
664C4—42no—
665C4—42no—
666C4—42no—
667C4—78no—
668C4—78no—
669C4—144no—
670C4—144no—
671C4—282no—
672C4—282no—
673C4—282no—
674C4—282no—
675C2#1173523218yesdirect product factor
676C2C2×#9029011yescharacteristic
677C2C2×#9031411yescharacteristic
678C2C2×#9032711yescharacteristic
679C2C2×#9034611yescharacteristic
680C2C2×#9037611yescharacteristic
681C2C2×D7×#12511yescharacteristic
682C2C2×D7×C4⋊Q811yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#398C2
socle, prime radicalC24×C7C24
hypercenterC2×#398D7
hypocenterC7C2×#2552
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
10. #11735232C2direct (N × H)
363. C2×Dic7#125semidirect
479. Dic7C2×#125semidirect
569. C2×C7#2552semidirect
645. C7C2×#2552semidirect
675. C2#11735232direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64522
C2×C7×#3982
C2×#897562
C2×#897442
C2×#897482
#117352322
C2×#894332
C2×#894292
C2×#894192
C2×#894212
C2×#25527