Finite Group Databasebeta

← C2×#11734857 #13560214

Subgroups — C2×#11734857 #13560214

Order 1792.

2110 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#396C211yesmaximal, characteristic
2C2×#89754C211yesmaximal, characteristic, complemented
3C2×#89755C211yesmaximal, characteristic, complemented
4C2×#89752C211yesmaximal, characteristic, complemented
5C2×#89752C211yesmaximal, characteristic, complemented
6C2×#89756C211yesmaximal, characteristic, complemented
7C2×#89751C211yesmaximal, characteristic, complemented
8C2×#89721C211yesmaximal, characteristic
9C2×#89720C211yesmaximal, characteristic
10C2×#89719C211yesmaximal, characteristic
11C2×#89715C211yesmaximal, characteristic
12C2×#89714C211yesmaximal, characteristic
13C2×#89714C211yesmaximal, characteristic
14#11734857C2116yesmaximal, direct product factor
15C2×#89430C211yesmaximal, characteristic, complemented
16C2×#89428C211yesmaximal, characteristic, complemented
17C24×Dic7C2211yescharacteristic
18C23×Dic14C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C7×#396C2218yes—
39C2×C7×#95C2211yescharacteristic
40C2×C7⋊#95C2211yescharacteristic
41C2×C7⋊#95C2211yescharacteristic
42C2×C7⋊#95C2211yescharacteristic
43C2×C7⋊#95C2211yescharacteristic
44C2×C7⋊#95C2211yescharacteristic
45C2×C7⋊#95C2211yescharacteristic
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53#89756C2218yescomplemented
54#89755C2218yescomplemented
55#89754C2218yescomplemented
56#89752C2218yescomplemented
57#89752C2218yescomplemented
58#89751C2218yescomplemented
59#89721C2218yes—
60#89720C2218yes—
61#89719C2218yes—
62#89715C2218yes—
63#89714C2218yes—
64#89714C2218yes—
65#89430C2218yescomplemented
66#89428C2218yescomplemented
67C2×#2841—71nomaximal, Sylow
68C25×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×Dic7—42no—
76C23×Dic7—42no—
77C23×Dic7Q818yescomplemented
78C23×Dic7C2311yescharacteristic
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2314yes—
87C22×Dic14—42no—
88C22×Dic14—42no—
89C22×Dic14—42no—
90C22×Dic14C2314yes—
91C2×C7×C4⋊C4—42no—
92C2×C7×C4⋊C4—42no—
93C2×C7×C4⋊C4—42no—
94C2×C7×C4⋊C4C2314yes—
95C2×C7×C4⋊C4C2314yes—
96C2×C7×C4⋊C4C2314yes—
97C2×C7×C22⋊C4—42no—
98C2×C7×C22⋊C4—42no—
99C2×C7×C22⋊C4—42no—
100C2×C7×C22⋊C4C2314yes—
101C2×C7×C22⋊C4C2314yes—
102C2×C7×C22⋊C4C2314yes—
103C2×C22⋊Dic7—42no—
104C2×C22⋊Dic7—42no—
105C2×C22⋊Dic7—42no—
106C2×C22⋊Dic7C2314yes—
107C2×C22⋊Dic7C2314yes—
108C2×C22⋊Dic7C2314yes—
109C2×C4⋊Dic7—42no—
110C2×C4⋊Dic7—42no—
111C2×C4⋊Dic7C2314yes—
112C2×C4⋊Dic7C2314yes—
113C2×Dic7⋊C4—42no—
114C2×Dic7⋊C4—42no—
115C2×Dic7⋊C4—42no—
116C2×Dic7⋊C4—42no—
117C2×Dic7⋊C4—42no—
118C2×Dic7⋊C4—42no—
119C2×Dic7⋊C4—42no—
120C2×Dic7⋊C4—42no—
121C2×Dic7⋊C4C2314yes—
122C2×Dic7⋊C4C2314yes—
123C2×Dic7⋊C4C2314yes—
124C2×Dic7⋊C4C2314yes—
125C2×Dic7⋊C4C2314yes—
126C2×Dic7⋊C4C2314yes—
127C2×Dic7⋊C4C2314yes—
128C2×Dic7⋊C4C2314yes—
129C7×#95C2314yes—
130C7⋊#95C2314yes—
131C7⋊#95C2314yes—
132C7⋊#95C2314yes—
133C7⋊#95C2314yes—
134C7⋊#95C2314yes—
135C7⋊#95C2314yes—
136C7⋊#95C2314yes—
137C7⋊#95C2314yes—
138C7⋊#95C2314yes—
139C7⋊#95C2314yes—
140C7⋊#95C2314yes—
141C7⋊#95C2314yes—
142C7⋊#95C2314yes—
143#2841—716no—
144C2×#400—71no—
145C2×#400—71no—
146C2×#399—71no—
147C2×#398—71no—
148C2×#398—71no—
149C2×#398—71no—
150C2×#398—71no—
151C2×#396—71no—
152C2×#396D711yescharacteristic
153C2×#395—71no—
154C2×#395—71no—
155C2×#393—71no—
156C2×#381—71no—
157C2×#380—71no—
158C2×#380—71no—
159C24×C7—22no—
160C24×C7—22no—
161C24×C7—22no—
162C24×C7—22no—
163C24×C7—22no—
164C24×C7—22no—
165C24×C7C2×Q814yes—
166C24×C7C2412yes—
167C24×C7C2411yescharacteristic
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×C7—22no—
185C22×C4×C7—22no—
186C22×C4×C7C2412yes—
187C22×C4×C7C2412yes—
188C22×C4×C7C2412yes—
189C22×C4×C7C2412yes—
190C22×C4×C7C2412yes—
191C22×C4×C7C2412yes—
192C22×Dic7—22no—
193C22×Dic7—22no—
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×Dic7—22no—
211C22×Dic7—22no—
212C22×Dic7—22no—
213C22×Dic7—22no—
214C22×Dic7—416no—
215C22×Dic7—44no—
216C22×Dic7—44no—
217C22×Dic7C2×Q814yes—
218C22×Dic7C2×Q814yes—
219C22×Dic7C2×Q8116yescomplemented
220C22×Dic7C2412yes—
221C22×Dic7C2412yes—
222C22×Dic7C2412yes—
223C22×Dic7C2412yes—
224C22×Dic7C2412yes—
225C22×Dic7C2412yes—
226C22×Dic7C2412yes—
227C22×Dic7C2412yes—
228C2×Dic14—44no—
229C2×Dic14—44no—
230C2×Dic14—44no—
231C2×Dic14—416no—
232C7×C4⋊C4—44no—
233C7×C4⋊C4—44no—
234C7×C4⋊C4—44no—
235C7×C22⋊C4—44no—
236C7×C22⋊C4—44no—
237C7×C22⋊C4—44no—
238C22⋊Dic7—44no—
239C22⋊Dic7—44no—
240C22⋊Dic7—44no—
241C4⋊Dic7—44no—
242C4⋊Dic7—44no—
243Dic7⋊C4—44no—
244Dic7⋊C4—44no—
245Dic7⋊C4—44no—
246Dic7⋊C4—44no—
247Dic7⋊C4—44no—
248Dic7⋊C4—44no—
249Dic7⋊C4—44no—
250Dic7⋊C4—44no—
251C23×Q8—71no—
252C24×C4—71no—
253C22×C4⋊C4—71no—
254C22×C4⋊C4—71no—
255C22×C4⋊C4—71no—
256C22×C4⋊C4—71no—
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⋊C4C2×D711yescharacteristic
264C22×C4⋊C4C2×D711yescharacteristic
265C22×C4⋊C4C2×D711yescharacteristic
266C22×C22⋊C4—71no—
267C22×C22⋊C4—71no—
268C22×C22⋊C4—71no—
269C22×C22⋊C4C2×D711yescharacteristic
270C22×C22⋊C4C2×D711yescharacteristic
271C22×C22⋊C4C2×D711yescharacteristic
272#400—78no—
273#400—78no—
274#399—78no—
275#398—78no—
276#398—78no—
277#398—78no—
278#398—78no—
279#396—78no—
280#396C2×D718yes—
281#395—78no—
282#395—78no—
283#393—78no—
284#381—78no—
285#380—78no—
286#380—78no—
287C2×#95—71no—
288C2×#95—71no—
289C2×#95—71no—
290C2×#95—71no—
291C2×#95—71no—
292C2×#95—71no—
293C2×#95—71no—
294C2×#95—71no—
295C2×#95—71no—
296C2×#95—71no—
297C2×#95—71no—
298C2×#95—71no—
299C2×#95—71no—
300C2×#95C2×D711yescharacteristic
301C23×C7—28no—
302C23×C7—28no—
303C23×C7—28no—
304C23×C7—22no—
305C23×C7—22no—
306C23×C7—22no—
307C23×C7—22no—
308C23×C7—22no—
309C23×C7—22no—
310C23×C7—44no—
311C23×C7—44no—
312C23×C7—44no—
313C23×C7—44no—
314C23×C7C22×Q814yes—
315C23×C7C22×Q812yes—
316C23×C7H(5,𝔽2)12yes—
317C23×C7H(5,𝔽2)12yes—
318C23×C7H(5,𝔽2)12yes—
319C23×C7H(5,𝔽2)12yes—
320C23×C72−1+412yes—
321C23×C72−1+412yes—
322C23×C7C2511yescharacteristic
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—22no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—44no—
342C2×C4×C7—44no—
343C2×C4×C7—44no—
344C2×C4×C7—44no—
345C2×C4×C7—44no—
346C2×C4×C7—44no—
347C2×Dic7—28no—
348C2×Dic7—28no—
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—22no—
360C2×Dic7—22no—
361C2×Dic7—22no—
362C2×Dic7—22no—
363C2×Dic7—22no—
364C2×Dic7—22no—
365C2×Dic7—22no—
366C2×Dic7—22no—
367C2×Dic7—22no—
368C2×Dic7—22no—
369C2×Dic7—22no—
370C2×Dic7—22no—
371C2×Dic7—416no—
372C2×Dic7—44no—
373C2×Dic7—44no—
374C2×Dic7—44no—
375C2×Dic7—44no—
376C2×Dic7—44no—
377C2×Dic7—44no—
378C2×Dic7C22×Q814yes—
379C2×Dic7C22×Q814yes—
380Dic14—416no—
381C25C22×D711yescharacteristic
382C22×Q8—74no—
383C22×Q8—282no—
384C22×Q8—282no—
385C22×Q8—282no—
386C23×C4—71no—
387C23×C4—71no—
388C23×C4—78no—
389C23×C4—74no—
390C23×C4—71no—
391C23×C4—71no—
392C23×C4—71no—
393C23×C4—71no—
394C23×C4—71no—
395C23×C4—71no—
396C23×C4—282no—
397C23×C4—282no—
398C23×C4C22×D711yescharacteristic
399C23×C4C22×D711yescharacteristic
400C23×C4C22×D711yescharacteristic
401C23×C4C22×D711yescharacteristic
402C23×C4C22×D711yescharacteristic
403C23×C4C22×D711yescharacteristic
404C2×C4⋊C4—42no—
405C2×C4⋊C4—42no—
406C2×C4⋊C4—42no—
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—74no—
415C2×C4⋊C4—74no—
416C2×C4⋊C4—74no—
417C2×C4⋊C4—282no—
418C2×C4⋊C4—282no—
419C2×C4⋊C4—282no—
420C2×C4⋊C4—282no—
421C2×C4⋊C4—282no—
422C2×C4⋊C4—282no—
423C2×C4⋊C4—282no—
424C2×C4⋊C4—282no—
425C2×C4⋊C4—282no—
426C2×C4⋊C4—282no—
427C2×C4⋊C4C22×D714yes—
428C2×C4⋊C4C22×D714yes—
429C2×C4⋊C4C22×D714yes—
430C2×C22⋊C4—42no—
431C2×C22⋊C4—42no—
432C2×C22⋊C4—42no—
433C2×C22⋊C4—74no—
434C2×C22⋊C4—74no—
435C2×C22⋊C4—74no—
436C2×C22⋊C4—282no—
437C2×C22⋊C4—282no—
438C2×C22⋊C4—282no—
439C2×C22⋊C4C22×D714yes—
440C2×C22⋊C4C22×D714yes—
441C2×C22⋊C4C22×D714yes—
442#95—74no—
443#95—74no—
444#95—74no—
445#95—74no—
446#95—74no—
447#95—74no—
448#95—74no—
449#95—74no—
450#95—74no—
451#95—74no—
452#95—74no—
453#95—74no—
454#95—74no—
455#95C22×D714yes—
456C22×C7—24no—
457C22×C7—24no—
458C22×C7—24no—
459C22×C7—416no—
460C22×C7—42no—
461C22×C7—42no—
462C22×C7—42no—
463C22×C7—42no—
464C22×C7#54314yes—
465C22×C7#54414yes—
466C22×C7#54414yes—
467C22×C7#56014yes—
468C22×C7#56214yes—
469C22×C7#56214yes—
470C22×C7#56314yes—
471C22×C7C23×Q811yescharacteristic
472C22×C7C2×H(5,𝔽2)11yescharacteristic
473C22×C7C2×H(5,𝔽2)11yescharacteristic
474C22×C7C2×H(5,𝔽2)11yescharacteristic
475C22×C7C2×H(5,𝔽2)11yescharacteristic
476C22×C7C2×2−1+411yescharacteristic
477C22×C7C2×2−1+411yescharacteristic
478C4×C7—42no—
479C4×C7—42no—
480C4×C7—42no—
481C4×C7—42no—
482C4×C7—42no—
483C4×C7—42no—
484Dic7—24no—
485Dic7—24no—
486Dic7—42no—
487Dic7—42no—
488Dic7—42no—
489Dic7—42no—
490Dic7—42no—
491Dic7—42no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24Q8×D714yes—
499C24C23×D712yes—
500C24C23×D711yescharacteristic
501C2×Q8—284no—
502C2×Q8—284no—
503C2×Q8—284no—
504C2×Q8—2816no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—74no—
524C22×C4—74no—
525C22×C4—72no—
526C22×C4—72no—
527C22×C4—716no—
528C22×C4—72no—
529C22×C4—72no—
530C22×C4—72no—
531C22×C4—72no—
532C22×C4—72no—
533C22×C4—72no—
534C22×C4—142no—
535C22×C4—142no—
536C22×C4—142no—
537C22×C4—142no—
538C22×C4—142no—
539C22×C4—142no—
540C22×C4—142no—
541C22×C4—142no—
542C22×C4—142no—
543C22×C4—142no—
544C22×C4—142no—
545C22×C4—142no—
546C22×C4—142no—
547C22×C4—142no—
548C22×C4—142no—
549C22×C4—142no—
550C22×C4—142no—
551C22×C4—142no—
552C22×C4—142no—
553C22×C4—142no—
554C22×C4—142no—
555C22×C4—142no—
556C22×C4—2816no—
557C22×C4—284no—
558C22×C4—284no—
559C22×C4C23×D712yes—
560C22×C4C23×D712yes—
561C22×C4C23×D712yes—
562C22×C4C23×D712yes—
563C22×C4C23×D712yes—
564C22×C4C23×D712yes—
565C4⋊C4—44no—
566C4⋊C4—44no—
567C4⋊C4—44no—
568C4⋊C4—284no—
569C4⋊C4—284no—
570C4⋊C4—284no—
571C4⋊C4—284no—
572C4⋊C4—284no—
573C4⋊C4—284no—
574C4⋊C4—284no—
575C4⋊C4—284no—
576C4⋊C4—284no—
577C4⋊C4—284no—
578C22⋊C4—44no—
579C22⋊C4—44no—
580C22⋊C4—44no—
581C22⋊C4—284no—
582C22⋊C4—284no—
583C22⋊C4—284no—
584C2×C7—44no—
585C2×C7#284118yescomplemented
586C2×C7C2×#54311yescharacteristic
587C2×C7C2×#54411yescharacteristic
588C2×C7C2×#54411yescharacteristic
589C2×C7C2×#56011yescharacteristic
590C2×C7C2×#56211yescharacteristic
591C2×C7C2×#56211yescharacteristic
592C2×C7C2×#56311yescharacteristic
593C23—28no—
594C23—28no—
595C23—28no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—44no—
603C23—44no—
604C23—44no—
605C23—44no—
606C23#654812yes—
607C23#654812yes—
608C23#654812yes—
609C23C2×Q8×D714yes—
610C23C2×Q8×D712yes—
611C23#655312yes—
612C23#655412yes—
613C23#655412yes—
614C23C24×D711yescharacteristic
615Q8—2816no—
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—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—44no—
635C2×C4—44no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—74no—
641C2×C4—74no—
642C2×C4—148no—
643C2×C4—148no—
644C2×C4—142no—
645C2×C4—142no—
646C2×C4—142no—
647C2×C4—142no—
648C2×C4—142no—
649C2×C4—142no—
650C2×C4—142no—
651C2×C4—142no—
652C2×C4—142no—
653C2×C4—142no—
654C2×C4—142no—
655C2×C4—142no—
656C2×C4—142no—
657C2×C4—142no—
658C2×C4—142no—
659C2×C4—142no—
660C2×C4—142no—
661C2×C4—142no—
662C2×C4—142no—
663C2×C4—142no—
664C2×C4—142no—
665C2×C4—142no—
666C2×C4—2816no—
667C2×C4—284no—
668C2×C4—284no—
669C2×C4—284no—
670C2×C4—284no—
671C2×C4—284no—
672C2×C4—284no—
673C7C2×#284111yescharacteristic, complemented, Sylow
674C22—24no—
675C22—24no—
676C22—24no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—416no—
681C22—42no—
682C22#9031114yes—
683C22#9031214yes—
684C22#9031214yes—
685C22#9031414yes—
686C22#9031414yes—
687C22#9032514yes—
688C22#9040314yes—
689C22C2×#654811yescharacteristic
690C22C2×#654811yescharacteristic
691C22C2×#654811yescharacteristic
692C22C22×Q8×D711yescharacteristic
693C22C2×#655311yescharacteristic
694C22C2×#655411yescharacteristic
695C22C2×#655411yescharacteristic
696C4—42no—
697C4—42no—
698C4—42no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—144no—
703C4—144no—
704C4—282no—
705C4—282no—
706C4—282no—
707C4—282no—
708C4—282no—
709C4—282no—
710C2—44no—
711C2#1173485718yesdirect product factor
712C2C2×#9031111yescharacteristic
713C2C2×#9031211yescharacteristic
714C2C2×#9031211yescharacteristic
715C2C2×#9031411yescharacteristic
716C2C2×#9031411yescharacteristic
717C2C2×#9032511yescharacteristic
718C2C2×#9040311yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#396C2
socleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#396D7
hypocenterC7C2×#2841
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
2. C2×#89754C2semidirect
3. C2×#89755C2semidirect
4. C2×#89752C2semidirect
5. C2×#89752C2semidirect
6. C2×#89756C2semidirect
7. C2×#89751C2semidirect
14. #11734857C2direct (N × H)
15. C2×#89430C2semidirect
16. C2×#89428C2semidirect
53. #89756C22semidirect
54. #89755C22semidirect
55. #89754C22semidirect
56. #89752C22semidirect
57. #89752C22semidirect
58. #89751C22semidirect
65. #89430C22semidirect
66. #89428C22semidirect
77. C23×Dic7Q8semidirect
219. C22×Dic7C2×Q8semidirect
585. C2×C7#2841semidirect
673. C7C2×#2841semidirect
711. C2#11734857direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3962
C2×#897542
C2×#897552
C2×#897522
C2×#897562
C2×#897512
C2×#897212
C2×#897202
C2×#897192
C2×#897152
C2×#897142
#117348572
C2×#894302
C2×#894282
C2×#28417