Finite Group Databasebeta

← C2×#11733012 #13522982

Subgroups — C2×#11733012 #13522982

Order 1792.

2270 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#388C211yesmaximal, characteristic
2C2×#89756C211yesmaximal, characteristic, complemented
3C2×#89757C211yesmaximal, characteristic, complemented
4C2×#89721C211yesmaximal, characteristic
5C2×#89720C211yesmaximal, characteristic
6C2×#89723C211yesmaximal, characteristic
7C2×#89722C211yesmaximal, characteristic
8C2×#89714C211yesmaximal, characteristic
9C2×C22⋊C4×Dic7C211yesmaximal, characteristic
10C2×#89700C211yesmaximal, characteristic, complemented
11C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
12#11733012C2116yesmaximal, direct product factor
13C2×#89429C211yesmaximal, characteristic, complemented
14C2×#89427C211yesmaximal, characteristic, complemented
15C2×#89427C211yesmaximal, characteristic, complemented
16C2×#89426C211yesmaximal, characteristic, complemented
17C24×Dic7C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C42×C7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×C4⋊Dic7C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×C4×Dic7C2211yescharacteristic
38C22×C4×Dic7C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C7×#388C2218yes—
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#89757C2218yescomplemented
54#89756C2218yescomplemented
55#89723C2218yes—
56#89722C2218yes—
57#89721C2218yes—
58#89720C2218yes—
59#89714C2218yes—
60C22⋊C4×Dic7C2218yes—
61C4×Dic7⋊C4C2218yescomplemented
62#89700C2218yescomplemented
63#89429C2218yescomplemented
64#89427C2218yescomplemented
65#89427C2218yescomplemented
66#89426C2218yescomplemented
67C2×#2522—71nomaximal, Sylow
68C25×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×Dic7—24no—
76C23×Dic7—24no—
77C23×Dic7—42no—
78C23×Dic7C2311yescharacteristic
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2314yes—
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C2×C7×C4⋊C4—24no—
88C2×C7×C4⋊C4C2314yes—
89C2×C7×C22⋊C4—24no—
90C2×C7×C22⋊C4—42no—
91C2×C7×C22⋊C4Q818yes—
92C2×C7×C22⋊C4C2314yes—
93C2×C7×C22⋊C4C2314yes—
94C2×C7×C22⋊C4C2314yes—
95C2×C42×C7—42no—
96C2×C42×C7C2314yes—
97C2×C22⋊Dic7—24no—
98C2×C22⋊Dic7—42no—
99C2×C22⋊Dic7—42no—
100C2×C22⋊Dic7C2314yes—
101C2×C22⋊Dic7C2314yes—
102C2×C22⋊Dic7C2314yes—
103C2×C4⋊Dic7—24no—
104C2×C4⋊Dic7—24no—
105C2×C4⋊Dic7—42no—
106C2×C4⋊Dic7—42no—
107C2×C4⋊Dic7—42no—
108C2×C4⋊Dic7C2314yes—
109C2×C4⋊Dic7C2314yes—
110C2×C4⋊Dic7C2314yes—
111C2×C4⋊Dic7C2314yes—
112C2×C4⋊Dic7C2314yes—
113C2×Dic7⋊C4—24no—
114C2×Dic7⋊C4—24no—
115C2×Dic7⋊C4—24no—
116C2×Dic7⋊C4—24no—
117C2×Dic7⋊C4—42no—
118C2×Dic7⋊C4—42no—
119C2×Dic7⋊C4C2314yes—
120C2×Dic7⋊C4C2314yes—
121C2×Dic7⋊C4C2314yes—
122C2×Dic7⋊C4C2314yes—
123C2×Dic7⋊C4C2314yes—
124C2×Dic7⋊C4C2314yes—
125C2×C4×Dic7—24no—
126C2×C4×Dic7—42no—
127C2×C4×Dic7—42no—
128C2×C4×Dic7C2314yes—
129C2×C4×Dic7C2314yes—
130C2×C4×Dic7C2314yes—
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#2522—716no—
144C2×#399—71no—
145C2×#398—71no—
146C2×#398—71no—
147C2×#396—71no—
148C2×#389—71no—
149C2×#389—71no—
150C2×#388—71no—
151C2×#388D711yescharacteristic
152C2×#387—71no—
153C2×#387—71no—
154C2×#387—71no—
155C2×#385—71no—
156C2×#380—71no—
157C2×C4×C4⋊C4—71no—
158C2×C4×C22⋊C4—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×C7C2×Q814yes—
184C22×C4×C7C2×Q814yes—
185C22×C4×C7#4114yes—
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—28no—
214C22×Dic7—28no—
215C22×Dic7—44no—
216C22×Dic7—416no—
217C22×Dic7#4114yes—
218C22×Dic7#4114yes—
219C22×Dic7#4114yes—
220C22×Dic7C2412yes—
221C22×Dic7C2412yes—
222C22×Dic7C2412yes—
223C22×Dic7C2412yes—
224C22×Dic7C2412yes—
225C22×Dic7C2412yes—
226C22×Dic7C2412yes—
227C22×Dic7C2412yes—
228C7×C4⋊C4—28no—
229C7×C22⋊C4—28no—
230C7×C22⋊C4—44no—
231C7×C22⋊C4C2×Q8116yes—
232C42×C7—44no—
233C22⋊Dic7—28no—
234C22⋊Dic7—44no—
235C22⋊Dic7—44no—
236C4⋊Dic7—28no—
237C4⋊Dic7—28no—
238C4⋊Dic7—44no—
239C4⋊Dic7—44no—
240C4⋊Dic7—44no—
241Dic7⋊C4—28no—
242Dic7⋊C4—28no—
243Dic7⋊C4—28no—
244Dic7⋊C4—28no—
245Dic7⋊C4—44no—
246Dic7⋊C4—44no—
247C4×Dic7—28no—
248C4×Dic7—44no—
249C4×Dic7—44no—
250C24×C4—71no—
251C22×C4⋊C4—71no—
252C22×C4⋊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⋊C4C2×D711yescharacteristic
263C22×C22⋊C4—71no—
264C22×C22⋊C4—71no—
265C22×C22⋊C4—71no—
266C22×C22⋊C4C2×D711yescharacteristic
267C22×C22⋊C4C2×D711yescharacteristic
268C22×C22⋊C4C2×D711yescharacteristic
269C22×C42—71no—
270C22×C42—71no—
271C22×C42—71no—
272C22×C42C2×D711yescharacteristic
273#399—78no—
274#398—78no—
275#398—78no—
276#396—78no—
277#389—78no—
278#389—78no—
279#388—78no—
280#388C2×D718yes—
281#387—78no—
282#387—78no—
283#387—78no—
284#385—78no—
285#380—78no—
286C4×C4⋊C4—78no—
287C4×C22⋊C4—78no—
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×#95C2×D711yescharacteristic
299C2×#95C2×D711yescharacteristic
300C23×C7—28no—
301C23×C7—28no—
302C23×C7—28no—
303C23×C7—22no—
304C23×C7—22no—
305C23×C7—22no—
306C23×C7—22no—
307C23×C7—22no—
308C23×C7—22no—
309C23×C7—44no—
310C23×C7—44no—
311C23×C7—44no—
312C23×C7—44no—
313C23×C7C22×Q814yes—
314C23×C7C22×Q812yes—
315C23×C7C2×#4112yes—
316C23×C7C2×#4112yes—
317C23×C7C2×#4112yes—
318C23×C7C2×#4112yes—
319C23×C7H(5,𝔽2)12yes—
320C23×C7H(5,𝔽2)12yes—
321C23×C7C2511yescharacteristic
322C2×C4×C7—28no—
323C2×C4×C7—28no—
324C2×C4×C7—28no—
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—44no—
341C2×C4×C7—44no—
342C2×C4×C7—44no—
343C2×C4×C7C22×Q814yes—
344C2×C4×C7C22×Q814yes—
345C2×C4×C7C2×#4114yes—
346C2×Dic7—28no—
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—416no—
371C2×Dic7—44no—
372C2×Dic7—44no—
373C2×Dic7—44no—
374C2×Dic7—44no—
375C2×Dic7—44no—
376C2×Dic7C2×#4114yes—
377C2×Dic7C2×#4114yes—
378C2×Dic7C2×#4114yes—
379C25C22×D711yescharacteristic
380C23×C4—71no—
381C23×C4—71no—
382C23×C4—71no—
383C23×C4—71no—
384C23×C4—71no—
385C23×C4—71no—
386C23×C4—71no—
387C23×C4—71no—
388C23×C4—74no—
389C23×C4—144no—
390C23×C4—144no—
391C23×C4—282no—
392C23×C4C22×D711yescharacteristic
393C23×C4C22×D711yescharacteristic
394C23×C4C22×D711yescharacteristic
395C23×C4C22×D711yescharacteristic
396C23×C4C22×D711yescharacteristic
397C23×C4C22×D711yescharacteristic
398C2×C4⋊C4—24no—
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—144no—
411C2×C4⋊C4—144no—
412C2×C4⋊C4—144no—
413C2×C4⋊C4—144no—
414C2×C4⋊C4—144no—
415C2×C4⋊C4—144no—
416C2×C4⋊C4—282no—
417C2×C4⋊C4—282no—
418C2×C4⋊C4—282no—
419C2×C4⋊C4—282no—
420C2×C4⋊C4—282no—
421C2×C4⋊C4C22×D714yes—
422C2×C22⋊C4—24no—
423C2×C22⋊C4—42no—
424C2×C22⋊C4—74no—
425C2×C22⋊C4—74no—
426C2×C22⋊C4—74no—
427C2×C22⋊C4—144no—
428C2×C22⋊C4—282no—
429C2×C22⋊C4—282no—
430C2×C22⋊C4Dic1418yes—
431C2×C22⋊C4C22×D714yes—
432C2×C22⋊C4C22×D714yes—
433C2×C22⋊C4C22×D714yes—
434C2×C42—42no—
435C2×C42—74no—
436C2×C42—74no—
437C2×C42—74no—
438C2×C42—144no—
439C2×C42—282no—
440C2×C42—282no—
441C2×C42C22×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#95C22×D714yes—
453#95C22×D714yes—
454C22×C7—24no—
455C22×C7—24no—
456C22×C7—24no—
457C22×C7—42no—
458C22×C7—42no—
459C22×C7—42no—
460C22×C7—42no—
461C22×C7—416no—
462C22×C7#52914yes—
463C22×C7#53314yes—
464C22×C7#54014yes—
465C22×C7#55114yes—
466C22×C7#55314yes—
467C22×C7#55414yes—
468C22×C7#55414yes—
469C22×C7C23×Q811yescharacteristic
470C22×C7C22×#4111yescharacteristic
471C22×C7C22×#4111yescharacteristic
472C22×C7C22×#4111yescharacteristic
473C22×C7C22×#4111yescharacteristic
474C22×C7C2×H(5,𝔽2)11yescharacteristic
475C22×C7C2×H(5,𝔽2)11yescharacteristic
476C4×C7—24no—
477C4×C7—24no—
478C4×C7—24no—
479C4×C7—42no—
480C4×C7—42no—
481C4×C7—42no—
482Dic7—24no—
483Dic7—24no—
484Dic7—24no—
485Dic7—42no—
486Dic7—42no—
487Dic7—42no—
488Dic7—42no—
489Dic7—42no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24C2×Dic1414yes—
497C24C23×D712yes—
498C24C23×D711yescharacteristic
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
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—74no—
515C22×C4—74no—
516C22×C4—74no—
517C22×C4—72no—
518C22×C4—72no—
519C22×C4—72no—
520C22×C4—72no—
521C22×C4—72no—
522C22×C4—72no—
523C22×C4—72no—
524C22×C4—72no—
525C22×C4—148no—
526C22×C4—148no—
527C22×C4—142no—
528C22×C4—142no—
529C22×C4—142no—
530C22×C4—142no—
531C22×C4—142no—
532C22×C4—142no—
533C22×C4—142no—
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—284no—
549C22×C4—2816no—
550C22×C4C2×Dic1414yes—
551C22×C4C2×Dic1414yes—
552C22×C4#115914yes—
553C22×C4C23×D712yes—
554C22×C4C23×D712yes—
555C22×C4C23×D712yes—
556C22×C4C23×D712yes—
557C22×C4C23×D712yes—
558C22×C4C23×D712yes—
559C4⋊C4—28no—
560C4⋊C4—148no—
561C4⋊C4—148no—
562C4⋊C4—148no—
563C4⋊C4—148no—
564C4⋊C4—148no—
565C4⋊C4—148no—
566C4⋊C4—284no—
567C4⋊C4—284no—
568C4⋊C4—284no—
569C4⋊C4—284no—
570C4⋊C4—284no—
571C22⋊C4—28no—
572C22⋊C4—44no—
573C22⋊C4—148no—
574C22⋊C4—284no—
575C22⋊C4—284no—
576C22⋊C4C2×Dic14116yes—
577C42—44no—
578C42—148no—
579C42—284no—
580C42—284no—
581C2×C7—44no—
582C2×C7#252218yescomplemented
583C2×C7C2×#52911yescharacteristic
584C2×C7C2×#53311yescharacteristic
585C2×C7C2×#54011yescharacteristic
586C2×C7C2×#55111yescharacteristic
587C2×C7C2×#55311yescharacteristic
588C2×C7C2×#55411yescharacteristic
589C2×C7C2×#55411yescharacteristic
590C23—28no—
591C23—28no—
592C23—28no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—44no—
600C23—44no—
601C23—44no—
602C23—44no—
603C23C22×Dic1414yes—
604C23C22×Dic1412yes—
605C23C2×#115912yes—
606C23#654812yes—
607C23D7×#4112yes—
608C23D7×#4112yes—
609C23D7×#4112yes—
610C23#655312yes—
611C23C24×D711yescharacteristic
612C2×C4—28no—
613C2×C4—28no—
614C2×C4—28no—
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—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—44no—
631C2×C4—44no—
632C2×C4—44no—
633C2×C4—74no—
634C2×C4—74no—
635C2×C4—74no—
636C2×C4—148no—
637C2×C4—148no—
638C2×C4—148no—
639C2×C4—142no—
640C2×C4—142no—
641C2×C4—142no—
642C2×C4—142no—
643C2×C4—142no—
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—2816no—
661C2×C4—284no—
662C2×C4—284no—
663C2×C4—284no—
664C2×C4—284no—
665C2×C4—284no—
666C2×C4C22×Dic1414yes—
667C2×C4C22×Dic1414yes—
668C2×C4C2×#115914yes—
669C7C2×#252211yescharacteristic, complemented, Sylow
670C22—24no—
671C22—24no—
672C22—24no—
673C22—416no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22#9020814yes—
679C22#9023014yes—
680C22#9023414yes—
681C22#9029214yes—
682C22#9035414yes—
683C22#9037114yes—
684C22#9039614yes—
685C22C23×Dic1411yescharacteristic
686C22C22×#115911yescharacteristic
687C22C2×#654811yescharacteristic
688C22C2×D7×#4111yescharacteristic
689C22C2×D7×#4111yescharacteristic
690C22C2×D7×#4111yescharacteristic
691C22C2×#655311yescharacteristic
692C4—24no—
693C4—24no—
694C4—24no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—144no—
699C4—144no—
700C4—144no—
701C4—282no—
702C4—282no—
703C4—282no—
704C4—282no—
705C4—282no—
706C2—44no—
707C2#1173301218yesdirect product factor
708C2C2×#9020811yescharacteristic
709C2C2×#9023411yescharacteristic
710C2C2×#9023011yescharacteristic
711C2C2×#9029211yescharacteristic
712C2C2×#9035411yescharacteristic
713C2C2×#9037111yescharacteristic
714C2C2×#9039611yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#388C2
socleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#388D7
hypocenterC7C2×#2522
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#89756C2semidirect
3. C2×#89757C2semidirect
10. C2×#89700C2semidirect
11. C2×C4×Dic7⋊C4C2semidirect
12. #11733012C2direct (N × H)
13. C2×#89429C2semidirect
14. C2×#89427C2semidirect
15. C2×#89427C2semidirect
16. C2×#89426C2semidirect
53. #89757C22semidirect
54. #89756C22semidirect
61. C4×Dic7⋊C4C22semidirect
62. #89700C22semidirect
63. #89429C22semidirect
64. #89427C22semidirect
65. #89427C22semidirect
66. #89426C22semidirect
582. C2×C7#2522semidirect
669. C7C2×#2522semidirect
707. C2#11733012direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3882
C2×#897562
C2×#897572
C2×#897212
C2×#897202
C2×#897232
C2×#897222
C2×#897142
C2×C22⋊C4×Dic72
C2×#897002
C2×C4×Dic7⋊C42
#117330122
C2×#894292
C2×#894272
C2×#894262
C2×#25227