Finite Group Databasebeta

← C2×#11735221 #13522993

Subgroups — C2×#11735221 #13522993

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×#398C211yesmaximal, characteristic, complemented
2C2×#89766C211yesmaximal, characteristic
3C2×#89761C211yesmaximal, characteristic
4C2×#89759C211yesmaximal, characteristic
5C2×#89757C211yesmaximal, characteristic, complemented
6C2×#89757C211yesmaximal, characteristic, complemented
7C2×#89762C211yesmaximal, characteristic
8C2×#89753C211yesmaximal, characteristic, complemented
9C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
10#11735221C2116yesmaximal, direct product factor
11C2×#89449C211yesmaximal, characteristic
12C2×#89433C211yesmaximal, characteristic, complemented
13C2×#89442C211yesmaximal, characteristic
14C2×#89427C211yesmaximal, characteristic, complemented
15C2×#89424C211yesmaximal, characteristic, complemented
16C2×#89438C211yesmaximal, characteristic
17C23×C4×D7C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×(C2×D7)⋊C4C2211yescharacteristic
27C22×(C2×D7)⋊C4C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×C4⋊Dic7C2211yescharacteristic
31C22×C4⋊Dic7C2211yescharacteristic
32C22×C4⋊Dic7C2211yescharacteristic
33C22×C4⋊Dic7C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×C4×Dic7C2211yescharacteristic
37C22×C4×Dic7C2211yescharacteristic
38C22×C4×Dic7C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C7×#398C2218yescomplemented
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#89766C2218yes—
54#89762C2218yes—
55#89761C2218yes—
56#89759C2218yes—
57#89757C2218yescomplemented
58#89757C2218yescomplemented
59#89753C2218yescomplemented
60C4⋊C4×Dic7C2218yescomplemented
61#89449C2218yes—
62#89442C2218yes—
63#89438C2218yes—
64#89433C2218yescomplemented
65#89427C2218yescomplemented
66#89424C2218yescomplemented
67C2×#2522—71nomaximal, Sylow
68C24×D7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C22×C4×D7—24no—
84C22×C4×D7—24no—
85C22×C4×D7—42no—
86C22×C4×D7C2314yes—
87C2×C7×C4⋊C4—24no—
88C2×C7×C4⋊C4—24no—
89C2×C7×C4⋊C4—24no—
90C2×C7×C4⋊C4—24no—
91C2×C7×C4⋊C4C2314yes—
92C2×C7×C4⋊C4C2314yes—
93C2×C7×C4⋊C4C2314yes—
94C2×C7×C4⋊C4C2314yes—
95C2×(C2×D7)⋊C4—24no—
96C2×(C2×D7)⋊C4—24no—
97C2×(C2×D7)⋊C4—42no—
98C2×(C2×D7)⋊C4—42no—
99C2×(C2×D7)⋊C4—42no—
100C2×(C2×D7)⋊C4Q818yes—
101C2×(C2×D7)⋊C4C2314yes—
102C2×(C2×D7)⋊C4C2314yes—
103C2×(C2×D7)⋊C4C2314yes—
104C2×(C2×D7)⋊C4C2314yes—
105C2×(C2×D7)⋊C4C2314yes—
106C2×(C2×D7)⋊C4C2314yes—
107C2×C4⋊Dic7—24no—
108C2×C4⋊Dic7—42no—
109C2×C4⋊Dic7—42no—
110C2×C4⋊Dic7—42no—
111C2×C4⋊Dic7—42no—
112C2×C4⋊Dic7—42no—
113C2×C4⋊Dic7C2314yes—
114C2×C4⋊Dic7C2314yes—
115C2×C4⋊Dic7C2314yes—
116C2×C4⋊Dic7C2314yes—
117C2×C4⋊Dic7C2314yes—
118C2×C4⋊Dic7C2314yes—
119C2×Dic7⋊C4—24no—
120C2×Dic7⋊C4—24no—
121C2×Dic7⋊C4C2314yes—
122C2×Dic7⋊C4C2314yes—
123C2×C4×Dic7—24no—
124C2×C4×Dic7—42no—
125C2×C4×Dic7—42no—
126C2×C4×Dic7—42no—
127C2×C4×Dic7C2314yes—
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×#398D711yescharacteristic, complemented
147C2×#396—71no—
148C2×#389—71no—
149C2×#389—71no—
150C2×#388—71no—
151C2×#388—71no—
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×C7C2411yescharacteristic
160C23×D7—22no—
161C23×D7—22no—
162C23×D7—22no—
163C23×D7—22no—
164C23×D7—22no—
165C23×D7—22no—
166C23×D7C2×Q814yes—
167C23×D7C2412yes—
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×C7C2×Q814yes—
186C22×C4×C7#4114yes—
187C22×C4×C7#4114yes—
188C22×C4×C7#4114yes—
189C22×C4×C7C2412yes—
190C22×C4×C7C2412yes—
191C22×C4×C7C2412yes—
192C22×C4×C7C2412yes—
193C22×C4×C7C2412yes—
194C22×C4×C7C2412yes—
195C22×C4×C7C2412yes—
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—22no—
215C22×Dic7C2×Q814yes—
216C22×Dic7#4114yes—
217C22×Dic7C2412yes—
218C22×Dic7C2412yes—
219C22×Dic7C2412yes—
220C22×Dic7C2412yes—
221C22×Dic7C2412yes—
222C22×Dic7C2412yes—
223C22×Dic7C2412yes—
224C2×C4×D7—28no—
225C2×C4×D7—28no—
226C2×C4×D7—44no—
227C2×C4×D7—416no—
228C7×C4⋊C4—28no—
229C7×C4⋊C4—28no—
230C7×C4⋊C4—28no—
231C7×C4⋊C4—28no—
232(C2×D7)⋊C4—28no—
233(C2×D7)⋊C4—28no—
234(C2×D7)⋊C4—44no—
235(C2×D7)⋊C4—44no—
236(C2×D7)⋊C4—44no—
237(C2×D7)⋊C4C2×Q8116yes—
238C4⋊Dic7—28no—
239C4⋊Dic7—44no—
240C4⋊Dic7—44no—
241C4⋊Dic7—44no—
242C4⋊Dic7—44no—
243C4⋊Dic7—44no—
244Dic7⋊C4—28no—
245Dic7⋊C4—28no—
246C4×Dic7—28no—
247C4×Dic7—44no—
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⋊C4C2×D711yescharacteristic
260C22×C4⋊C4C2×D711yescharacteristic
261C22×C4⋊C4C2×D711yescharacteristic
262C22×C4⋊C4C2×D711yescharacteristic
263C22×C22⋊C4—71no—
264C22×C22⋊C4—71no—
265C22×C22⋊C4—71no—
266C22×C22⋊C4—71no—
267C22×C22⋊C4—71no—
268C22×C22⋊C4—71no—
269C22×C42—71no—
270C22×C42—71no—
271C22×C42—71no—
272C22×C42—71no—
273#399—78no—
274#398—78no—
275#398C2×D718yescomplemented
276#396—78no—
277#389—78no—
278#389—78no—
279#388—78no—
280#388—78no—
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×#95C2×D711yescharacteristic
298C2×#95C2×D711yescharacteristic
299C2×#95C2×D711yescharacteristic
300C23×C7C22×Q812yes—
301C23×C7C2×#4112yes—
302C23×C7C2×#4112yes—
303C23×C7C2×#4112yes—
304C23×C7C2×#4112yes—
305C23×C7H(5,𝔽2)12yes—
306C23×C7H(5,𝔽2)12yes—
307C23×C7C2511yescharacteristic
308C22×D7—28no—
309C22×D7—28no—
310C22×D7—28no—
311C22×D7—22no—
312C22×D7—22no—
313C22×D7—22no—
314C22×D7—22no—
315C22×D7—22no—
316C22×D7—22no—
317C22×D7—44no—
318C22×D7—44no—
319C22×D7—44no—
320C22×D7—44no—
321C22×D7C22×Q814yes—
322C2×C4×C7—28no—
323C2×C4×C7—28no—
324C2×C4×C7—28no—
325C2×C4×C7—28no—
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—22no—
342C2×C4×C7—22no—
343C2×C4×C7—44no—
344C2×C4×C7—44no—
345C2×C4×C7—44no—
346C2×C4×C7C22×Q814yes—
347C2×C4×C7C2×#4114yes—
348C2×C4×C7C2×#4114yes—
349C2×C4×C7C2×#4114yes—
350C2×Dic7—28no—
351C2×Dic7—28no—
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—44no—
372C2×Dic7—44no—
373C2×Dic7—44no—
374C2×Dic7—44no—
375C2×Dic7—44no—
376C2×Dic7C22×Q814yes—
377C2×Dic7C2×#4114yes—
378C4×D7—416no—
379C25—71no—
380C23×C4—71no—
381C23×C4—71no—
382C23×C4—71no—
383C23×C4—71no—
384C23×C4—71no—
385C23×C4—71no—
386C23×C4—71no—
387C23×C4—74no—
388C23×C4—144no—
389C23×C4—144no—
390C23×C4—282no—
391C23×C4C22×D711yescharacteristic
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—24no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—24no—
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—282no—
414C2×C4⋊C4—282no—
415C2×C4⋊C4—282no—
416C2×C4⋊C4—282no—
417C2×C4⋊C4—282no—
418C2×C4⋊C4C22×D714yes—
419C2×C4⋊C4C22×D714yes—
420C2×C4⋊C4C22×D714yes—
421C2×C4⋊C4C22×D714yes—
422C2×C22⋊C4—78no—
423C2×C22⋊C4—74no—
424C2×C22⋊C4—74no—
425C2×C22⋊C4—74no—
426C2×C22⋊C4—74no—
427C2×C22⋊C4—74no—
428C2×C22⋊C4—74no—
429C2×C22⋊C4—144no—
430C2×C22⋊C4—144no—
431C2×C22⋊C4—282no—
432C2×C22⋊C4—282no—
433C2×C22⋊C4—282no—
434C2×C42—74no—
435C2×C42—74no—
436C2×C42—74no—
437C2×C42—74no—
438C2×C42—144no—
439C2×C42—282no—
440C2×C42—282no—
441C2×C42—282no—
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#95C22×D714yes—
452#95C22×D714yes—
453#95C22×D714yes—
454C22×C7#52914yes—
455C22×C7#53314yes—
456C22×C7#54014yes—
457C22×C7#55114yes—
458C22×C7#55314yes—
459C22×C7#55414yes—
460C22×C7#55414yes—
461C22×C7C23×Q811yescharacteristic
462C22×C7C22×#4111yescharacteristic
463C22×C7C22×#4111yescharacteristic
464C22×C7C22×#4111yescharacteristic
465C22×C7C22×#4111yescharacteristic
466C22×C7C2×H(5,𝔽2)11yescharacteristic
467C22×C7C2×H(5,𝔽2)11yescharacteristic
468C2×D7—24no—
469C2×D7—24no—
470C2×D7—24no—
471C2×D7—42no—
472C2×D7—42no—
473C2×D7—42no—
474C2×D7—42no—
475C2×D7—416no—
476C4×C7—24no—
477C4×C7—24no—
478C4×C7—24no—
479C4×C7—24no—
480C4×C7—42no—
481C4×C7—42no—
482C4×C7—42no—
483Dic7—24no—
484Dic7—24no—
485Dic7—42no—
486Dic7—42no—
487Dic7—42no—
488Dic7—42no—
489Dic7—42no—
490C24—74no—
491C24—72no—
492C24—142no—
493C24—142no—
494C24—142no—
495C24—142no—
496C24—142no—
497C24—142no—
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—22no—
515C22×C4—22no—
516C22×C4—74no—
517C22×C4—74no—
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—142no—
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—148no—
546C22×C4—284no—
547C22×C4—2816no—
548C22×C4#115914yes—
549C22×C4#115914yes—
550C22×C4Q8×D714yes—
551C22×C4#116114yes—
552C22×C4C23×D712yes—
553C22×C4C23×D712yes—
554C22×C4C23×D712yes—
555C22×C4C23×D712yes—
556C22×C4C23×D712yes—
557C22×C4C23×D712yes—
558C22×C4C23×D712yes—
559C4⋊C4—28no—
560C4⋊C4—28no—
561C4⋊C4—28no—
562C4⋊C4—28no—
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—716no—
572C22⋊C4—148no—
573C22⋊C4—148no—
574C22⋊C4—284no—
575C22⋊C4—284no—
576C22⋊C4—284no—
577C42—148no—
578C42—284no—
579C42—284no—
580C42—284no—
581C2×C7#252218yescomplemented
582C2×C7C2×#52911yescharacteristic
583C2×C7C2×#53311yescharacteristic
584C2×C7C2×#54011yescharacteristic
585C2×C7C2×#55111yescharacteristic
586C2×C7C2×#55311yescharacteristic
587C2×C7C2×#55411yescharacteristic
588C2×C7C2×#55411yescharacteristic
589D7—44no—
590C23—74no—
591C23—148no—
592C23—148no—
593C23—148no—
594C23—142no—
595C23—142no—
596C23—142no—
597C23—142no—
598C23—142no—
599C23—142no—
600C23—284no—
601C23—284no—
602C23—284no—
603C23—284no—
604C23C2×#115912yes—
605C23C2×#115912yes—
606C23C2×Q8×D712yes—
607C23C2×#116112yes—
608C23D7×#4112yes—
609C23#655312yes—
610C23#655312yes—
611C23C24×D711yescharacteristic
612C2×C4—28no—
613C2×C4—28no—
614C2×C4—28no—
615C2×C4—28no—
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—44no—
634C2×C4—44no—
635C2×C4—44no—
636C2×C4—74no—
637C2×C4—74no—
638C2×C4—148no—
639C2×C4—148no—
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—2816no—
660C2×C4—284no—
661C2×C4—284no—
662C2×C4—284no—
663C2×C4—284no—
664C2×C4—284no—
665C2×C4C2×#115914yes—
666C2×C4C2×#115914yes—
667C2×C4C2×Q8×D714yes—
668C2×C4C2×#116114yes—
669C7C2×#252211yescharacteristic, complemented, Sylow
670C22—144no—
671C22—144no—
672C22—144no—
673C22—282no—
674C22—282no—
675C22—282no—
676C22—2816no—
677C22—282no—
678C22#9030914yes—
679C22#9031514yes—
680C22#9032614yes—
681C22#9034914yes—
682C22#9038114yes—
683C22#9038914yes—
684C22#9041914yes—
685C22C22×#115911yescharacteristic
686C22C22×#115911yescharacteristic
687C22C22×Q8×D711yescharacteristic
688C22C22×#116111yescharacteristic
689C22C2×D7×#4111yescharacteristic
690C22C2×#655311yescharacteristic
691C22C2×#655311yescharacteristic
692C4—24no—
693C4—24no—
694C4—24no—
695C4—24no—
696C4—42no—
697C4—42no—
698C4—42no—
699C4—144no—
700C4—144no—
701C4—282no—
702C4—282no—
703C4—282no—
704C4—282no—
705C4—282no—
706C2—284no—
707C2#1173522118yesdirect product factor
708C2C2×#9030911yescharacteristic
709C2C2×#9031511yescharacteristic
710C2C2×#9032611yescharacteristic
711C2C2×#9034911yescharacteristic
712C2C2×#9038111yescharacteristic
713C2C2×#9038911yescharacteristic
714C2C2×#9041911yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#398C2
socleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×#398D7
hypocenterC7C2×#2522
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C2×C7×#398C2semidirect
5. C2×#89757C2semidirect
6. C2×#89757C2semidirect
8. C2×#89753C2semidirect
9. C2×C4⋊C4×Dic7C2semidirect
10. #11735221C2direct (N × H)
12. C2×#89433C2semidirect
14. C2×#89427C2semidirect
15. C2×#89424C2semidirect
40. C7×#398C22semidirect
57. #89757C22semidirect
58. #89757C22semidirect
59. #89753C22semidirect
60. C4⋊C4×Dic7C22semidirect
64. #89433C22semidirect
65. #89427C22semidirect
66. #89424C22semidirect
146. C2×#398D7semidirect
275. #398C2×D7semidirect
581. C2×C7#2522semidirect
669. C7C2×#2522semidirect
707. C2#11735221direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3982
C2×#897662
C2×#897612
C2×#897592
C2×#897572
C2×#897622
C2×#897532
C2×C4⋊C4×Dic72
#117352212
C2×#894492
C2×#894332
C2×#894422
C2×#894272
C2×#894242
C2×#894382
C2×#25227