Finite Group Databasebeta

← C2×#11733741 #13512543

Subgroups — C2×#11733741 #13512543

Order 1792.

3934 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6502C211yesmaximal, characteristic
2C22×(C22⋊D7)⋊C4C211yesmaximal, characteristic, complemented
3C22×#6440C211yesmaximal, characteristic, complemented
4C2×C7×#390C211yesmaximal, characteristic, complemented
5C2×#89992C211yesmaximal, characteristic, complemented
6C2×#89761C211yesmaximal, characteristic, complemented
7C2×#89744C211yesmaximal, characteristic, complemented
8C2×#89728C211yesmaximal, characteristic, complemented
9C2×#89729C211yesmaximal, characteristic, complemented
10C2×#89729C211yesmaximal, characteristic, complemented
11C2×#89717C211yesmaximal, characteristic, complemented
12C2×#89718C211yesmaximal, characteristic, complemented
13C2×#89714C211yesmaximal, characteristic, complemented
14C2×#89712C211yesmaximal, characteristic, complemented
15C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
16#11733741C2116yesmaximal, direct product factor
17C23×C7×D4C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C24×Dic7C2211yescharacteristic
21C24×Dic7C2211yescharacteristic
22C23×C4×D7C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C42×C7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
33C2×#6502C4116yescomplemented
34C2×#6502C2218yes—
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×(C2×D7)⋊C4C2211yescharacteristic
37C22×(C2×D7)⋊C4C2211yescharacteristic
38C22×(C2×D7)⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×Dic7⋊C4C2211yescharacteristic
44C22×Dic7⋊C4C2211yescharacteristic
45C22×C4×Dic7C2211yescharacteristic
46C22×C4×Dic7C2211yescharacteristic
47C22×C4×Dic7C2211yescharacteristic
48C2×(C22⋊D7)⋊C4—28no—
49C2×(C22⋊D7)⋊C4C2218yescomplemented
50C2×#6440—28no—
51C2×#6440C2218yescomplemented
52C7×#390C2218yescomplemented
53#89992C2218yescomplemented
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60#89761C2218yescomplemented
61#89744C2218yescomplemented
62#89729C2218yescomplemented
63#89729C2218yescomplemented
64#89728C2218yescomplemented
65#89718C2218yescomplemented
66#89717C2218yescomplemented
67#89714C2218yescomplemented
68#89712C2218yescomplemented
69C4×Dic7⋊C4C2218yescomplemented
70C2×#2324—71nomaximal, Sylow
71C25×C7C2311yescharacteristic
72C25×C7C2311yescharacteristic
73C24×D7C2311yescharacteristic
74C22×C7×D4—42no—
75C22×C7×D4—42no—
76C22×C7×D4C2×C418yescomplemented
77C22×C7×D4C2314yes—
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C22×C22⋊D7—24no—
84C22×C22⋊D7—24no—
85C22×C22⋊D7—42no—
86C22×C22⋊D7—42no—
87C22×C22⋊D7C2×C418yes—
88C22×C22⋊D7C2×C418yescomplemented
89C22×C22⋊D7C2314yes—
90C22×C22⋊D7C2314yes—
91C23×Dic7—24no—
92C23×Dic7—24no—
93C23×Dic7—24no—
94C23×Dic7—42no—
95C23×Dic7—42no—
96C23×Dic7C2×C418yescomplemented
97C23×Dic7C2311yescharacteristic
98C23×Dic7C2311yescharacteristic
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C23×Dic7C2311yescharacteristic
102C23×Dic7C2314yes—
103C23×Dic7C2311yescharacteristic
104C23×Dic7C2314yes—
105C23×Dic7C2311yescharacteristic
106C22×C4×D7—24no—
107C22×C4×D7—42no—
108C22×C4×D7—42no—
109C22×C4×D7C2314yes—
110C2×C7×C4⋊C4—42no—
111C2×C7×C4⋊C4C2314yes—
112C2×C7×C22⋊C4—24no—
113C2×C7×C22⋊C4—24no—
114C2×C7×C22⋊C4—42no—
115C2×C7×C22⋊C4—42no—
116C2×C7×C22⋊C4C2314yes—
117C2×C7×C22⋊C4C2314yes—
118C2×C7×C22⋊C4C2314yes—
119C2×C7×C22⋊C4C2314yes—
120C2×C42×C7—42no—
121C2×C42×C7C2314yes—
122C2×C22⋊Dic7—24no—
123C2×C22⋊Dic7—42no—
124C2×C22⋊Dic7—42no—
125C2×C22⋊Dic7C2×C418yescomplemented
126C2×C22⋊Dic7C2314yes—
127C2×C22⋊Dic7C2314yes—
128C2×C22⋊Dic7C2314yes—
129C2×C22⋊Dic7C2314yes—
130#6502C2×C4164yescomplemented
131C2×(C2×D7)⋊C4—24no—
132C2×(C2×D7)⋊C4—42no—
133C2×(C2×D7)⋊C4—42no—
134C2×(C2×D7)⋊C4C2×C418yescomplemented
135C2×(C2×D7)⋊C4C2314yes—
136C2×(C2×D7)⋊C4C2314yes—
137C2×(C2×D7)⋊C4C2314yes—
138C2×(C2×D7)⋊C4C2314yes—
139C2×Dic7⋊C4—24no—
140C2×Dic7⋊C4—24no—
141C2×Dic7⋊C4—24no—
142C2×Dic7⋊C4—24no—
143C2×Dic7⋊C4—42no—
144C2×Dic7⋊C4C2×C418yescomplemented
145C2×Dic7⋊C4C2314yes—
146C2×Dic7⋊C4C2314yes—
147C2×Dic7⋊C4C2314yes—
148C2×Dic7⋊C4C2314yes—
149C2×Dic7⋊C4C2314yes—
150C2×Dic7⋊C4C2314yes—
151C2×C4×Dic7—24no—
152C2×C4×Dic7—42no—
153C2×C4×Dic7D418yescomplemented
154C2×C4×Dic7C2314yes—
155C2×C4×Dic7C2314yes—
156C2×C4×Dic7C2314yes—
157(C22⋊D7)⋊C4—232no—
158#6440—232no—
159C7⋊#95C2314yes—
160C7⋊#95C2314yes—
161C7⋊#95C2314yes—
162C7⋊#95C2314yes—
163C7⋊#95C2314yes—
164C7⋊#95C2314yes—
165C22×#121—71no—
166C22×C4×D4—71no—
167C22×#117—71no—
168#2324—716no—
169C2×#390—71no—
170C2×#390—71no—
171C2×#390D711yescharacteristic, complemented
172C2×#389—71no—
173C2×#388—71no—
174C2×#388—71no—
175C2×#386—71no—
176C2×#386—71no—
177C2×#385—71no—
178C2×#385—71no—
179C2×#380—71no—
180C2×C4×C4⋊C4—71no—
181C24×C7—22no—
182C24×C7—22no—
183C24×C7—22no—
184C24×C7—22no—
185C24×C7—22no—
186C24×C7—22no—
187C24×C7—22no—
188C24×C7—22no—
189C24×C7—22no—
190C24×C7—22no—
191C24×C7—22no—
192C24×C7—22no—
193C24×C7C22×C414yes—
194C24×C7C22×C414yes—
195C24×C7C2412yes—
196C24×C7C2412yes—
197C24×C7C2411yescharacteristic
198C23×D7—22no—
199C23×D7—22no—
200C23×D7—22no—
201C23×D7—22no—
202C23×D7—22no—
203C23×D7—22no—
204C23×D7C22×C414yes—
205C23×D7C2412yes—
206C2×C7×D4—416no—
207C2×C7×D4—44no—
208C2×C7×D4—44no—
209C2×C7×D4C22×C4116yescomplemented
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7—22no—
219C22×C4×C7—22no—
220C22×C4×C7—22no—
221C22×C4×C7—22no—
222C22×C4×C7—22no—
223C22×C4×C7C22×C414yes—
224C22×C4×C7C2×D414yes—
225C22×C4×C7C2412yes—
226C22×C4×C7C2412yes—
227C22×C4×C7C2412yes—
228C22×C4×C7C2412yes—
229C22×C4×C7C2412yes—
230C2×C22⋊D7—232no—
231C2×C22⋊D7—28no—
232C2×C22⋊D7—28no—
233C2×C22⋊D7—416no—
234C2×C22⋊D7—44no—
235C2×C22⋊D7—44no—
236C2×C22⋊D7C22×C4116yes—
237C2×C22⋊D7C22×C4116yescomplemented
238C22×Dic7—22no—
239C22×Dic7—22no—
240C22×Dic7—22no—
241C22×Dic7—22no—
242C22×Dic7—22no—
243C22×Dic7—22no—
244C22×Dic7—232no—
245C22×Dic7—28no—
246C22×Dic7—28no—
247C22×Dic7—22no—
248C22×Dic7—22no—
249C22×Dic7—22no—
250C22×Dic7—22no—
251C22×Dic7—22no—
252C22×Dic7—22no—
253C22×Dic7—22no—
254C22×Dic7—22no—
255C22×Dic7—22no—
256C22×Dic7—28no—
257C22×Dic7—44no—
258C22×Dic7—44no—
259C22×Dic7—416no—
260C22×Dic7C22×C414yes—
261C22×Dic7C22×C414yes—
262C22×Dic7C22×C414yes—
263C22×Dic7C22×C4116yescomplemented
264C22×Dic7C2×D414yes—
265C22×Dic7C2×D414yes—
266C22×Dic7#4114yes—
267C22×Dic7C2412yes—
268C22×Dic7C2412yes—
269C22×Dic7C2412yes—
270C22×Dic7C2412yes—
271C22×Dic7C2412yes—
272C22×Dic7C2412yes—
273C22×Dic7C2412yes—
274C2×C4×D7—28no—
275C2×C4×D7—44no—
276C2×C4×D7—44no—
277C2×C4×D7—416no—
278C7×C4⋊C4—44no—
279C7×C22⋊C4—28no—
280C7×C22⋊C4—28no—
281C7×C22⋊C4—44no—
282C7×C22⋊C4—44no—
283C42×C7—44no—
284C22⋊Dic7—28no—
285C22⋊Dic7—44no—
286C22⋊Dic7—44no—
287C22⋊Dic7C22×C4116yescomplemented
288(C2×D7)⋊C4—28no—
289(C2×D7)⋊C4—44no—
290(C2×D7)⋊C4—44no—
291(C2×D7)⋊C4C22×C4116yescomplemented
292Dic7⋊C4—28no—
293Dic7⋊C4—28no—
294Dic7⋊C4—28no—
295Dic7⋊C4—28no—
296Dic7⋊C4—44no—
297Dic7⋊C4C22×C4116yescomplemented
298C4×Dic7—28no—
299C4×Dic7—44no—
300C4×Dic7C2×D4116yescomplemented
301C23×D4—71no—
302C23×D4—71no—
303C23×D4C2×D711yescharacteristic
304C24×C4—71no—
305C24×C4—71no—
306C24×C4—71no—
307C2×#121—716no—
308C2×#121—78no—
309C2×C4×D4—78no—
310C2×C4×D4—148no—
311C2×#117—78no—
312C2×#117—148no—
313C22×C4⋊C4—71no—
314C22×C4⋊C4—71no—
315C22×C4⋊C4—71no—
316C22×C4⋊C4—71no—
317C22×C4⋊C4—71no—
318C22×C4⋊C4—71no—
319C22×C4⋊C4C2×D711yescharacteristic
320C22×C22⋊C4—71no—
321C22×C22⋊C4—71no—
322C22×C22⋊C4—71no—
323C22×C22⋊C4—71no—
324C22×C22⋊C4—71no—
325C22×C22⋊C4—71no—
326C22×C22⋊C4—71no—
327C22×C22⋊C4—71no—
328C22×C22⋊C4C2×D711yescharacteristic
329C22×C22⋊C4C2×D711yescharacteristic
330C22×C22⋊C4C2×D711yescharacteristic
331C22×C22⋊C4C2×D711yescharacteristic
332C22×C42—71no—
333C22×C42—71no—
334C22×C42—71no—
335C22×C42C2×D711yescharacteristic
336#390—78no—
337#390—78no—
338#390C2×D718yescomplemented
339#389—78no—
340#388—78no—
341#388—78no—
342#386—78no—
343#386—78no—
344#385—78no—
345#385—78no—
346#380—78no—
347C4×C4⋊C4—78no—
348C2×#95—71no—
349C2×#95—71no—
350C2×#95—71no—
351C2×#95—71no—
352C2×#95—71no—
353C2×#95—71no—
354C23×C7—28no—
355C23×C7—28no—
356C23×C7—28no—
357C23×C7—28no—
358C23×C7—28no—
359C23×C7—28no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—44no—
373C23×C7—44no—
374C23×C7—44no—
375C23×C7—44no—
376C23×C7—44no—
377C23×C7—44no—
378C23×C7—44no—
379C23×C7—44no—
380C23×C7C23×C414yes—
381C23×C7C23×C414yes—
382C23×C7C23×C412yes—
383C23×C7C22×D412yes—
384C23×C7C2×#4112yes—
385C23×C7H(5,𝔽2)12yes—
386C23×C7H(5,𝔽2)12yes—
387C23×C7H(5,𝔽2)12yes—
388C23×C72−1+412yes—
389C23×C7C2511yescharacteristic
390C22×D7—28no—
391C22×D7—28no—
392C22×D7—28no—
393C22×D7—22no—
394C22×D7—22no—
395C22×D7—22no—
396C22×D7—22no—
397C22×D7—22no—
398C22×D7—22no—
399C22×D7—44no—
400C22×D7—44no—
401C22×D7—44no—
402C22×D7—44no—
403C22×D7C23×C414yes—
404C7×D4—416no—
405C2×C4×C7—28no—
406C2×C4×C7—28no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—44no—
421C2×C4×C7—44no—
422C2×C4×C7—44no—
423C2×C4×C7C23×C414yes—
424C2×C4×C7C22×D414yes—
425C22⋊D7—232no—
426C22⋊D7—416no—
427C2×Dic7—28no—
428C2×Dic7—28no—
429C2×Dic7—28no—
430C2×Dic7—22no—
431C2×Dic7—22no—
432C2×Dic7—22no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—232no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—22no—
440C2×Dic7—22no—
441C2×Dic7—22no—
442C2×Dic7—22no—
443C2×Dic7—22no—
444C2×Dic7—22no—
445C2×Dic7—22no—
446C2×Dic7—416no—
447C2×Dic7—44no—
448C2×Dic7—44no—
449C2×Dic7—44no—
450C2×Dic7C4×D4116yes—
451C2×Dic7C23×C414yes—
452C2×Dic7C23×C414yes—
453C2×Dic7C23×C414yes—
454C2×Dic7C22×D414yes—
455C2×Dic7C22×D414yes—
456C2×Dic7C2×#4114yes—
457C4×D7—416no—
458C25—71no—
459C25C22×D711yescharacteristic
460C25C22×D711yescharacteristic
461C22×D4—42no—
462C22×D4—42no—
463C22×D4—78no—
464C22×D4—74no—
465C22×D4—78no—
466C22×D4—74no—
467C22×D4—144no—
468C22×D4—144no—
469C22×D4—282no—
470C22×D4—282no—
471C22×D4C4×D718yescomplemented
472C22×D4C22×D714yes—
473C23×C4—71no—
474C23×C4—78no—
475C23×C4—74no—
476C23×C4—71no—
477C23×C4—71no—
478C23×C4—71no—
479C23×C4—71no—
480C23×C4—71no—
481C23×C4—71no—
482C23×C4—74no—
483C23×C4—74no—
484C23×C4—144no—
485C23×C4—144no—
486C23×C4—144no—
487C23×C4—144no—
488C23×C4—282no—
489C23×C4—282no—
490C23×C4—282no—
491C23×C4—282no—
492C23×C4C22×D711yescharacteristic
493C23×C4C22×D711yescharacteristic
494C23×C4C22×D711yescharacteristic
495C23×C4C22×D711yescharacteristic
496C23×C4C22×D711yescharacteristic
497#121—764no—
498C4×D4—1432no—
499#117—1432no—
500C2×C4⋊C4—42no—
501C2×C4⋊C4—78no—
502C2×C4⋊C4—74no—
503C2×C4⋊C4—74no—
504C2×C4⋊C4—74no—
505C2×C4⋊C4—74no—
506C2×C4⋊C4—74no—
507C2×C4⋊C4—74no—
508C2×C4⋊C4—144no—
509C2×C4⋊C4—144no—
510C2×C4⋊C4—144no—
511C2×C4⋊C4—144no—
512C2×C4⋊C4—282no—
513C2×C4⋊C4C22×D714yes—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—78no—
519C2×C22⋊C4—74no—
520C2×C22⋊C4—78no—
521C2×C22⋊C4—74no—
522C2×C22⋊C4—74no—
523C2×C22⋊C4—74no—
524C2×C22⋊C4—74no—
525C2×C22⋊C4—74no—
526C2×C22⋊C4—74no—
527C2×C22⋊C4—74no—
528C2×C22⋊C4—144no—
529C2×C22⋊C4—144no—
530C2×C22⋊C4—282no—
531C2×C22⋊C4—282no—
532C2×C22⋊C4—282no—
533C2×C22⋊C4—282no—
534C2×C22⋊C4C22×D714yes—
535C2×C22⋊C4C22×D714yes—
536C2×C22⋊C4C22×D714yes—
537C2×C22⋊C4C22×D714yes—
538C2×C42—42no—
539C2×C42—78no—
540C2×C42—74no—
541C2×C42—74no—
542C2×C42—74no—
543C2×C42—144no—
544C2×C42—282no—
545C2×C42C22×D714yes—
546#95—74no—
547#95—74no—
548#95—74no—
549#95—74no—
550#95—74no—
551#95—74no—
552C22×C7—24no—
553C22×C7—24no—
554C22×C7—24no—
555C22×C7—24no—
556C22×C7—24no—
557C22×C7—24no—
558C22×C7—416no—
559C22×C7—416no—
560C22×C7—42no—
561C22×C7—42no—
562C22×C7—42no—
563C22×C7—42no—
564C22×C7—42no—
565C22×C7—42no—
566C22×C7—42no—
567C22×C7—42no—
568C22×C7C2×C4×D414yes—
569C22×C7#51814yes—
570C22×C7#52014yes—
571C22×C7#53514yes—
572C22×C7#53714yes—
573C22×C7#54014yes—
574C22×C7#54214yes—
575C22×C7C24×C411yescharacteristic
576C22×C7C23×D411yescharacteristic
577C22×C7C22×#4111yescharacteristic
578C22×C7C2×H(5,𝔽2)11yescharacteristic
579C22×C7C2×H(5,𝔽2)11yescharacteristic
580C22×C7C2×H(5,𝔽2)11yescharacteristic
581C22×C7C2×2−1+411yescharacteristic
582C2×D7—24no—
583C2×D7—24no—
584C2×D7—24no—
585C2×D7—416no—
586C2×D7—42no—
587C2×D7—42no—
588C2×D7—42no—
589C2×D7—42no—
590C4×C7—24no—
591C4×C7—24no—
592C4×C7—42no—
593C4×C7—42no—
594C4×C7—42no—
595Dic7—24no—
596Dic7—24no—
597Dic7—24no—
598Dic7—42no—
599Dic7—42no—
600Dic7—42no—
601Dic7C2×C4×D418yes—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—74no—
615C24—72no—
616C24—142no—
617C24—142no—
618C24—142no—
619C24—142no—
620C24—142no—
621C24—142no—
622C24C2×C4×D714yes—
623C24C2×C4×D714yes—
624C24C23×D712yes—
625C24C23×D712yes—
626C24C23×D711yescharacteristic
627C2×D4—416no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—716no—
631C2×D4—716no—
632C2×D4—148no—
633C2×D4—1432no—
634C2×D4—148no—
635C2×D4—2816no—
636C2×D4—284no—
637C2×D4—284no—
638C2×D4C2×C4×D7116yescomplemented
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—74no—
653C22×C4—74no—
654C22×C4—74no—
655C22×C4—72no—
656C22×C4—74no—
657C22×C4—74no—
658C22×C4—716no—
659C22×C4—74no—
660C22×C4—72no—
661C22×C4—72no—
662C22×C4—72no—
663C22×C4—72no—
664C22×C4—72no—
665C22×C4—72no—
666C22×C4—148no—
667C22×C4—148no—
668C22×C4—1432no—
669C22×C4—148no—
670C22×C4—148no—
671C22×C4—142no—
672C22×C4—142no—
673C22×C4—142no—
674C22×C4—142no—
675C22×C4—142no—
676C22×C4—142no—
677C22×C4—142no—
678C22×C4—142no—
679C22×C4—142no—
680C22×C4—142no—
681C22×C4—142no—
682C22×C4—142no—
683C22×C4—142no—
684C22×C4—142no—
685C22×C4—142no—
686C22×C4—284no—
687C22×C4—284no—
688C22×C4—2816no—
689C22×C4—284no—
690C22×C4—284no—
691C22×C4—2816no—
692C22×C4C2×C4×D714yes—
693C22×C4D4×D714yes—
694C22×C4C23×D712yes—
695C22×C4C23×D712yes—
696C22×C4C23×D712yes—
697C22×C4C23×D712yes—
698C22×C4C23×D712yes—
699C4⋊C4—44no—
700C4⋊C4—716no—
701C4⋊C4—148no—
702C4⋊C4—148no—
703C4⋊C4—148no—
704C4⋊C4—148no—
705C4⋊C4—284no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—44no—
709C22⋊C4—44no—
710C22⋊C4—716no—
711C22⋊C4—716no—
712C22⋊C4—148no—
713C22⋊C4—148no—
714C22⋊C4—284no—
715C22⋊C4—284no—
716C22⋊C4—284no—
717C22⋊C4—284no—
718C42—44no—
719C42—716no—
720C42—148no—
721C42—284no—
722C2×C7—44no—
723C2×C7—44no—
724C2×C7#232418yescomplemented
725C2×C7C22×C4×D411yescharacteristic
726C2×C7C2×#51811yescharacteristic
727C2×C7C2×#52011yescharacteristic
728C2×C7C2×#53511yescharacteristic
729C2×C7C2×#53711yescharacteristic
730C2×C7C2×#54011yescharacteristic
731C2×C7C2×#54211yescharacteristic
732D7—44no—
733C23—28no—
734C23—28no—
735C23—28no—
736C23—28no—
737C23—28no—
738C23—28no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—74no—
760C23—148no—
761C23—148no—
762C23—148no—
763C23—142no—
764C23—142no—
765C23—142no—
766C23—142no—
767C23—142no—
768C23—142no—
769C23—284no—
770C23—284no—
771C23—284no—
772C23—284no—
773C23C22×C4×D714yes—
774C23C22×C4×D714yes—
775C23C22×C4×D712yes—
776C23C2×D4×D712yes—
777C23#654812yes—
778C23#654812yes—
779C23#654812yes—
780C23D7×#4112yes—
781C23#655412yes—
782C23C24×D711yescharacteristic
783D4—416no—
784D4—1432no—
785D4—2816no—
786C2×C4—28no—
787C2×C4—28no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—716no—
805C2×C4—74no—
806C2×C4—74no—
807C2×C4—74no—
808C2×C4—74no—
809C2×C4—74no—
810C2×C4—74no—
811C2×C4—1432no—
812C2×C4—148no—
813C2×C4—148no—
814C2×C4—148no—
815C2×C4—142no—
816C2×C4—142no—
817C2×C4—142no—
818C2×C4—142no—
819C2×C4—142no—
820C2×C4—142no—
821C2×C4—142no—
822C2×C4—142no—
823C2×C4—142no—
824C2×C4—142no—
825C2×C4—142no—
826C2×C4—142no—
827C2×C4—142no—
828C2×C4—142no—
829C2×C4—142no—
830C2×C4—2816no—
831C2×C4—2816no—
832C2×C4—284no—
833C2×C4—284no—
834C2×C4—284no—
835C2×C4C22×C4×D714yes—
836C2×C4C2×D4×D714yes—
837C7C2×#232411yescharacteristic, complemented, Sylow
838C22—24no—
839C22—24no—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—416no—
853C22—416no—
854C22—144no—
855C22—144no—
856C22—144no—
857C22—282no—
858C22—282no—
859C22—282no—
860C22—282no—
861C22—2816no—
862C22#9017714yes—
863C22C4×D4×D714yes—
864C22#9023714yes—
865C22#9028814yes—
866C22#9030614yes—
867C22#9036014yes—
868C22#9040614yes—
869C22C23×C4×D711yescharacteristic
870C22C22×D4×D711yescharacteristic
871C22C2×#654811yescharacteristic
872C22C2×#654811yescharacteristic
873C22C2×#654811yescharacteristic
874C22C2×D7×#4111yescharacteristic
875C22C2×#655411yescharacteristic
876C4—24no—
877C4—24no—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—78no—
882C4—144no—
883C4—144no—
884C4—144no—
885C4—282no—
886C4—282no—
887C4—282no—
888C2—44no—
889C2—44no—
890C2—284no—
891C2#1173374118yesdirect product factor
892C2C2×#9017711yescharacteristic
893C2C2×#9023711yescharacteristic
894C2C2×C4×D4×D711yescharacteristic
895C2C2×#9028811yescharacteristic
896C2C2×#9030611yescharacteristic
897C2C2×#9036011yescharacteristic
898C2C2×#9040611yescharacteristic
subgroupG/H
centerC24C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC2×C7×#390C2
socleC24×C7C24
prime radicalC22×#6502C2
cosocleC23×C7C25
hypercenterC2×#390D7
hypocenterC7C2×#2324
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C22×(C22⋊D7)⋊C4C2semidirect
3. C22×#6440C2semidirect
4. C2×C7×#390C2semidirect
5. C2×#89992C2semidirect
6. C2×#89761C2semidirect
7. C2×#89744C2semidirect
8. C2×#89728C2semidirect
9. C2×#89729C2semidirect
10. C2×#89729C2semidirect
11. C2×#89717C2semidirect
12. C2×#89718C2semidirect
13. C2×#89714C2semidirect
14. C2×#89712C2semidirect
15. C2×C4×Dic7⋊C4C2semidirect
16. #11733741C2direct (N × H)
33. C2×#6502C4semidirect
49. C2×(C22⋊D7)⋊C4C22semidirect
51. C2×#6440C22semidirect
52. C7×#390C22semidirect
53. #89992C22semidirect
60. #89761C22semidirect
61. #89744C22semidirect
62. #89729C22semidirect
63. #89729C22semidirect
64. #89728C22semidirect
65. #89718C22semidirect
66. #89717C22semidirect
67. #89714C22semidirect
68. #89712C22semidirect
69. C4×Dic7⋊C4C22semidirect
76. C22×C7×D4C2×C4semidirect
88. C22×C22⋊D7C2×C4semidirect
96. C23×Dic7C2×C4semidirect
125. C2×C22⋊Dic7C2×C4semidirect
130. #6502C2×C4semidirect
134. C2×(C2×D7)⋊C4C2×C4semidirect
144. C2×Dic7⋊C4C2×C4semidirect
153. C2×C4×Dic7D4semidirect
171. C2×#390D7semidirect
209. C2×C7×D4C22×C4semidirect
237. C2×C22⋊D7C22×C4semidirect
263. C22×Dic7C22×C4semidirect
287. C22⋊Dic7C22×C4semidirect
291. (C2×D7)⋊C4C22×C4semidirect
297. Dic7⋊C4C22×C4semidirect
300. C4×Dic7C2×D4semidirect
338. #390C2×D7semidirect
471. C22×D4C4×D7semidirect
638. C2×D4C2×C4×D7semidirect
724. C2×C7#2324semidirect
837. C7C2×#2324semidirect
891. C2#11733741direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#65022
C22×(C22⋊D7)⋊C42
C22×#64402
C2×C7×#3902
C2×#899922
C2×#897612
C2×#897442
C2×#897282
C2×#897292
C2×#897172
C2×#897182
C2×#897142
C2×#897122
C2×C4×Dic7⋊C42
#117337412
C2×#23247