Finite Group Databasebeta

← C2×#11732742 #13512528

Subgroups — C2×#11732742 #13512528

Order 1792.

3718 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6457C211yesmaximal, characteristic
2C22×D7×C4⋊C4C211yesmaximal, characteristic, complemented
3C22×C4×D28C211yesmaximal, characteristic
4C2×C7×#387C211yesmaximal, characteristic, complemented
5C2×#89761C211yesmaximal, characteristic, complemented
6C2×#89757C211yesmaximal, characteristic, complemented
7C2×#89705C211yesmaximal, characteristic, complemented
8#11732742C2116yesmaximal, direct product factor
9C2×#89437C211yesmaximal, characteristic
10C2×#89440C211yesmaximal, characteristic, complemented
11C2×#89440C211yesmaximal, characteristic, complemented
12C2×#89436C211yesmaximal, characteristic, complemented
13C2×#89419C211yesmaximal, characteristic, complemented
14C2×#89442C211yesmaximal, characteristic, complemented
15C2×#89441C211yesmaximal, characteristic, complemented
16C2×#89438C211yesmaximal, characteristic, complemented
17C23×D28C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C23×C4×D7C2211yescharacteristic
20C23×C4×D7C2211yescharacteristic
21C23×C4×D7C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C42×C7C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×(C2×D7)⋊C4C2211yescharacteristic
27C22×(C2×D7)⋊C4C2211yescharacteristic
28C22×(C2×D7)⋊C4C2211yescharacteristic
29C22×(C2×D7)⋊C4C2211yescharacteristic
30C22×(C2×D7)⋊C4C2211yescharacteristic
31C22×(C2×D7)⋊C4C2211yescharacteristic
32C22×(C2×D7)⋊C4C2211yescharacteristic
33C22×C4⋊Dic7C2211yescharacteristic
34C22×C4⋊Dic7C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×C4×Dic7C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C2×#6457C4116yescomplemented
43C2×#6457C2218yes—
44C2×D7×C4⋊C4—28no—
45C2×D7×C4⋊C4C2218yescomplemented
46C2×C4×D28—28no—
47C2×C4×D28C2218yes—
48C7×#387C2218yescomplemented
49C2×C7×#95C2211yescharacteristic
50C2×C7×#95C2211yescharacteristic
51C2×C7×#95C2211yescharacteristic
52C2×C7×#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59#89761C2218yescomplemented
60#89757C2218yescomplemented
61#89705C2218yescomplemented
62#89442C2218yescomplemented
63#89441C2218yescomplemented
64#89440C2218yescomplemented
65#89440C2218yescomplemented
66#89438C2218yescomplemented
67#89437C2218yes—
68#89436C2218yescomplemented
69#89419C2218yescomplemented
70C2×#2322—71nomaximal, Sylow
71C24×D7C2311yescharacteristic
72C24×D7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C22×D28—24no—
87C22×D28—24no—
88C22×D28C2×C418yes—
89C22×D28C2314yes—
90C22×C4×D7—24no—
91C22×C4×D7—24no—
92C22×C4×D7—24no—
93C22×C4×D7—24no—
94C22×C4×D7—42no—
95C22×C4×D7—42no—
96C22×C4×D7—42no—
97C22×C4×D7—42no—
98C22×C4×D7—42no—
99C22×C4×D7—42no—
100C22×C4×D7C2×C418yescomplemented
101C22×C4×D7D418yes—
102C22×C4×D7C2314yes—
103C22×C4×D7C2314yes—
104C22×C4×D7C2314yes—
105C22×C4×D7C2314yes—
106C2×C7×C4⋊C4—24no—
107C2×C7×C4⋊C4C2×C418yescomplemented
108C2×C7×C4⋊C4C2314yes—
109C2×C7×C4⋊C4C2314yes—
110C2×C42×C7—24no—
111C2×C42×C7C2314yes—
112C2×(C2×D7)⋊C4—24no—
113C2×(C2×D7)⋊C4—24no—
114C2×(C2×D7)⋊C4—24no—
115C2×(C2×D7)⋊C4—42no—
116C2×(C2×D7)⋊C4—42no—
117C2×(C2×D7)⋊C4C2×C418yescomplemented
118C2×(C2×D7)⋊C4C2×C418yescomplemented
119C2×(C2×D7)⋊C4C2×C418yescomplemented
120C2×(C2×D7)⋊C4C2314yes—
121C2×(C2×D7)⋊C4C2314yes—
122C2×(C2×D7)⋊C4C2314yes—
123C2×(C2×D7)⋊C4C2314yes—
124C2×(C2×D7)⋊C4C2314yes—
125C2×(C2×D7)⋊C4C2314yes—
126C2×(C2×D7)⋊C4C2314yes—
127C2×(C2×D7)⋊C4C2314yes—
128C2×C4⋊Dic7—24no—
129C2×C4⋊Dic7—24no—
130C2×C4⋊Dic7—42no—
131C2×C4⋊Dic7C2314yes—
132C2×C4⋊Dic7C2314yes—
133C2×C4⋊Dic7C2314yes—
134C2×Dic7⋊C4—24no—
135C2×Dic7⋊C4—24no—
136C2×Dic7⋊C4—42no—
137C2×Dic7⋊C4C2×C418yescomplemented
138C2×Dic7⋊C4C2314yes—
139C2×Dic7⋊C4C2314yes—
140C2×Dic7⋊C4C2314yes—
141C2×Dic7⋊C4C2314yes—
142C2×C4×Dic7—42no—
143C2×C4×Dic7—42no—
144C2×C4×Dic7C2314yes—
145C2×C4×Dic7C2314yes—
146#6457C2×C4164yescomplemented
147D7×C4⋊C4—232no—
148C4×D28—232no—
149C7×#95C2314yes—
150C7×#95C2314yes—
151C7×#95C2314yes—
152C7×#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×#123—71no—
160C22×C4×D4—71no—
161C23×C4⋊C4—71no—
162#2322—716no—
163C2×#389—71no—
164C2×#389—71no—
165C2×#388—71no—
166C2×#388—71no—
167C2×#387—71no—
168C2×#387D711yescharacteristic, complemented
169C2×#386—71no—
170C2×#385—71no—
171C2×#385—71no—
172C2×#385—71no—
173C2×#381—71no—
174C2×C4×C22⋊C4—71no—
175C24×C7C2411yescharacteristic
176C23×D7—22no—
177C23×D7—22no—
178C23×D7—22no—
179C23×D7—22no—
180C23×D7—22no—
181C23×D7—22no—
182C23×D7—22no—
183C23×D7—22no—
184C23×D7—22no—
185C23×D7—22no—
186C23×D7C22×C414yes—
187C23×D7C22×C414yes—
188C23×D7C2×D414yes—
189C23×D7#4114yes—
190C23×D7C2412yes—
191C23×D7C2412yes—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
195C22×C4×C7—22no—
196C22×C4×C7—22no—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7C22×C414yes—
210C22×C4×C7C22×C414yes—
211C22×C4×C7C22×C414yes—
212C22×C4×C7C2×D414yes—
213C22×C4×C7C2412yes—
214C22×C4×C7C2412yes—
215C22×C4×C7C2412yes—
216C22×C4×C7C2412yes—
217C22×C4×C7C2412yes—
218C22×C4×C7C2412yes—
219C22×C4×C7C2412yes—
220C22×Dic7—22no—
221C22×Dic7—22no—
222C22×Dic7—22no—
223C22×Dic7—22no—
224C22×Dic7—22no—
225C22×Dic7—22no—
226C22×Dic7—22no—
227C22×Dic7—22no—
228C22×Dic7—22no—
229C22×Dic7—22no—
230C22×Dic7—22no—
231C22×Dic7—22no—
232C22×Dic7—22no—
233C22×Dic7—22no—
234C22×Dic7—22no—
235C22×Dic7C22×C414yes—
236C22×Dic7C22×C414yes—
237C22×Dic7C2×D414yes—
238C22×Dic7C2412yes—
239C22×Dic7C2412yes—
240C22×Dic7C2412yes—
241C22×Dic7C2412yes—
242C22×Dic7C2412yes—
243C22×Dic7C2412yes—
244C2×D28—232no—
245C2×D28—28no—
246C2×D28—28no—
247C2×D28C22×C4116yes—
248C2×C4×D7—232no—
249C2×C4×D7—28no—
250C2×C4×D7—28no—
251C2×C4×D7—28no—
252C2×C4×D7—28no—
253C2×C4×D7—416no—
254C2×C4×D7—44no—
255C2×C4×D7—44no—
256C2×C4×D7—44no—
257C2×C4×D7—44no—
258C2×C4×D7—44no—
259C2×C4×D7—44no—
260C2×C4×D7—416no—
261C2×C4×D7—416no—
262C2×C4×D7C22×C4116yescomplemented
263C2×C4×D7C2×D4116yes—
264C7×C4⋊C4—28no—
265C7×C4⋊C4C22×C4116yescomplemented
266C42×C7—28no—
267(C2×D7)⋊C4—28no—
268(C2×D7)⋊C4—28no—
269(C2×D7)⋊C4—28no—
270(C2×D7)⋊C4—44no—
271(C2×D7)⋊C4—44no—
272(C2×D7)⋊C4C22×C4116yescomplemented
273(C2×D7)⋊C4C22×C4116yescomplemented
274(C2×D7)⋊C4C22×C4116yescomplemented
275C4⋊Dic7—28no—
276C4⋊Dic7—28no—
277C4⋊Dic7—44no—
278Dic7⋊C4—28no—
279Dic7⋊C4—28no—
280Dic7⋊C4—44no—
281Dic7⋊C4C22×C4116yescomplemented
282C4×Dic7—44no—
283C4×Dic7—44no—
284C23×D4—71no—
285C24×C4—71no—
286C24×C4—71no—
287C24×C4—71no—
288C24×C4—71no—
289C2×#123—716no—
290C2×#123—78no—
291C2×C4×D4—78no—
292C2×C4×D4—148no—
293C22×C4⋊C4—71no—
294C22×C4⋊C4—71no—
295C22×C4⋊C4—71no—
296C22×C4⋊C4—71no—
297C22×C4⋊C4—71no—
298C22×C4⋊C4—71no—
299C22×C4⋊C4—71no—
300C22×C4⋊C4—78no—
301C22×C4⋊C4—148no—
302C22×C4⋊C4C2×D711yescharacteristic
303C22×C4⋊C4C2×D711yescharacteristic
304C22×C22⋊C4—71no—
305C22×C22⋊C4—71no—
306C22×C22⋊C4—71no—
307C22×C22⋊C4—71no—
308C22×C22⋊C4—71no—
309C22×C22⋊C4—71no—
310C22×C22⋊C4—71no—
311C22×C22⋊C4—71no—
312C22×C42—71no—
313C22×C42—71no—
314C22×C42C2×D711yescharacteristic
315#389—78no—
316#389—78no—
317#388—78no—
318#388—78no—
319#387—78no—
320#387C2×D718yescomplemented
321#386—78no—
322#385—78no—
323#385—78no—
324#385—78no—
325#381—78no—
326C4×C22⋊C4—78no—
327C2×#95—71no—
328C2×#95—71no—
329C2×#95—71no—
330C2×#95—71no—
331C2×#95—71no—
332C2×#95—71no—
333C2×#95C2×D711yescharacteristic
334C2×#95C2×D711yescharacteristic
335C2×#95C2×D711yescharacteristic
336C2×#95C2×D711yescharacteristic
337C23×C7C23×C412yes—
338C23×C7C22×D412yes—
339C23×C7C2×#4112yes—
340C23×C7H(5,𝔽2)12yes—
341C23×C7H(5,𝔽2)12yes—
342C23×C72−1+412yes—
343C23×C72−1+412yes—
344C23×C7C2511yescharacteristic
345C22×D7—28no—
346C22×D7—28no—
347C22×D7—28no—
348C22×D7—28no—
349C22×D7—28no—
350C22×D7—28no—
351C22×D7—22no—
352C22×D7—22no—
353C22×D7—22no—
354C22×D7—22no—
355C22×D7—28no—
356C22×D7—28no—
357C22×D7—28no—
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—22no—
361C22×D7—22no—
362C22×D7—22no—
363C22×D7—22no—
364C22×D7—44no—
365C22×D7—44no—
366C22×D7—44no—
367C22×D7—44no—
368C22×D7C4×D4116yes—
369C22×D7C23×C414yes—
370C22×D7C23×C414yes—
371C22×D7C22×D414yes—
372C22×D7C2×#4114yes—
373C2×C4×C7—28no—
374C2×C4×C7—28no—
375C2×C4×C7—28no—
376C2×C4×C7—28no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—44no—
395C2×C4×C7—44no—
396C2×C4×C7—44no—
397C2×C4×C7C23×C414yes—
398C2×C4×C7C23×C414yes—
399C2×C4×C7C23×C414yes—
400C2×C4×C7C22×D414yes—
401C2×Dic7—28no—
402C2×Dic7—28no—
403C2×Dic7—28no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—22no—
410C2×Dic7—22no—
411C2×Dic7—22no—
412C2×Dic7—22no—
413C2×Dic7—22no—
414C2×Dic7—22no—
415C2×Dic7—22no—
416C2×Dic7—22no—
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—44no—
420C2×Dic7—44no—
421C2×Dic7—44no—
422C2×Dic7C23×C414yes—
423C2×Dic7C23×C414yes—
424C2×Dic7C22×D414yes—
425D28—232no—
426C4×D7—232no—
427C4×D7—416no—
428C4×D7—416no—
429C4×D7—416no—
430C25—71no—
431C25—71no—
432C22×D4—78no—
433C22×D4—74no—
434C22×D4—144no—
435C22×D4—144no—
436C23×C4—71no—
437C23×C4—71no—
438C23×C4—71no—
439C23×C4—78no—
440C23×C4—74no—
441C23×C4—78no—
442C23×C4—74no—
443C23×C4—71no—
444C23×C4—71no—
445C23×C4—71no—
446C23×C4—74no—
447C23×C4—74no—
448C23×C4—144no—
449C23×C4—144no—
450C23×C4—144no—
451C23×C4—144no—
452C23×C4—282no—
453C23×C4—282no—
454C23×C4—282no—
455C23×C4—282no—
456C23×C4—282no—
457C23×C4—282no—
458C23×C4C22×D711yescharacteristic
459C23×C4C22×D711yescharacteristic
460C23×C4C22×D711yescharacteristic
461C23×C4C22×D711yescharacteristic
462C23×C4C22×D711yescharacteristic
463C23×C4C22×D711yescharacteristic
464C23×C4C22×D711yescharacteristic
465#123—764no—
466C4×D4—1432no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—78no—
469C2×C4⋊C4—74no—
470C2×C4⋊C4—74no—
471C2×C4⋊C4—74no—
472C2×C4⋊C4—74no—
473C2×C4⋊C4—74no—
474C2×C4⋊C4—74no—
475C2×C4⋊C4—74no—
476C2×C4⋊C4—1432no—
477C2×C4⋊C4—144no—
478C2×C4⋊C4—144no—
479C2×C4⋊C4—144no—
480C2×C4⋊C4—144no—
481C2×C4⋊C4—282no—
482C2×C4⋊C4—282no—
483C2×C4⋊C4C4×D718yescomplemented
484C2×C4⋊C4C22×D714yes—
485C2×C4⋊C4C22×D714yes—
486C2×C22⋊C4—78no—
487C2×C22⋊C4—78no—
488C2×C22⋊C4—78no—
489C2×C22⋊C4—74no—
490C2×C22⋊C4—74no—
491C2×C22⋊C4—74no—
492C2×C22⋊C4—74no—
493C2×C22⋊C4—74no—
494C2×C22⋊C4—74no—
495C2×C22⋊C4—74no—
496C2×C22⋊C4—74no—
497C2×C22⋊C4—144no—
498C2×C22⋊C4—144no—
499C2×C22⋊C4—144no—
500C2×C22⋊C4—282no—
501C2×C22⋊C4—282no—
502C2×C42—24no—
503C2×C42—74no—
504C2×C42—74no—
505C2×C42—282no—
506C2×C42—282no—
507C2×C42C22×D714yes—
508#95—74no—
509#95—74no—
510#95—74no—
511#95—74no—
512#95—74no—
513#95—74no—
514#95C22×D714yes—
515#95C22×D714yes—
516#95C22×D714yes—
517#95C22×D714yes—
518C22×C7C2×C4×D414yes—
519C22×C7#52014yes—
520C22×C7#52014yes—
521C22×C7#53414yes—
522C22×C7#53614yes—
523C22×C7#53914yes—
524C22×C7#53914yes—
525C22×C7C24×C411yescharacteristic
526C22×C7C23×D411yescharacteristic
527C22×C7C22×#4111yescharacteristic
528C22×C7C2×H(5,𝔽2)11yescharacteristic
529C22×C7C2×H(5,𝔽2)11yescharacteristic
530C22×C7C2×2−1+411yescharacteristic
531C22×C7C2×2−1+411yescharacteristic
532C2×D7—232no—
533C2×D7—24no—
534C2×D7—24no—
535C2×D7—24no—
536C2×D7—24no—
537C2×D7—24no—
538C2×D7—24no—
539C2×D7—24no—
540C2×D7—24no—
541C2×D7—24no—
542C2×D7—416no—
543C2×D7—42no—
544C2×D7—42no—
545C2×D7—42no—
546C2×D7—42no—
547C2×D7C2×C4×D418yes—
548C4×C7—24no—
549C4×C7—24no—
550C4×C7—24no—
551C4×C7—24no—
552C4×C7—42no—
553C4×C7—42no—
554C4×C7—42no—
555Dic7—24no—
556Dic7—24no—
557Dic7—24no—
558Dic7—42no—
559Dic7—42no—
560Dic7—42no—
561C24—74no—
562C24—74no—
563C24—74no—
564C24—72no—
565C24—74no—
566C24—72no—
567C24—142no—
568C24—142no—
569C24—142no—
570C24—142no—
571C24—142no—
572C24—142no—
573C24—142no—
574C24—142no—
575C24—142no—
576C24—142no—
577C24C23×D711yescharacteristic
578C2×D4—716no—
579C2×D4—148no—
580C2×D4—1432no—
581C2×D4—148no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—74no—
600C22×C4—74no—
601C22×C4—74no—
602C22×C4—72no—
603C22×C4—72no—
604C22×C4—72no—
605C22×C4—716no—
606C22×C4—716no—
607C22×C4—72no—
608C22×C4—72no—
609C22×C4—72no—
610C22×C4—148no—
611C22×C4—1432no—
612C22×C4—148no—
613C22×C4—148no—
614C22×C4—142no—
615C22×C4—142no—
616C22×C4—142no—
617C22×C4—142no—
618C22×C4—142no—
619C22×C4—142no—
620C22×C4—142no—
621C22×C4—142no—
622C22×C4—142no—
623C22×C4—142no—
624C22×C4—142no—
625C22×C4—142no—
626C22×C4—142no—
627C22×C4—142no—
628C22×C4—142no—
629C22×C4—148no—
630C22×C4—2816no—
631C22×C4—284no—
632C22×C4—284no—
633C22×C4—284no—
634C22×C4—284no—
635C22×C4—284no—
636C22×C4—284no—
637C22×C4—2816no—
638C22×C4—2816no—
639C22×C4C2×C4×D714yes—
640C22×C4C2×C4×D714yes—
641C22×C4C2×C4×D714yes—
642C22×C4D4×D714yes—
643C22×C4C23×D712yes—
644C22×C4C23×D712yes—
645C22×C4C23×D712yes—
646C22×C4C23×D712yes—
647C22×C4C23×D712yes—
648C22×C4C23×D712yes—
649C22×C4C23×D712yes—
650C4⋊C4—28no—
651C4⋊C4—716no—
652C4⋊C4—148no—
653C4⋊C4—148no—
654C4⋊C4—148no—
655C4⋊C4—148no—
656C4⋊C4—284no—
657C4⋊C4—284no—
658C4⋊C4C2×C4×D7116yescomplemented
659C22⋊C4—716no—
660C22⋊C4—716no—
661C22⋊C4—716no—
662C22⋊C4—148no—
663C22⋊C4—148no—
664C22⋊C4—148no—
665C22⋊C4—284no—
666C22⋊C4—284no—
667C42—28no—
668C42—284no—
669C42—284no—
670C2×C7#232218yescomplemented
671C2×C7C22×C4×D411yescharacteristic
672C2×C7C2×#52011yescharacteristic
673C2×C7C2×#52011yescharacteristic
674C2×C7C2×#53411yescharacteristic
675C2×C7C2×#53611yescharacteristic
676C2×C7C2×#53911yescharacteristic
677C2×C7C2×#53911yescharacteristic
678D7—28no—
679D7—44no—
680C23—716no—
681C23—74no—
682C23—74no—
683C23—74no—
684C23—74no—
685C23—148no—
686C23—148no—
687C23—148no—
688C23—148no—
689C23—148no—
690C23—148no—
691C23—142no—
692C23—142no—
693C23—142no—
694C23—142no—
695C23—148no—
696C23—148no—
697C23—148no—
698C23—142no—
699C23—142no—
700C23—142no—
701C23—142no—
702C23—142no—
703C23—142no—
704C23—284no—
705C23—284no—
706C23—284no—
707C23—284no—
708C23C22×C4×D712yes—
709C23C2×D4×D712yes—
710C23#655112yes—
711C23D7×#4112yes—
712C23#655312yes—
713C23#655312yes—
714C23#655412yes—
715C23C24×D711yescharacteristic
716D4—1432no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—74no—
742C2×C4—74no—
743C2×C4—74no—
744C2×C4—1432no—
745C2×C4—148no—
746C2×C4—148no—
747C2×C4—148no—
748C2×C4—142no—
749C2×C4—142no—
750C2×C4—142no—
751C2×C4—142no—
752C2×C4—142no—
753C2×C4—142no—
754C2×C4—142no—
755C2×C4—142no—
756C2×C4—142no—
757C2×C4—142no—
758C2×C4—142no—
759C2×C4—142no—
760C2×C4—142no—
761C2×C4—142no—
762C2×C4—142no—
763C2×C4—2816no—
764C2×C4—2816no—
765C2×C4—2816no—
766C2×C4—284no—
767C2×C4—284no—
768C2×C4—284no—
769C2×C4C22×C4×D714yes—
770C2×C4C22×C4×D714yes—
771C2×C4C22×C4×D714yes—
772C2×C4C2×D4×D714yes—
773C7C2×#232211yescharacteristic, complemented, Sylow
774C22—78no—
775C22—1432no—
776C22—144no—
777C22—144no—
778C22—144no—
779C22—144no—
780C22—144no—
781C22—144no—
782C22—144no—
783C22—144no—
784C22—144no—
785C22—2816no—
786C22—282no—
787C22—282no—
788C22—282no—
789C22—282no—
790C22#9021414yes—
791C22C4×D4×D714yes—
792C22#9026514yes—
793C22#9031914yes—
794C22#9034414yes—
795C22#9038314yes—
796C22#9039814yes—
797C22C23×C4×D711yescharacteristic
798C22C22×D4×D711yescharacteristic
799C22C2×#655111yescharacteristic
800C22C2×D7×#4111yescharacteristic
801C22C2×#655311yescharacteristic
802C22C2×#655311yescharacteristic
803C22C2×#655411yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—24no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—144no—
812C4—144no—
813C4—144no—
814C4—282no—
815C4—282no—
816C4—282no—
817C2—148no—
818C2—284no—
819C2#1173274218yesdirect product factor
820C2C2×#9021411yescharacteristic
821C2C2×C4×D4×D711yescharacteristic
822C2C2×#9026511yescharacteristic
823C2C2×#9031911yescharacteristic
824C2C2×#9034411yescharacteristic
825C2C2×#9038311yescharacteristic
826C2C2×#9039811yescharacteristic
subgroupG/H
centerC24C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC2×C7×#387C2
socleC24×C7C24
prime radicalC23×D28C22
cosocleC23×C7C25
hypercenterC2×#387D7
hypocenterC7C2×#2322
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. C22×D7×C4⋊C4C2semidirect
4. C2×C7×#387C2semidirect
5. C2×#89761C2semidirect
6. C2×#89757C2semidirect
7. C2×#89705C2semidirect
8. #11732742C2direct (N × H)
10. C2×#89440C2semidirect
11. C2×#89440C2semidirect
12. C2×#89436C2semidirect
13. C2×#89419C2semidirect
14. C2×#89442C2semidirect
15. C2×#89441C2semidirect
16. C2×#89438C2semidirect
42. C2×#6457C4semidirect
45. C2×D7×C4⋊C4C22semidirect
48. C7×#387C22semidirect
59. #89761C22semidirect
60. #89757C22semidirect
61. #89705C22semidirect
62. #89442C22semidirect
63. #89441C22semidirect
64. #89440C22semidirect
65. #89440C22semidirect
66. #89438C22semidirect
68. #89436C22semidirect
69. #89419C22semidirect
100. C22×C4×D7C2×C4semidirect
107. C2×C7×C4⋊C4C2×C4semidirect
117. C2×(C2×D7)⋊C4C2×C4semidirect
118. C2×(C2×D7)⋊C4C2×C4semidirect
119. C2×(C2×D7)⋊C4C2×C4semidirect
137. C2×Dic7⋊C4C2×C4semidirect
146. #6457C2×C4semidirect
168. C2×#387D7semidirect
262. C2×C4×D7C22×C4semidirect
265. C7×C4⋊C4C22×C4semidirect
272. (C2×D7)⋊C4C22×C4semidirect
273. (C2×D7)⋊C4C22×C4semidirect
274. (C2×D7)⋊C4C22×C4semidirect
281. Dic7⋊C4C22×C4semidirect
320. #387C2×D7semidirect
483. C2×C4⋊C4C4×D7semidirect
658. C4⋊C4C2×C4×D7semidirect
670. C2×C7#2322semidirect
773. C7C2×#2322semidirect
819. C2#11732742direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64572
C22×D7×C4⋊C42
C22×C4×D282
C2×C7×#3872
C2×#897612
C2×#897572
C2×#897052
#117327422
C2×#894372
C2×#894402
C2×#894362
C2×#894192
C2×#894422
C2×#894412
C2×#894382
C2×#23227