Finite Group Databasebeta

← C2×#11730917 #13513404

Subgroups — C2×#11730917 #13513404

Order 1792.

3678 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D7C211yesmaximal, characteristic
2C22×#6448C211yesmaximal, characteristic
3C22×C4×Dic14C211yesmaximal, characteristic, complemented
4C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
5C2×#89982C211yesmaximal, characteristic, complemented
6C2×#89729C211yesmaximal, characteristic
7C2×#89717C211yesmaximal, characteristic, complemented
8C2×#89723C211yesmaximal, characteristic, complemented
9C2×#89712C211yesmaximal, characteristic, complemented
10C2×#89712C211yesmaximal, characteristic, complemented
11C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
12#11730917C2116yesmaximal, direct product factor
13C2×#89440C211yesmaximal, characteristic, complemented
14C2×#89418C211yesmaximal, characteristic, complemented
15C2×#89421C211yesmaximal, characteristic, complemented
16C2×#89438C211yesmaximal, characteristic, complemented
17C24×C4×C7C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×C4×D7C2211yescharacteristic
20C23×Dic14C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C42×C7C2211yescharacteristic
24C22×C42×C7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C2×C4×C22⋊D7—28no—
29C2×C4×C22⋊D7C2218yes—
30C22×(C2×D7)⋊C4C2211yescharacteristic
31C22×(C2×D7)⋊C4C2211yescharacteristic
32C22×(C2×D7)⋊C4C2211yescharacteristic
33C22×(C2×D7)⋊C4C2211yescharacteristic
34C22×(C2×D7)⋊C4C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C22×C4×Dic7C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C22×C4×Dic7C2211yescharacteristic
45C22×C4×Dic7C2211yescharacteristic
46C2×#6448C4116yescomplemented
47C2×#6448C2218yes—
48C2×C4×Dic14—28no—
49C2×C4×Dic14C2218yescomplemented
50C4×C7×C22⋊C4C2218yescomplemented
51C2×C7×#95C2211yescharacteristic
52C2×C7×#95C2211yescharacteristic
53#89982C2218yescomplemented
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60#89729C2218yes—
61#89723C2218yescomplemented
62#89717C2218yescomplemented
63#89712C2218yescomplemented
64#89712C2218yescomplemented
65C4×Dic7⋊C4C2218yescomplemented
66#89440C2218yescomplemented
67#89438C2218yescomplemented
68#89421C2218yescomplemented
69#89418C2218yescomplemented
70C2×#2367—71nomaximal, Sylow
71C25×C7C2311yescharacteristic
72C24×D7C2311yescharacteristic
73C23×C4×C7—24no—
74C23×C4×C7—24no—
75C23×C4×C7—42no—
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2314yes—
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⋊D7C2×C418yes—
86C22×C22⋊D7C2314yes—
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C22×C4×D7—24no—
95C22×C4×D7—24no—
96C22×C4×D7—42no—
97C22×C4×D7C2314yes—
98C22×Dic14—24no—
99C22×Dic14—24no—
100C22×Dic14C2×C418yescomplemented
101C22×Dic14C2314yes—
102C2×C7×C22⋊C4—24no—
103C2×C7×C22⋊C4C2×C418yescomplemented
104C2×C7×C22⋊C4C2314yes—
105C2×C7×C22⋊C4C2314yes—
106C2×C42×C7—24no—
107C2×C42×C7—42no—
108C2×C42×C7C2314yes—
109C2×C42×C7C2314yes—
110C2×C22⋊Dic7—24no—
111C2×C22⋊Dic7—42no—
112C2×C22⋊Dic7C2×C418yescomplemented
113C2×C22⋊Dic7C2314yes—
114C2×C22⋊Dic7C2314yes—
115C2×C22⋊Dic7C2314yes—
116C4×C22⋊D7—232no—
117C2×(C2×D7)⋊C4—24no—
118C2×(C2×D7)⋊C4—24no—
119C2×(C2×D7)⋊C4—42no—
120C2×(C2×D7)⋊C4C2×C418yescomplemented
121C2×(C2×D7)⋊C4C2×C418yescomplemented
122C2×(C2×D7)⋊C4C2314yes—
123C2×(C2×D7)⋊C4C2314yes—
124C2×(C2×D7)⋊C4C2314yes—
125C2×(C2×D7)⋊C4C2314yes—
126C2×(C2×D7)⋊C4C2314yes—
127C2×C4⋊Dic7—24no—
128C2×C4⋊Dic7C2314yes—
129C2×Dic7⋊C4—24no—
130C2×Dic7⋊C4—24no—
131C2×Dic7⋊C4—24no—
132C2×Dic7⋊C4—24no—
133C2×Dic7⋊C4D418yes—
134C2×Dic7⋊C4C2314yes—
135C2×Dic7⋊C4C2314yes—
136C2×Dic7⋊C4C2314yes—
137C2×Dic7⋊C4C2314yes—
138C2×Dic7⋊C4C2314yes—
139C2×C4×Dic7—24no—
140C2×C4×Dic7—24no—
141C2×C4×Dic7—24no—
142C2×C4×Dic7—42no—
143C2×C4×Dic7C2×C418yescomplemented
144C2×C4×Dic7C2314yes—
145C2×C4×Dic7C2314yes—
146C2×C4×Dic7C2314yes—
147C2×C4×Dic7C2314yes—
148C2×C4×Dic7C2314yes—
149#6448C2×C4164yescomplemented
150C4×Dic14—232no—
151C7×#95C2314yes—
152C7×#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×#124—71no—
160C22×C4×Q8—71no—
161C22×C4×D4—71no—
162#2367—716no—
163C2×#391—71no—
164C2×#390—71no—
165C2×#388—71no—
166C2×#388—71no—
167C2×#388—71no—
168C2×#388—71no—
169C2×#385—71no—
170C2×#385—71no—
171C2×C4×C4⋊C4—71no—
172C2×C4×C4⋊C4—71no—
173C2×C4×C22⋊C4—71no—
174C2×C4×C22⋊C4D711yescharacteristic, complemented
175C24×C7—22no—
176C24×C7—22no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7—22no—
180C24×C7—22no—
181C24×C7C22×C414yes—
182C24×C7C2412yes—
183C24×C7C2411yescharacteristic
184C23×D7—22no—
185C23×D7—22no—
186C23×D7—22no—
187C23×D7—22no—
188C23×D7—22no—
189C23×D7—22no—
190C23×D7C22×C414yes—
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—28no—
206C22×C4×C7—28no—
207C22×C4×C7—44no—
208C22×C4×C7—416no—
209C22×C4×C7C22×C414yes—
210C22×C4×C7C22×C414yes—
211C22×C4×C7C2×D414yes—
212C22×C4×C7#4114yes—
213C22×C4×C7#4114yes—
214C22×C4×C7C2412yes—
215C22×C4×C7C2412yes—
216C22×C4×C7C2412yes—
217C22×C4×C7C2412yes—
218C22×C4×C7C2412yes—
219C22×C4×C7C2412yes—
220C2×C22⋊D7—232no—
221C2×C22⋊D7—28no—
222C2×C22⋊D7—28no—
223C2×C22⋊D7C22×C4116yes—
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×Dic7—22no—
236C22×Dic7—22no—
237C22×Dic7—22no—
238C22×Dic7—22no—
239C22×Dic7C22×C414yes—
240C22×Dic7C22×C414yes—
241C22×Dic7C22×C414yes—
242C22×Dic7C2×D414yes—
243C22×Dic7C2×D414yes—
244C22×Dic7#4114yes—
245C22×Dic7C2412yes—
246C22×Dic7C2412yes—
247C22×Dic7C2412yes—
248C22×Dic7C2412yes—
249C22×Dic7C2412yes—
250C22×Dic7C2412yes—
251C22×Dic7C2412yes—
252C2×C4×D7—28no—
253C2×C4×D7—28no—
254C2×C4×D7—44no—
255C2×C4×D7—416no—
256C2×Dic14—232no—
257C2×Dic14—28no—
258C2×Dic14—28no—
259C2×Dic14C22×C4116yescomplemented
260C7×C22⋊C4—28no—
261C7×C22⋊C4C22×C4116yescomplemented
262C42×C7—28no—
263C42×C7—44no—
264C22⋊Dic7—28no—
265C22⋊Dic7—44no—
266C22⋊Dic7C22×C4116yescomplemented
267(C2×D7)⋊C4—28no—
268(C2×D7)⋊C4—28no—
269(C2×D7)⋊C4—44no—
270(C2×D7)⋊C4C22×C4116yescomplemented
271(C2×D7)⋊C4C22×C4116yescomplemented
272C4⋊Dic7—28no—
273Dic7⋊C4—28no—
274Dic7⋊C4—28no—
275Dic7⋊C4—28no—
276Dic7⋊C4—28no—
277Dic7⋊C4C2×D4116yes—
278C4×Dic7—28no—
279C4×Dic7—28no—
280C4×Dic7—28no—
281C4×Dic7—44no—
282C4×Dic7C22×C4116yescomplemented
283C23×Q8—71no—
284C23×D4—71no—
285C24×C4—71no—
286C24×C4C2×D711yescharacteristic
287C2×#124—716no—
288C2×#124—78no—
289C2×C4×Q8—78no—
290C2×C4×Q8—148no—
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×C22⋊C4—71no—
300C22×C22⋊C4—71no—
301C22×C22⋊C4—71no—
302C22×C22⋊C4—71no—
303C22×C22⋊C4—71no—
304C22×C22⋊C4—71no—
305C22×C22⋊C4—71no—
306C22×C22⋊C4—71no—
307C22×C22⋊C4C2×D711yescharacteristic
308C22×C22⋊C4C2×D711yescharacteristic
309C22×C42—71no—
310C22×C42—71no—
311C22×C42—71no—
312C22×C42—71no—
313C22×C42—71no—
314C22×C42C2×D711yescharacteristic
315C22×C42C2×D711yescharacteristic
316#391—78no—
317#390—78no—
318#388—78no—
319#388—78no—
320#388—78no—
321#388—78no—
322#385—78no—
323#385—78no—
324C4×C4⋊C4—78no—
325C4×C4⋊C4—78no—
326C4×C22⋊C4—78no—
327C4×C22⋊C4C2×D718yescomplemented
328C2×#95—71no—
329C2×#95—71no—
330C2×#95—71no—
331C2×#95—71no—
332C2×#95—71no—
333C2×#95—71no—
334C2×#95C2×D711yescharacteristic
335C2×#95C2×D711yescharacteristic
336C23×C7—28no—
337C23×C7—28no—
338C23×C7—28no—
339C23×C7—22no—
340C23×C7—22no—
341C23×C7—22no—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—22no—
345C23×C7—44no—
346C23×C7—44no—
347C23×C7—44no—
348C23×C7—44no—
349C23×C7C23×C414yes—
350C23×C7C23×C412yes—
351C23×C7C22×D412yes—
352C23×C7C2×#4112yes—
353C23×C7C2×#4112yes—
354C23×C7C2×#4112yes—
355C23×C7H(5,𝔽2)12yes—
356C23×C72−1+412yes—
357C23×C7C2511yescharacteristic
358C22×D7—28no—
359C22×D7—28no—
360C22×D7—28no—
361C22×D7—22no—
362C22×D7—22no—
363C22×D7—22no—
364C22×D7—22no—
365C22×D7—22no—
366C22×D7—22no—
367C22×D7—44no—
368C22×D7—44no—
369C22×D7—44no—
370C22×D7—44no—
371C22×D7C23×C414yes—
372C2×C4×C7—28no—
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—416no—
391C2×C4×C7—44no—
392C2×C4×C7C23×C414yes—
393C2×C4×C7C23×C414yes—
394C2×C4×C7C22×D414yes—
395C2×C4×C7C2×#4114yes—
396C2×C4×C7C2×#4114yes—
397C22⋊D7—232no—
398C2×Dic7—28no—
399C2×Dic7—28no—
400C2×Dic7—28no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
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—44no—
417C2×Dic7—44no—
418C2×Dic7—44no—
419C2×Dic7C4×D4116yes—
420C2×Dic7C23×C414yes—
421C2×Dic7C23×C414yes—
422C2×Dic7C23×C414yes—
423C2×Dic7C22×D414yes—
424C2×Dic7C22×D414yes—
425C2×Dic7C2×#4114yes—
426C4×D7—416no—
427Dic14—232no—
428C25—71no—
429C25C22×D711yescharacteristic
430C22×Q8—78no—
431C22×Q8—74no—
432C22×Q8—144no—
433C22×Q8—144no—
434C22×D4—78no—
435C22×D4—74no—
436C22×D4—144no—
437C22×D4—144no—
438C23×C4—24no—
439C23×C4—24no—
440C23×C4—42no—
441C23×C4—71no—
442C23×C4—71no—
443C23×C4—71no—
444C23×C4—71no—
445C23×C4—71no—
446C23×C4—71no—
447C23×C4—71no—
448C23×C4—74no—
449C23×C4—144no—
450C23×C4—144no—
451C23×C4—282no—
452C23×C4C22×D711yescharacteristic
453C23×C4C22×D714yes—
454C23×C4C22×D711yescharacteristic
455C23×C4C22×D711yescharacteristic
456C23×C4C22×D711yescharacteristic
457C23×C4C22×D711yescharacteristic
458C23×C4C22×D711yescharacteristic
459#124—764no—
460C4×Q8—1432no—
461C4×D4—1432no—
462C2×C4⋊C4—78no—
463C2×C4⋊C4—74no—
464C2×C4⋊C4—74no—
465C2×C4⋊C4—74no—
466C2×C4⋊C4—74no—
467C2×C4⋊C4—74no—
468C2×C4⋊C4—74no—
469C2×C4⋊C4—144no—
470C2×C4⋊C4—144no—
471C2×C4⋊C4—144no—
472C2×C4⋊C4—144no—
473C2×C4⋊C4—144no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—78no—
476C2×C22⋊C4—74no—
477C2×C22⋊C4—78no—
478C2×C22⋊C4—78no—
479C2×C22⋊C4—74no—
480C2×C22⋊C4—74no—
481C2×C22⋊C4—74no—
482C2×C22⋊C4—74no—
483C2×C22⋊C4—74no—
484C2×C22⋊C4—74no—
485C2×C22⋊C4—74no—
486C2×C22⋊C4—144no—
487C2×C22⋊C4—144no—
488C2×C22⋊C4—144no—
489C2×C22⋊C4—282no—
490C2×C22⋊C4—282no—
491C2×C22⋊C4C4×D718yescomplemented
492C2×C22⋊C4C22×D714yes—
493C2×C22⋊C4C22×D714yes—
494C2×C42—24no—
495C2×C42—42no—
496C2×C42—78no—
497C2×C42—74no—
498C2×C42—74no—
499C2×C42—74no—
500C2×C42—74no—
501C2×C42—74no—
502C2×C42—144no—
503C2×C42—144no—
504C2×C42—144no—
505C2×C42—282no—
506C2×C42C22×D714yes—
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—
516C22×C7—24no—
517C22×C7—24no—
518C22×C7—24no—
519C22×C7—416no—
520C22×C7—42no—
521C22×C7—42no—
522C22×C7—42no—
523C22×C7—42no—
524C22×C7C2×C4×D414yes—
525C22×C7C4×#4114yes—
526C22×C7#52014yes—
527C22×C7#54614yes—
528C22×C7#54814yes—
529C22×C7#55614yes—
530C22×C7#55914yes—
531C22×C7C24×C411yescharacteristic
532C22×C7C23×D411yescharacteristic
533C22×C7C22×#4111yescharacteristic
534C22×C7C22×#4111yescharacteristic
535C22×C7C22×#4111yescharacteristic
536C22×C7C2×H(5,𝔽2)11yescharacteristic
537C22×C7C2×2−1+411yescharacteristic
538C2×D7—24no—
539C2×D7—24no—
540C2×D7—24no—
541C2×D7—416no—
542C2×D7—42no—
543C2×D7—42no—
544C2×D7—42no—
545C2×D7—42no—
546C4×C7—24no—
547C4×C7—24no—
548C4×C7—24no—
549C4×C7—24no—
550C4×C7—24no—
551C4×C7—42no—
552Dic7—24no—
553Dic7—24no—
554Dic7—24no—
555Dic7—42no—
556Dic7—42no—
557Dic7—42no—
558Dic7C2×C4×D418yes—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24—74no—
566C24—72no—
567C24—142no—
568C24—142no—
569C24—142no—
570C24—142no—
571C24—142no—
572C24—142no—
573C24C2×C4×D714yes—
574C24C23×D712yes—
575C24C23×D711yescharacteristic
576C2×Q8—716no—
577C2×Q8—148no—
578C2×Q8—1432no—
579C2×Q8—148no—
580C2×D4—716no—
581C2×D4—148no—
582C2×D4—1432no—
583C2×D4—148no—
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—28no—
598C22×C4—28no—
599C22×C4—44no—
600C22×C4—416no—
601C22×C4—74no—
602C22×C4—74no—
603C22×C4—74no—
604C22×C4—72no—
605C22×C4—74no—
606C22×C4—74no—
607C22×C4—74no—
608C22×C4—72no—
609C22×C4—72no—
610C22×C4—72no—
611C22×C4—72no—
612C22×C4—72no—
613C22×C4—72no—
614C22×C4—148no—
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—142no—
630C22×C4—148no—
631C22×C4—284no—
632C22×C4—2816no—
633C22×C4C2×C4×D714yes—
634C22×C4C2×C4×D714yes—
635C22×C4#115714yes—
636C22×C4#115714yes—
637C22×C4D4×D714yes—
638C22×C4C23×D712yes—
639C22×C4C23×D712yes—
640C22×C4C23×D712yes—
641C22×C4C23×D712yes—
642C22×C4C23×D712yes—
643C22×C4C23×D712yes—
644C4⋊C4—716no—
645C4⋊C4—148no—
646C4⋊C4—148no—
647C4⋊C4—148no—
648C4⋊C4—148no—
649C4⋊C4—148no—
650C22⋊C4—28no—
651C22⋊C4—716no—
652C22⋊C4—716no—
653C22⋊C4—716no—
654C22⋊C4—148no—
655C22⋊C4—148no—
656C22⋊C4—148no—
657C22⋊C4—284no—
658C22⋊C4—284no—
659C22⋊C4C2×C4×D7116yescomplemented
660C42—28no—
661C42—44no—
662C42—716no—
663C42—148no—
664C42—148no—
665C42—148no—
666C42—284no—
667C2×C7—44no—
668C2×C7#236718yescomplemented
669C2×C7C22×C4×D411yescharacteristic
670C2×C7C2×C4×#4111yescharacteristic
671C2×C7C2×#52011yescharacteristic
672C2×C7C2×#54611yescharacteristic
673C2×C7C2×#54811yescharacteristic
674C2×C7C2×#55611yescharacteristic
675C2×C7C2×#55911yescharacteristic
676D7—44no—
677C23—28no—
678C23—28no—
679C23—28no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—74no—
691C23—148no—
692C23—148no—
693C23—148no—
694C23—142no—
695C23—142no—
696C23—142no—
697C23—142no—
698C23—142no—
699C23—142no—
700C23—284no—
701C23—284no—
702C23—284no—
703C23—284no—
704C23C22×C4×D714yes—
705C23C22×C4×D712yes—
706C23C2×#115712yes—
707C23C2×#115712yes—
708C23C2×D4×D712yes—
709C23#654812yes—
710C23D7×#4112yes—
711C23#655412yes—
712C23C24×D711yescharacteristic
713Q8—1432no—
714D4—1432no—
715C2×C4—28no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—22no—
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—416no—
734C2×C4—44no—
735C2×C4—716no—
736C2×C4—74no—
737C2×C4—74no—
738C2×C4—74no—
739C2×C4—74no—
740C2×C4—74no—
741C2×C4—74no—
742C2×C4—148no—
743C2×C4—148no—
744C2×C4—148no—
745C2×C4—142no—
746C2×C4—142no—
747C2×C4—142no—
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—2816no—
761C2×C4—284no—
762C2×C4—284no—
763C2×C4—284no—
764C2×C4C22×C4×D714yes—
765C2×C4C22×C4×D714yes—
766C2×C4C2×#115714yes—
767C2×C4C2×#115714yes—
768C2×C4C2×D4×D714yes—
769C7C2×#236711yescharacteristic, complemented, Sylow
770C22—24no—
771C22—24no—
772C22—24no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—416no—
778C22—144no—
779C22—144no—
780C22—144no—
781C22—282no—
782C22—282no—
783C22—282no—
784C22—282no—
785C22—2816no—
786C22C4×#115714yes—
787C22#9018114yes—
788C22#9022414yes—
789C22C4×D4×D714yes—
790C22#9023714yes—
791C22#9024314yes—
792C22#9025014yes—
793C22C23×C4×D711yescharacteristic
794C22C22×#115711yescharacteristic
795C22C22×#115711yescharacteristic
796C22C22×D4×D711yescharacteristic
797C22C2×#654811yescharacteristic
798C22C2×D7×#4111yescharacteristic
799C22C2×#655411yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—24no—
804C4—24no—
805C4—42no—
806C4—78no—
807C4—144no—
808C4—144no—
809C4—144no—
810C4—282no—
811C4—282no—
812C4—282no—
813C2—44no—
814C2—284no—
815C2#1173091718yesdirect product factor
816C2C2×C4×#115711yescharacteristic
817C2C2×#9018111yescharacteristic
818C2C2×#9022411yescharacteristic
819C2C2×#9023711yescharacteristic
820C2C2×#9024311yescharacteristic
821C2C2×#9025011yescharacteristic
822C2C2×C4×D4×D711yescharacteristic
subgroupG/H
centerC24C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC2×C4×C7×C22⋊C4C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
cosocleC23×C7C25
hypercenterC2×C4×C22⋊C4D7
hypocenterC7C2×#2367
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×C4×Dic14C2semidirect
4. C2×C4×C7×C22⋊C4C2semidirect
5. C2×#89982C2semidirect
7. C2×#89717C2semidirect
8. C2×#89723C2semidirect
9. C2×#89712C2semidirect
10. C2×#89712C2semidirect
11. C2×C4×Dic7⋊C4C2semidirect
12. #11730917C2direct (N × H)
13. C2×#89440C2semidirect
14. C2×#89418C2semidirect
15. C2×#89421C2semidirect
16. C2×#89438C2semidirect
46. C2×#6448C4semidirect
49. C2×C4×Dic14C22semidirect
50. C4×C7×C22⋊C4C22semidirect
53. #89982C22semidirect
61. #89723C22semidirect
62. #89717C22semidirect
63. #89712C22semidirect
64. #89712C22semidirect
65. C4×Dic7⋊C4C22semidirect
66. #89440C22semidirect
67. #89438C22semidirect
68. #89421C22semidirect
69. #89418C22semidirect
100. C22×Dic14C2×C4semidirect
103. C2×C7×C22⋊C4C2×C4semidirect
112. C2×C22⋊Dic7C2×C4semidirect
120. C2×(C2×D7)⋊C4C2×C4semidirect
121. C2×(C2×D7)⋊C4C2×C4semidirect
143. C2×C4×Dic7C2×C4semidirect
149. #6448C2×C4semidirect
174. C2×C4×C22⋊C4D7semidirect
259. C2×Dic14C22×C4semidirect
261. C7×C22⋊C4C22×C4semidirect
266. C22⋊Dic7C22×C4semidirect
270. (C2×D7)⋊C4C22×C4semidirect
271. (C2×D7)⋊C4C22×C4semidirect
282. C4×Dic7C22×C4semidirect
327. C4×C22⋊C4C2×D7semidirect
491. C2×C22⋊C4C4×D7semidirect
659. C22⋊C4C2×C4×D7semidirect
668. C2×C7#2367semidirect
769. C7C2×#2367semidirect
815. C2#11730917direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D72
C22×#64482
C22×C4×Dic142
C2×C4×C7×C22⋊C42
C2×#899822
C2×#897292
C2×#897172
C2×#897232
C2×#897122
C2×C4×Dic7⋊C42
#117309172
C2×#894402
C2×#894182
C2×#894212
C2×#894382
C2×#23677