Finite Group Databasebeta

← C2×C4×#6446 #13512230

Subgroups — C2×C4×#6446 #13512230

Order 1792.

4070 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×C4×C22⋊D7C211yesmaximal, characteristic
2C22×#6446C211yesmaximal, characteristic
3C22×C42×D7C211yesmaximal, characteristic, complemented
4C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊Dic7C211yesmaximal, characteristic, complemented
6C2×#89728C211yesmaximal, characteristic
7C2×#89717C211yesmaximal, characteristic, complemented
8C2×#89723C211yesmaximal, characteristic, complemented
9C2×C4×C4⋊Dic7C211yesmaximal, characteristic, complemented
10C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
11C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
12C4×#6446C2116yesmaximal, direct product factor
13C2×#89440C211yesmaximal, characteristic, complemented
14C2×#89436C211yesmaximal, characteristic, complemented
15C2×#89426C211yesmaximal, characteristic, complemented
16C2×#89424C211yesmaximal, characteristic, complemented
17C24×C4×C7C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×C4×D7C2211yescharacteristic
20C23×C4×D7C2211yescharacteristic
21C23×C4×D7C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C42×C7C2211yescharacteristic
25C22×C42×C7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C2×C4×C22⋊D7—28no—
30C2×C4×C22⋊D7C2218yes—
31C22×(C2×D7)⋊C4C2211yescharacteristic
32C22×(C2×D7)⋊C4C2211yescharacteristic
33C22×(C2×D7)⋊C4C2211yescharacteristic
34C22×C4⋊Dic7C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C22×C4×Dic7C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C22×C4×Dic7C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C2×#6446C4116yesdirect product factor
45C2×#6446C2218yes—
46C2×C42×D7—28no—
47C2×C42×D7C2218yescomplemented
48C4×C7×C22⋊C4C2218yescomplemented
49C2×C7×#95C2211yescharacteristic
50C2×C7×#95C2211yescharacteristic
51C4×C22⋊Dic7C2218yescomplemented
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60#89728C2218yes—
61#89723C2218yescomplemented
62#89717C2218yescomplemented
63C4×(C2×D7)⋊C4C2218yescomplemented
64C4×C4⋊Dic7C2218yescomplemented
65C4×Dic7⋊C4C2218yescomplemented
66#89440C2218yescomplemented
67#89436C2218yescomplemented
68#89426C2218yescomplemented
69#89424C2218yescomplemented
70C2×C4×#123—71nomaximal, Sylow
71C25×C7C2311yescharacteristic
72C24×D7C2311yescharacteristic
73C23×C4×C7—24no—
74C23×C4×C7—24no—
75C23×C4×C7—24no—
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2314yes—
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—24no—
97C22×C4×D7—24no—
98C22×C4×D7—24no—
99C22×C4×D7—24no—
100C22×C4×D7—24no—
101C22×C4×D7C2×C418yescomplemented
102C22×C4×D7D418yes—
103C22×C4×D7C2314yes—
104C22×C4×D7C2314yes—
105C22×C4×D7C2314yes—
106C2×C7×C22⋊C4—24no—
107C2×C7×C22⋊C4C2×C418yescomplemented
108C2×C7×C22⋊C4C2314yes—
109C2×C7×C22⋊C4C2314yes—
110C2×C42×C7—24no—
111C2×C42×C7—24no—
112C2×C42×C7C2314yes—
113C2×C42×C7C2314yes—
114C2×C22⋊Dic7—24no—
115C2×C22⋊Dic7—24no—
116C2×C22⋊Dic7C2×C418yescomplemented
117C2×C22⋊Dic7C2314yes—
118C2×C22⋊Dic7C2314yes—
119C2×C22⋊Dic7C2314yes—
120C4×C22⋊D7—232no—
121C2×(C2×D7)⋊C4—24no—
122C2×(C2×D7)⋊C4—24no—
123C2×(C2×D7)⋊C4C2×C418yescomplemented
124C2×(C2×D7)⋊C4C2314yes—
125C2×(C2×D7)⋊C4C2314yes—
126C2×(C2×D7)⋊C4C2314yes—
127C2×C4⋊Dic7—24no—
128C2×C4⋊Dic7C2×C418yescomplemented
129C2×C4⋊Dic7C2314yes—
130C2×C4⋊Dic7C2314yes—
131C2×Dic7⋊C4—24no—
132C2×Dic7⋊C4—24no—
133C2×Dic7⋊C4C2×C418yescomplemented
134C2×Dic7⋊C4C2314yes—
135C2×Dic7⋊C4C2314yes—
136C2×Dic7⋊C4C2314yes—
137C2×C4×Dic7—24no—
138C2×C4×Dic7—24no—
139C2×C4×Dic7—24no—
140C2×C4×Dic7—24no—
141C2×C4×Dic7—24no—
142C2×C4×Dic7C2314yes—
143C2×C4×Dic7C2314yes—
144C2×C4×Dic7C2314yes—
145C2×C4×Dic7C2314yes—
146C2×C4×Dic7C2314yes—
147#6446C2×C4164yesdirect product factor
148C42×D7—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×C42—71no—
162C4×#123—716no—
163C2×#388—71no—
164C2×#388—71no—
165C2×#387—71no—
166C2×#387—71no—
167C2×#386—71no—
168C2×#385—71no—
169C2×#381—71no—
170C2×C4×C4⋊C4—71no—
171C2×C4×C4⋊C4—71no—
172C2×C4×C22⋊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×D7C22×C414yes—
189C23×D7C2×D414yes—
190C23×D7#4114yes—
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—28no—
205C22×C4×C7—28no—
206C22×C4×C7—28no—
207C22×C4×C7—416no—
208C22×C4×C7C22×C414yes—
209C22×C4×C7C22×C414yes—
210C22×C4×C7C2×D414yes—
211C22×C4×C7#4114yes—
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×Dic7—22no—
240C22×Dic7C22×C414yes—
241C22×Dic7C22×C414yes—
242C22×Dic7C22×C414yes—
243C22×Dic7C2×D414yes—
244C22×Dic7#4114yes—
245C22×Dic7C2412yes—
246C22×Dic7C2412yes—
247C22×Dic7C2412yes—
248C22×Dic7C2412yes—
249C22×Dic7C2412yes—
250C22×Dic7C2412yes—
251C22×Dic7C2412yes—
252C2×C4×D7—232no—
253C2×C4×D7—232no—
254C2×C4×D7—28no—
255C2×C4×D7—28no—
256C2×C4×D7—28no—
257C2×C4×D7—232no—
258C2×C4×D7—28no—
259C2×C4×D7—28no—
260C2×C4×D7—28no—
261C2×C4×D7—28no—
262C2×C4×D7C22×C4116yescomplemented
263C2×C4×D7C2×D4116yes—
264C7×C22⋊C4—28no—
265C7×C22⋊C4C22×C4116yescomplemented
266C42×C7—28no—
267C42×C7—28no—
268C22⋊Dic7—28no—
269C22⋊Dic7—28no—
270C22⋊Dic7C22×C4116yescomplemented
271(C2×D7)⋊C4—28no—
272(C2×D7)⋊C4—28no—
273(C2×D7)⋊C4C22×C4116yescomplemented
274C4⋊Dic7—28no—
275C4⋊Dic7C22×C4116yescomplemented
276Dic7⋊C4—28no—
277Dic7⋊C4—28no—
278Dic7⋊C4C22×C4116yescomplemented
279C4×Dic7—28no—
280C4×Dic7—28no—
281C4×Dic7—28no—
282C4×Dic7—28no—
283C4×Dic7—28no—
284C23×D4—71no—
285C24×C4—71no—
286C24×C4—71no—
287C24×C4—71no—
288C24×C4C2×D711yescharacteristic
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×C22⋊C4—71no—
299C22×C22⋊C4—71no—
300C22×C22⋊C4—71no—
301C22×C22⋊C4—71no—
302C22×C22⋊C4—71no—
303C22×C22⋊C4—71no—
304C22×C22⋊C4C2×D711yescharacteristic
305C22×C22⋊C4C2×D711yescharacteristic
306C22×C42—71no—
307C22×C42—71no—
308C22×C42—71no—
309C22×C42—71no—
310C22×C42—71no—
311C22×C42—78no—
312C22×C42—148no—
313C22×C42C2×D711yescharacteristic
314C22×C42C2×D711yescharacteristic
315#388—78no—
316#388—78no—
317#387—78no—
318#387—78no—
319#386—78no—
320#385—78no—
321#381—78no—
322C4×C4⋊C4—78no—
323C4×C4⋊C4—78no—
324C4×C22⋊C4—78no—
325C4×C22⋊C4—78no—
326C4×C22⋊C4C2×D718yescomplemented
327C2×#95—71no—
328C2×#95—71no—
329C2×#95—71no—
330C2×#95—71no—
331C2×#95—71no—
332C2×#95—71no—
333C2×#95—71no—
334C2×#95—71no—
335C2×#95C2×D711yescharacteristic
336C2×#95C2×D711yescharacteristic
337C23×C7—28no—
338C23×C7—28no—
339C23×C7—28no—
340C23×C7—22no—
341C23×C7—22no—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—22no—
345C23×C7—22no—
346C23×C7—44no—
347C23×C7—44no—
348C23×C7—44no—
349C23×C7—44no—
350C23×C7C23×C414yes—
351C23×C7C23×C412yes—
352C23×C7C22×D412yes—
353C23×C7C2×#4112yes—
354C23×C7C2×#4112yes—
355C23×C7C2×#4112yes—
356C23×C7C2×#4112yes—
357C23×C7C2×#4112yes—
358C23×C7C2511yescharacteristic
359C22×D7—28no—
360C22×D7—28no—
361C22×D7—28no—
362C22×D7—28no—
363C22×D7—28no—
364C22×D7—28no—
365C22×D7—22no—
366C22×D7—22no—
367C22×D7—22no—
368C22×D7—22no—
369C22×D7C4×D4116yes—
370C22×D7C23×C414yes—
371C22×D7C22×D414yes—
372C22×D7C2×#4114yes—
373C2×C4×C7—28no—
374C2×C4×C7—28no—
375C2×C4×C7—28no—
376C2×C4×C7—22no—
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—44no—
389C2×C4×C7—44no—
390C2×C4×C7—416no—
391C2×C4×C7#123116yescomplemented
392C2×C4×C7C23×C414yes—
393C2×C4×C7C23×C414yes—
394C2×C4×C7C22×D414yes—
395C2×C4×C7C2×#4114yes—
396C2×C4×C7C2×#4114yes—
397C2×C4×C7C2×#4114yes—
398C22⋊D7—232no—
399C2×Dic7—28no—
400C2×Dic7—28no—
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—22no—
420C2×Dic7—44no—
421C2×Dic7—44no—
422C2×Dic7C23×C414yes—
423C2×Dic7C23×C414yes—
424C2×Dic7C23×C414yes—
425C2×Dic7C22×D414yes—
426C2×Dic7C2×#4114yes—
427C4×D7—232no—
428C4×D7—232no—
429C4×D7—232no—
430C25—71no—
431C25C22×D711yescharacteristic
432C22×D4—78no—
433C22×D4—74no—
434C22×D4—144no—
435C22×D4—144no—
436C23×C4—24no—
437C23×C4—24no—
438C23×C4—24no—
439C23×C4—71no—
440C23×C4—71no—
441C23×C4—71no—
442C23×C4—71no—
443C23×C4—71no—
444C23×C4—78no—
445C23×C4—78no—
446C23×C4—74no—
447C23×C4—74no—
448C23×C4—71no—
449C23×C4—71no—
450C23×C4—74no—
451C23×C4—144no—
452C23×C4—144no—
453C23×C4—144no—
454C23×C4—144no—
455C23×C4—144no—
456C23×C4—144no—
457C23×C4—144no—
458C23×C4C22×D711yescharacteristic
459C23×C4C22×D711yescharacteristic
460C23×C4C22×D714yes—
461C23×C4C22×D711yescharacteristic
462C23×C4C22×D711yescharacteristic
463C23×C4C22×D711yescharacteristic
464C23×C4C22×D711yescharacteristic
465#123—764no—
466C4×D4—1432no—
467C2×C4⋊C4—78no—
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—144no—
475C2×C4⋊C4—144no—
476C2×C4⋊C4—144no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—78no—
479C2×C22⋊C4—74no—
480C2×C22⋊C4—78no—
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—144no—
490C2×C22⋊C4C4×D718yescomplemented
491C2×C22⋊C4C22×D714yes—
492C2×C22⋊C4C22×D714yes—
493C2×C42—24no—
494C2×C42—24no—
495C2×C42—74no—
496C2×C42—74no—
497C2×C42—74no—
498C2×C42—74no—
499C2×C42—74no—
500C2×C42—1432no—
501C2×C42—144no—
502C2×C42—144no—
503C2×C42—144no—
504C2×C42—144no—
505C2×C42—144no—
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#95—74no—
515#95—74no—
516#95C22×D714yes—
517#95C22×D714yes—
518C22×C7—24no—
519C22×C7—24no—
520C22×C7—24no—
521C22×C7—42no—
522C22×C7—42no—
523C22×C7—42no—
524C22×C7—42no—
525C22×C7—416no—
526C22×C7C2×C4×D414yes—
527C22×C7C4×#4114yes—
528C22×C7C4×#4114yes—
529C22×C7C2×#12314yes—
530C22×C7#52514yes—
531C22×C7#52914yes—
532C22×C7#52914yes—
533C22×C7C24×C411yescharacteristic
534C22×C7C23×D411yescharacteristic
535C22×C7C22×#4111yescharacteristic
536C22×C7C22×#4111yescharacteristic
537C22×C7C22×#4111yescharacteristic
538C22×C7C22×#4111yescharacteristic
539C22×C7C22×#4111yescharacteristic
540C2×D7—24no—
541C2×D7—24no—
542C2×D7—24no—
543C2×D7—24no—
544C2×D7—24no—
545C2×D7—24no—
546C2×D7—232no—
547C2×D7C2×C4×D418yes—
548C4×C7—24no—
549C4×C7—24no—
550C4×C7—24no—
551C4×C7—42no—
552C4×C7—42no—
553C4×C7C2×#12318yescomplemented
554Dic7—24no—
555Dic7—24no—
556Dic7—24no—
557Dic7—24no—
558Dic7—24no—
559Dic7—42no—
560Dic7—42no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—74no—
568C24—74no—
569C24—74no—
570C24—72no—
571C24—142no—
572C24—142no—
573C24—142no—
574C24—142no—
575C24C2×C4×D714yes—
576C24C23×D712yes—
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—28no—
595C22×C4—28no—
596C22×C4—28no—
597C22×C4—416no—
598C22×C4—74no—
599C22×C4—74no—
600C22×C4—74no—
601C22×C4—74no—
602C22×C4—74no—
603C22×C4—72no—
604C22×C4—72no—
605C22×C4—72no—
606C22×C4—72no—
607C22×C4—72no—
608C22×C4—716no—
609C22×C4—716no—
610C22×C4—72no—
611C22×C4—72no—
612C22×C4—148no—
613C22×C4—148no—
614C22×C4—148no—
615C22×C4—1432no—
616C22×C4—148no—
617C22×C4—1432no—
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—1432no—
629C22×C4—148no—
630C22×C4—148no—
631C22×C4—148no—
632C22×C4—142no—
633C22×C4—142no—
634C22×C4—142no—
635C22×C4—142no—
636C22×C4—142no—
637C22×C4—142no—
638C22×C4C2×C4×D714yes—
639C22×C4C2×C4×D714yes—
640C22×C4#115714yes—
641C22×C4#115714yes—
642C22×C4D4×D714yes—
643C22×C4#115914yes—
644C22×C4C23×D712yes—
645C22×C4C23×D712yes—
646C22×C4C23×D712yes—
647C22×C4C23×D712yes—
648C22×C4C23×D712yes—
649C22×C4C23×D712yes—
650C4⋊C4—716no—
651C4⋊C4—716no—
652C4⋊C4—148no—
653C4⋊C4—148no—
654C4⋊C4—148no—
655C22⋊C4—28no—
656C22⋊C4—716no—
657C22⋊C4—716no—
658C22⋊C4—148no—
659C22⋊C4—148no—
660C22⋊C4—148no—
661C22⋊C4—148no—
662C22⋊C4C2×C4×D7116yescomplemented
663C42—28no—
664C42—28no—
665C42—148no—
666C42—148no—
667C42—148no—
668C42—148no—
669C42—148no—
670C2×C7—44no—
671C2×C7C4×#12318yescomplemented
672C2×C7C22×C4×D411yescharacteristic
673C2×C7C2×C4×#4111yescharacteristic
674C2×C7C2×C4×#4111yescharacteristic
675C2×C7C22×#12311yescharacteristic
676C2×C7C2×#52511yescharacteristic
677C2×C7C2×#52911yescharacteristic
678C2×C7C2×#52911yescharacteristic
679D7—28no—
680C23—28no—
681C23—28no—
682C23—28no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—716no—
694C23—74no—
695C23—74no—
696C23—74no—
697C23—148no—
698C23—148no—
699C23—148no—
700C23—148no—
701C23—148no—
702C23—148no—
703C23—142no—
704C23—142no—
705C23—142no—
706C23—142no—
707C23C22×C4×D714yes—
708C23C22×C4×D712yes—
709C23C2×#115712yes—
710C23C2×#115712yes—
711C23C2×D4×D712yes—
712C23C2×#115912yes—
713C23D7×#4112yes—
714C23D7×#4112yes—
715C23C24×D711yescharacteristic
716D4—1432no—
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—44no—
733C2×C4—44no—
734C2×C4—416no—
735C2×C4—74no—
736C2×C4—74no—
737C2×C4—74no—
738C2×C4—74no—
739C2×C4—74no—
740C2×C4—1432no—
741C2×C4—1432no—
742C2×C4—148no—
743C2×C4—148no—
744C2×C4—148no—
745C2×C4—148no—
746C2×C4—148no—
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—1432no—
758C2×C4—142no—
759C2×C4—142no—
760C2×C4—142no—
761C2×C4—142no—
762C2×C4—142no—
763C2×C4—142no—
764C2×C4—284no—
765C2×C4—284no—
766C2×C4#6446116yesdirect product factor
767C2×C4C22×C4×D714yes—
768C2×C4C22×C4×D714yes—
769C2×C4C2×#115714yes—
770C2×C4C2×#115714yes—
771C2×C4C2×D4×D714yes—
772C2×C4C2×#115914yes—
773C7C2×C4×#12311yescharacteristic, complemented, Sylow
774C22—24no—
775C22—24no—
776C22—24no—
777C22—42no—
778C22—416no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—78no—
783C22—144no—
784C22—144no—
785C22—1432no—
786C22—144no—
787C22—144no—
788C22—144no—
789C22—144no—
790C22C4×#115714yes—
791C22C2×#644614yes—
792C22#9021914yes—
793C22C4×#115914yes—
794C22C4×D4×D714yes—
795C22#9023814yes—
796C22#9024814yes—
797C22C23×C4×D711yescharacteristic
798C22C22×#115711yescharacteristic
799C22C22×#115711yescharacteristic
800C22C22×D4×D711yescharacteristic
801C22C22×#115911yescharacteristic
802C22C2×D7×#4111yescharacteristic
803C22C2×D7×#4111yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—144no—
810C4—144no—
811C4—144no—
812C4—144no—
813C4—144no—
814C4—282no—
815C4—282no—
816C4C2×#644618yesdirect product factor
817C2—44no—
818C2—148no—
819C2C4×#644618yesdirect product factor
820C2C2×C4×#115711yescharacteristic
821C2C22×#644611yescharacteristic
822C2C2×#9021911yescharacteristic
823C2C2×C4×#115911yescharacteristic
824C2C2×C4×D4×D711yescharacteristic
825C2C2×#9023811yescharacteristic
826C2C2×#9024811yescharacteristic
subgroupG/H
centerC23×C4C22×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC2×C4×C7×C22⋊C4C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
cosocleC23×C7C25
hypercenterC2×C4×C22⋊C4D7
hypocenterC7C2×C4×#123
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×C42×D7C2semidirect
4. C2×C4×C7×C22⋊C4C2semidirect
5. C2×C4×C22⋊Dic7C2semidirect
7. C2×#89717C2semidirect
8. C2×#89723C2semidirect
9. C2×C4×C4⋊Dic7C2semidirect
10. C2×C4×Dic7⋊C4C2semidirect
11. C2×C4×(C2×D7)⋊C4C2semidirect
12. C4×#6446C2direct (N × H)
13. C2×#89440C2semidirect
14. C2×#89436C2semidirect
15. C2×#89426C2semidirect
16. C2×#89424C2semidirect
44. C2×#6446C4direct (N × H)
47. C2×C42×D7C22semidirect
48. C4×C7×C22⋊C4C22semidirect
51. C4×C22⋊Dic7C22semidirect
61. #89723C22semidirect
62. #89717C22semidirect
63. C4×(C2×D7)⋊C4C22semidirect
64. C4×C4⋊Dic7C22semidirect
65. C4×Dic7⋊C4C22semidirect
66. #89440C22semidirect
67. #89436C22semidirect
68. #89426C22semidirect
69. #89424C22semidirect
101. C22×C4×D7C2×C4semidirect
107. C2×C7×C22⋊C4C2×C4semidirect
116. C2×C22⋊Dic7C2×C4semidirect
123. C2×(C2×D7)⋊C4C2×C4semidirect
128. C2×C4⋊Dic7C2×C4semidirect
133. C2×Dic7⋊C4C2×C4semidirect
147. #6446C2×C4direct (N × H)
174. C2×C4×C22⋊C4D7semidirect
262. C2×C4×D7C22×C4semidirect
265. C7×C22⋊C4C22×C4semidirect
270. C22⋊Dic7C22×C4semidirect
273. (C2×D7)⋊C4C22×C4semidirect
275. C4⋊Dic7C22×C4semidirect
278. Dic7⋊C4C22×C4semidirect
326. C4×C22⋊C4C2×D7semidirect
391. C2×C4×C7#123semidirect
490. C2×C22⋊C4C4×D7semidirect
553. C4×C7C2×#123semidirect
662. C22⋊C4C2×C4×D7semidirect
671. C2×C7C4×#123semidirect
766. C2×C4#6446direct (N × H)
773. C7C2×C4×#123semidirect
816. C4C2×#6446direct (N × H)
819. C2C4×#6446direct (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×#64462
C22×C42×D72
C2×C4×C7×C22⋊C42
C2×C4×C22⋊Dic72
C2×#897282
C2×#897172
C2×#897232
C2×C4×C4⋊Dic72
C2×C4×Dic7⋊C42
C2×C4×(C2×D7)⋊C42
C4×#64462
C2×#894402
C2×#894362
C2×#894262
C2×#894242
C2×C4×#1237