Finite Group Databasebeta

← C2×#11731830 #13512549

Subgroups — C2×#11731830 #13512549

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×C4×C22⋊D7C211yesmaximal, characteristic, complemented
2C22×#6455C211yesmaximal, characteristic, complemented
3C22×#6447C211yesmaximal, characteristic
4C2×C7×#385C211yesmaximal, characteristic, complemented
5C2×#89985C211yesmaximal, characteristic, complemented
6C2×#89761C211yesmaximal, characteristic, complemented
7C2×#89760C211yesmaximal, characteristic, complemented
8C2×#89744C211yesmaximal, characteristic, complemented
9C2×#89729C211yesmaximal, characteristic, complemented
10C2×#89729C211yesmaximal, characteristic, complemented
11C2×#89723C211yesmaximal, characteristic, complemented
12#11731830C2116yesmaximal, direct product factor
13C2×#89437C211yesmaximal, characteristic, complemented
14C2×#89439C211yesmaximal, characteristic, complemented
15C2×#89442C211yesmaximal, characteristic, complemented
16C2×#89421C211yesmaximal, characteristic, complemented
17C24×C4×C7C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×D28C2211yescharacteristic
21C23×C4×D7C2211yescharacteristic
22C23×C4×D7C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C2×C4×C22⋊D7—28no—
30C2×C4×C22⋊D7C2218yescomplemented
31C22×(C2×D7)⋊C4C2211yescharacteristic
32C22×(C2×D7)⋊C4C2211yescharacteristic
33C22×(C2×D7)⋊C4C2211yescharacteristic
34C22×(C2×D7)⋊C4C2211yescharacteristic
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×(C2×D7)⋊C4C2211yescharacteristic
37C22×(C2×D7)⋊C4C2211yescharacteristic
38C22×(C2×D7)⋊C4C2211yescharacteristic
39C22×C4⋊Dic7C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×Dic7⋊C4C2211yescharacteristic
44C22×C4×Dic7C2211yescharacteristic
45C22×C4×Dic7C2211yescharacteristic
46C22×C4×Dic7C2211yescharacteristic
47C22×C4×Dic7C2211yescharacteristic
48C2×#6455—28no—
49C2×#6455C2218yescomplemented
50C2×#6447C4116yescomplemented
51C2×#6447C2218yes—
52C7×#385C2218yescomplemented
53C2×C7×#95C2211yescharacteristic
54C2×C7×#95C2211yescharacteristic
55#89985C2218yescomplemented
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60#89761C2218yescomplemented
61#89760C2218yescomplemented
62#89744C2218yescomplemented
63#89729C2218yescomplemented
64#89729C2218yescomplemented
65#89723C2218yescomplemented
66#89442C2218yescomplemented
67#89439C2218yescomplemented
68#89437C2218yescomplemented
69#89421C2218yescomplemented
70C2×#2324—71nomaximal, Sylow
71C25×C7C2311yescharacteristic
72C24×D7C2311yescharacteristic
73C24×D7C2311yescharacteristic
74C23×C4×C7—24no—
75C23×C4×C7—42no—
76C23×C4×C7—42no—
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2314yes—
84C22×C22⋊D7—24no—
85C22×C22⋊D7—24no—
86C22×C22⋊D7—42no—
87C22×C22⋊D7—42no—
88C22×C22⋊D7C2×C418yes—
89C22×C22⋊D7C2×C418yescomplemented
90C22×C22⋊D7C2314yes—
91C22×C22⋊D7C2314yes—
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2311yescharacteristic
96C23×Dic7C2311yescharacteristic
97C23×Dic7C2311yescharacteristic
98C22×D28—42no—
99C22×D28—42no—
100C22×D28C2×C418yescomplemented
101C22×D28C2314yes—
102C22×C4×D7—24no—
103C22×C4×D7—24no—
104C22×C4×D7—24no—
105C22×C4×D7—42no—
106C22×C4×D7—42no—
107C22×C4×D7C2×C418yescomplemented
108C22×C4×D7C2314yes—
109C22×C4×D7C2314yes—
110C2×C7×C4⋊C4—24no—
111C2×C7×C4⋊C4—42no—
112C2×C7×C4⋊C4C2314yes—
113C2×C7×C4⋊C4C2314yes—
114C2×C7×C22⋊C4—42no—
115C2×C7×C22⋊C4C2×C418yescomplemented
116C2×C7×C22⋊C4C2314yes—
117C2×C7×C22⋊C4C2314yes—
118C2×C22⋊Dic7—24no—
119C2×C22⋊Dic7—42no—
120C2×C22⋊Dic7C2314yes—
121C2×C22⋊Dic7C2314yes—
122C4×C22⋊D7—232no—
123C2×(C2×D7)⋊C4—24no—
124C2×(C2×D7)⋊C4—24no—
125C2×(C2×D7)⋊C4—24no—
126C2×(C2×D7)⋊C4—42no—
127C2×(C2×D7)⋊C4—42no—
128C2×(C2×D7)⋊C4—42no—
129C2×(C2×D7)⋊C4—42no—
130C2×(C2×D7)⋊C4C2×C418yescomplemented
131C2×(C2×D7)⋊C4C2314yes—
132C2×(C2×D7)⋊C4C2314yes—
133C2×(C2×D7)⋊C4C2314yes—
134C2×(C2×D7)⋊C4C2314yes—
135C2×(C2×D7)⋊C4C2314yes—
136C2×(C2×D7)⋊C4C2314yes—
137C2×(C2×D7)⋊C4C2314yes—
138C2×(C2×D7)⋊C4C2314yes—
139C2×C4⋊Dic7—24no—
140C2×C4⋊Dic7C2314yes—
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×C4×Dic7—24no—
150C2×C4×Dic7—42no—
151C2×C4×Dic7—42no—
152C2×C4×Dic7D418yescomplemented
153C2×C4×Dic7C2314yes—
154C2×C4×Dic7C2314yes—
155C2×C4×Dic7C2314yes—
156C2×C4×Dic7C2314yes—
157#6455—232no—
158#6447C2×C4164yescomplemented
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×#390—71no—
172C2×#389—71no—
173C2×#388—71no—
174C2×#388—71no—
175C2×#386—71no—
176C2×#386—71no—
177C2×#385—71no—
178C2×#385D711yescharacteristic, complemented
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×C7C22×C414yes—
188C24×C7C2412yes—
189C24×C7C2411yescharacteristic
190C23×D7—22no—
191C23×D7—22no—
192C23×D7—22no—
193C23×D7—22no—
194C23×D7—22no—
195C23×D7—22no—
196C23×D7—22no—
197C23×D7—22no—
198C23×D7—22no—
199C23×D7—22no—
200C23×D7—22no—
201C23×D7—22no—
202C23×D7C22×C414yes—
203C23×D7C22×C414yes—
204C23×D7C2412yes—
205C23×D7C2412yes—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
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—28no—
222C22×C4×C7—44no—
223C22×C4×C7—44no—
224C22×C4×C7—416no—
225C22×C4×C7C22×C414yes—
226C22×C4×C7C22×C414yes—
227C22×C4×C7C2×D414yes—
228C22×C4×C7C2412yes—
229C22×C4×C7C2412yes—
230C22×C4×C7C2412yes—
231C22×C4×C7C2412yes—
232C22×C4×C7C2412yes—
233C22×C4×C7C2412yes—
234C2×C22⋊D7—232no—
235C2×C22⋊D7—28no—
236C2×C22⋊D7—28no—
237C2×C22⋊D7—416no—
238C2×C22⋊D7—44no—
239C2×C22⋊D7—44no—
240C2×C22⋊D7C22×C4116yes—
241C2×C22⋊D7C22×C4116yescomplemented
242C22×Dic7—22no—
243C22×Dic7—22no—
244C22×Dic7—22no—
245C22×Dic7—22no—
246C22×Dic7—22no—
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×Dic7C22×C414yes—
256C22×Dic7C22×C414yes—
257C22×Dic7C2×D414yes—
258C22×Dic7C2×D414yes—
259C22×Dic7#4114yes—
260C22×Dic7C2412yes—
261C22×Dic7C2412yes—
262C22×Dic7C2412yes—
263C22×Dic7C2412yes—
264C22×Dic7C2412yes—
265C22×Dic7C2412yes—
266C2×D28—416no—
267C2×D28—44no—
268C2×D28—44no—
269C2×D28C22×C4116yescomplemented
270C2×C4×D7—232no—
271C2×C4×D7—28no—
272C2×C4×D7—28no—
273C2×C4×D7—28no—
274C2×C4×D7—44no—
275C2×C4×D7—44no—
276C2×C4×D7—416no—
277C2×C4×D7C22×C4116yescomplemented
278C7×C4⋊C4—28no—
279C7×C4⋊C4—44no—
280C7×C22⋊C4—44no—
281C7×C22⋊C4C22×C4116yescomplemented
282C22⋊Dic7—28no—
283C22⋊Dic7—44no—
284(C2×D7)⋊C4—28no—
285(C2×D7)⋊C4—28no—
286(C2×D7)⋊C4—28no—
287(C2×D7)⋊C4—44no—
288(C2×D7)⋊C4—44no—
289(C2×D7)⋊C4—44no—
290(C2×D7)⋊C4—44no—
291(C2×D7)⋊C4C22×C4116yescomplemented
292C4⋊Dic7—28no—
293Dic7⋊C4—28no—
294Dic7⋊C4—28no—
295Dic7⋊C4—44no—
296Dic7⋊C4C22×C4116yescomplemented
297C4×Dic7—28no—
298C4×Dic7—44no—
299C4×Dic7—44no—
300C4×Dic7C2×D4116yescomplemented
301C23×D4—71no—
302C23×D4—71no—
303C23×D4—71no—
304C24×C4—71no—
305C24×C4—71no—
306C24×C4C2×D711yescharacteristic
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⋊C4C2×D711yescharacteristic
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⋊C4—71no—
329C22×C22⋊C4—71no—
330C22×C22⋊C4C2×D711yescharacteristic
331C22×C22⋊C4C2×D711yescharacteristic
332C22×C42—71no—
333C22×C42—71no—
334C22×C42—71no—
335C22×C42—71no—
336#390—78no—
337#390—78no—
338#390—78no—
339#389—78no—
340#388—78no—
341#388—78no—
342#386—78no—
343#386—78no—
344#385—78no—
345#385C2×D718yescomplemented
346#380—78no—
347C4×C4⋊C4—78no—
348C2×#95—71no—
349C2×#95—71no—
350C2×#95—71no—
351C2×#95—71no—
352C2×#95C2×D711yescharacteristic
353C2×#95C2×D711yescharacteristic
354C23×C7—28no—
355C23×C7—28no—
356C23×C7—28no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—44no—
364C23×C7—44no—
365C23×C7—44no—
366C23×C7—44no—
367C23×C7C23×C414yes—
368C23×C7C23×C412yes—
369C23×C7C22×D412yes—
370C23×C7C2×#4112yes—
371C23×C7H(5,𝔽2)12yes—
372C23×C7H(5,𝔽2)12yes—
373C23×C7H(5,𝔽2)12yes—
374C23×C72−1+412yes—
375C23×C7C2511yescharacteristic
376C22×D7—28no—
377C22×D7—28no—
378C22×D7—28no—
379C22×D7—28no—
380C22×D7—28no—
381C22×D7—28no—
382C22×D7—22no—
383C22×D7—22no—
384C22×D7—22no—
385C22×D7—22no—
386C22×D7—22no—
387C22×D7—22no—
388C22×D7—22no—
389C22×D7—22no—
390C22×D7—22no—
391C22×D7—22no—
392C22×D7—22no—
393C22×D7—22no—
394C22×D7—44no—
395C22×D7—44no—
396C22×D7—44no—
397C22×D7—44no—
398C22×D7—44no—
399C22×D7—44no—
400C22×D7—44no—
401C22×D7—44no—
402C22×D7C23×C414yes—
403C22×D7C23×C414yes—
404C2×C4×C7—28no—
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—22no—
421C2×C4×C7—22no—
422C2×C4×C7—416no—
423C2×C4×C7—44no—
424C2×C4×C7—44no—
425C2×C4×C7—44no—
426C2×C4×C7C23×C414yes—
427C2×C4×C7C23×C414yes—
428C2×C4×C7C22×D414yes—
429C22⋊D7—232no—
430C22⋊D7—416no—
431C2×Dic7—28no—
432C2×Dic7—28no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
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—44no—
447C2×Dic7—44no—
448C2×Dic7—44no—
449C2×Dic7C4×D4116yes—
450C2×Dic7C23×C414yes—
451C2×Dic7C23×C414yes—
452C2×Dic7C22×D414yes—
453C2×Dic7C22×D414yes—
454C2×Dic7C2×#4114yes—
455D28—416no—
456C4×D7—232no—
457C4×D7—416no—
458C25—71no—
459C25—71no—
460C25C22×D711yescharacteristic
461C22×D4—78no—
462C22×D4—74no—
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×D4—282no—
472C22×D4—282no—
473C23×C4—24no—
474C23×C4—42no—
475C23×C4—42no—
476C23×C4—71no—
477C23×C4—71no—
478C23×C4—71no—
479C23×C4—78no—
480C23×C4—74no—
481C23×C4—71no—
482C23×C4—71no—
483C23×C4—71no—
484C23×C4—74no—
485C23×C4—144no—
486C23×C4—144no—
487C23×C4—144no—
488C23×C4—282no—
489C23×C4—282no—
490C23×C4C22×D711yescharacteristic
491C23×C4C22×D711yescharacteristic
492C23×C4C22×D711yescharacteristic
493C23×C4C22×D711yescharacteristic
494C23×C4C22×D711yescharacteristic
495C23×C4C22×D711yescharacteristic
496C23×C4C22×D714yes—
497#121—764no—
498C4×D4—1432no—
499#117—1432no—
500C2×C4⋊C4—24no—
501C2×C4⋊C4—42no—
502C2×C4⋊C4—78no—
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—282no—
512C2×C4⋊C4C22×D714yes—
513C2×C4⋊C4C22×D714yes—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—78no—
516C2×C22⋊C4—74no—
517C2×C22⋊C4—74no—
518C2×C22⋊C4—74no—
519C2×C22⋊C4—74no—
520C2×C22⋊C4—74no—
521C2×C22⋊C4—74no—
522C2×C22⋊C4—74no—
523C2×C22⋊C4—74no—
524C2×C22⋊C4—74no—
525C2×C22⋊C4—74no—
526C2×C22⋊C4—144no—
527C2×C22⋊C4—144no—
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⋊C4—282no—
535C2×C22⋊C4C4×D718yescomplemented
536C2×C22⋊C4C22×D714yes—
537C2×C22⋊C4C22×D714yes—
538C2×C42—78no—
539C2×C42—74no—
540C2×C42—74no—
541C2×C42—74no—
542C2×C42—74no—
543C2×C42—144no—
544C2×C42—282no—
545C2×C42—282no—
546#95—74no—
547#95—74no—
548#95—74no—
549#95—74no—
550#95C22×D714yes—
551#95C22×D714yes—
552C22×C7—24no—
553C22×C7—24no—
554C22×C7—24no—
555C22×C7—416no—
556C22×C7—42no—
557C22×C7—42no—
558C22×C7—42no—
559C22×C7—42no—
560C22×C7C2×C4×D414yes—
561C22×C7#51814yes—
562C22×C7#52014yes—
563C22×C7#53514yes—
564C22×C7#53714yes—
565C22×C7#54014yes—
566C22×C7#54214yes—
567C22×C7C24×C411yescharacteristic
568C22×C7C23×D411yescharacteristic
569C22×C7C22×#4111yescharacteristic
570C22×C7C2×H(5,𝔽2)11yescharacteristic
571C22×C7C2×H(5,𝔽2)11yescharacteristic
572C22×C7C2×H(5,𝔽2)11yescharacteristic
573C22×C7C2×2−1+411yescharacteristic
574C2×D7—24no—
575C2×D7—24no—
576C2×D7—24no—
577C2×D7—24no—
578C2×D7—24no—
579C2×D7—24no—
580C2×D7—416no—
581C2×D7—416no—
582C2×D7—42no—
583C2×D7—42no—
584C2×D7—42no—
585C2×D7—42no—
586C2×D7—42no—
587C2×D7—42no—
588C2×D7—42no—
589C2×D7—42no—
590C4×C7—24no—
591C4×C7—24no—
592C4×C7—24no—
593C4×C7—42no—
594C4×C7—42no—
595C4×C7—42no—
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—74no—
609C24—74no—
610C24—72no—
611C24—72no—
612C24—142no—
613C24—142no—
614C24—142no—
615C24—142no—
616C24—142no—
617C24—142no—
618C24—142no—
619C24—142no—
620C24—142no—
621C24—142no—
622C24—142no—
623C24—142no—
624C24C2×C4×D714yes—
625C24C23×D712yes—
626C24C23×D711yescharacteristic
627C2×D4—716no—
628C2×D4—716no—
629C2×D4—716no—
630C2×D4—148no—
631C2×D4—1432no—
632C2×D4—148no—
633C2×D4—2816no—
634C2×D4—284no—
635C2×D4—284no—
636C2×D4—2816no—
637C2×D4—284no—
638C2×D4—284no—
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—22no—
653C22×C4—22no—
654C22×C4—28no—
655C22×C4—44no—
656C22×C4—44no—
657C22×C4—416no—
658C22×C4—74no—
659C22×C4—74no—
660C22×C4—74no—
661C22×C4—72no—
662C22×C4—74no—
663C22×C4—74no—
664C22×C4—72no—
665C22×C4—72no—
666C22×C4—716no—
667C22×C4—72no—
668C22×C4—72no—
669C22×C4—72no—
670C22×C4—148no—
671C22×C4—1432no—
672C22×C4—148no—
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—148no—
687C22×C4—284no—
688C22×C4—284no—
689C22×C4—2816no—
690C22×C4C2×C4×D714yes—
691C22×C4C2×C4×D714yes—
692C22×C4D4×D714yes—
693C22×C4C23×D712yes—
694C22×C4C23×D712yes—
695C22×C4C23×D712yes—
696C22×C4C23×D712yes—
697C22×C4C23×D712yes—
698C22×C4C23×D712yes—
699C4⋊C4—28no—
700C4⋊C4—44no—
701C4⋊C4—716no—
702C4⋊C4—148no—
703C4⋊C4—148no—
704C4⋊C4—148no—
705C4⋊C4—284no—
706C22⋊C4—44no—
707C22⋊C4—716no—
708C22⋊C4—148no—
709C22⋊C4—148no—
710C22⋊C4—148no—
711C22⋊C4—148no—
712C22⋊C4—284no—
713C22⋊C4—284no—
714C22⋊C4—284no—
715C22⋊C4—284no—
716C22⋊C4—284no—
717C22⋊C4C2×C4×D7116yescomplemented
718C42—716no—
719C42—148no—
720C42—284no—
721C42—284no—
722C2×C7—44no—
723C2×C7#232418yescomplemented
724C2×C7C22×C4×D411yescharacteristic
725C2×C7C2×#51811yescharacteristic
726C2×C7C2×#52011yescharacteristic
727C2×C7C2×#53511yescharacteristic
728C2×C7C2×#53711yescharacteristic
729C2×C7C2×#54011yescharacteristic
730C2×C7C2×#54211yescharacteristic
731D7—44no—
732D7—44no—
733C23—28no—
734C23—28no—
735C23—28no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—74no—
747C23—74no—
748C23—148no—
749C23—148no—
750C23—148no—
751C23—148no—
752C23—148no—
753C23—148no—
754C23—142no—
755C23—142no—
756C23—142no—
757C23—142no—
758C23—142no—
759C23—142no—
760C23—142no—
761C23—142no—
762C23—142no—
763C23—142no—
764C23—142no—
765C23—142no—
766C23—284no—
767C23—284no—
768C23—284no—
769C23—284no—
770C23—284no—
771C23—284no—
772C23—284no—
773C23—284no—
774C23C22×C4×D714yes—
775C23C22×C4×D712yes—
776C23C2×D4×D712yes—
777C23#654812yes—
778C23#654812yes—
779C23#655112yes—
780C23D7×#4112yes—
781C23#655312yes—
782C23C24×D711yescharacteristic
783D4—1432no—
784D4—2816no—
785D4—2816no—
786C2×C4—28no—
787C2×C4—28no—
788C2×C4—28no—
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—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—416no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—716no—
809C2×C4—74no—
810C2×C4—74no—
811C2×C4—74no—
812C2×C4—74no—
813C2×C4—74no—
814C2×C4—1432no—
815C2×C4—148no—
816C2×C4—148no—
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—284no—
832C2×C4—284no—
833C2×C4—284no—
834C2×C4C22×C4×D714yes—
835C2×C4C22×C4×D714yes—
836C2×C4C2×D4×D714yes—
837C7C2×#232411yescharacteristic, complemented, Sylow
838C22—24no—
839C22—24no—
840C22—24no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—416no—
846C22—144no—
847C22—144no—
848C22—144no—
849C22—144no—
850C22—144no—
851C22—144no—
852C22—282no—
853C22—282no—
854C22—282no—
855C22—282no—
856C22—282no—
857C22—282no—
858C22—282no—
859C22—282no—
860C22—2816no—
861C22—2816no—
862C22#9019514yes—
863C22C4×D4×D714yes—
864C22#9023614yes—
865C22#9028314yes—
866C22#9032014yes—
867C22#9033114yes—
868C22#9035414yes—
869C22C23×C4×D711yescharacteristic
870C22C22×D4×D711yescharacteristic
871C22C2×#654811yescharacteristic
872C22C2×#654811yescharacteristic
873C22C2×#655111yescharacteristic
874C22C2×D7×#4111yescharacteristic
875C22C2×#655311yescharacteristic
876C4—24no—
877C4—24no—
878C4—24no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—78no—
883C4—144no—
884C4—144no—
885C4—282no—
886C4—282no—
887C4—282no—
888C2—44no—
889C2—284no—
890C2—284no—
891C2#1173183018yesdirect product factor
892C2C2×#9019511yescharacteristic
893C2C2×C4×D4×D711yescharacteristic
894C2C2×#9023611yescharacteristic
895C2C2×#9028311yescharacteristic
896C2C2×#9033111yescharacteristic
897C2C2×#9032011yescharacteristic
898C2C2×#9035411yescharacteristic
subgroupG/H
centerC24C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC2×C7×#385C2
socleC24×C7C24
prime radicalC22×#6447C2
cosocleC23×C7C25
hypercenterC2×#385D7
hypocenterC7C2×#2324
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×C4×C22⋊D7C2semidirect
2. C22×#6455C2semidirect
4. C2×C7×#385C2semidirect
5. C2×#89985C2semidirect
6. C2×#89761C2semidirect
7. C2×#89760C2semidirect
8. C2×#89744C2semidirect
9. C2×#89729C2semidirect
10. C2×#89729C2semidirect
11. C2×#89723C2semidirect
12. #11731830C2direct (N × H)
13. C2×#89437C2semidirect
14. C2×#89439C2semidirect
15. C2×#89442C2semidirect
16. C2×#89421C2semidirect
30. C2×C4×C22⋊D7C22semidirect
49. C2×#6455C22semidirect
50. C2×#6447C4semidirect
52. C7×#385C22semidirect
55. #89985C22semidirect
60. #89761C22semidirect
61. #89760C22semidirect
62. #89744C22semidirect
63. #89729C22semidirect
64. #89729C22semidirect
65. #89723C22semidirect
66. #89442C22semidirect
67. #89439C22semidirect
68. #89437C22semidirect
69. #89421C22semidirect
89. C22×C22⋊D7C2×C4semidirect
100. C22×D28C2×C4semidirect
107. C22×C4×D7C2×C4semidirect
115. C2×C7×C22⋊C4C2×C4semidirect
130. C2×(C2×D7)⋊C4C2×C4semidirect
144. C2×Dic7⋊C4C2×C4semidirect
152. C2×C4×Dic7D4semidirect
158. #6447C2×C4semidirect
178. C2×#385D7semidirect
241. C2×C22⋊D7C22×C4semidirect
269. C2×D28C22×C4semidirect
277. C2×C4×D7C22×C4semidirect
281. C7×C22⋊C4C22×C4semidirect
291. (C2×D7)⋊C4C22×C4semidirect
296. Dic7⋊C4C22×C4semidirect
300. C4×Dic7C2×D4semidirect
345. #385C2×D7semidirect
535. C2×C22⋊C4C4×D7semidirect
717. C22⋊C4C2×C4×D7semidirect
723. C2×C7#2324semidirect
837. C7C2×#2324semidirect
891. C2#11731830direct (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×#64552
C22×#64472
C2×C7×#3852
C2×#899852
C2×#897612
C2×#897602
C2×#897442
C2×#897292
C2×#897232
#117318302
C2×#894372
C2×#894392
C2×#894422
C2×#894212
C2×#23247