Finite Group Databasebeta

← C2×#11734895 #13560329

Subgroups — C2×#11734895 #13560329

Order 1792.

2502 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6461C211yesmaximal, characteristic, complemented
2C22×#6442C211yesmaximal, characteristic, complemented
3C2×C7×#396C211yesmaximal, characteristic, complemented
4C2×#89766C211yesmaximal, characteristic, complemented
5C2×#89766C211yesmaximal, characteristic, complemented
6C2×#89752C211yesmaximal, characteristic, complemented
7C2×#89756C211yesmaximal, characteristic, complemented
8C2×#89748C211yesmaximal, characteristic, complemented
9C2×#89731C211yesmaximal, characteristic
10C2×#89731C211yesmaximal, characteristic
11C2×#89720C211yesmaximal, characteristic, complemented
12C2×#89720C211yesmaximal, characteristic, complemented
13C2×#89733C211yesmaximal, characteristic
14#11734895C2116yesmaximal, direct product factor
15C2×#89448C211yesmaximal, characteristic, complemented
16C2×#89433C211yesmaximal, characteristic, complemented
17C23×C22⋊D7C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
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×C4⋊Dic7C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×Dic7⋊C4C2211yescharacteristic
44C22×Dic7⋊C4C2211yescharacteristic
45C22×C4×Dic7C2211yescharacteristic
46C2×#6461—28no—
47C2×#6461C2218yescomplemented
48C2×#6442—28no—
49C2×#6442C2218yescomplemented
50C7×#396C2218yescomplemented
51C2×C7×#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57#89766C2218yescomplemented
58#89766C2218yescomplemented
59#89756C2218yescomplemented
60#89752C2218yescomplemented
61#89748C2218yescomplemented
62#89733C2218yes—
63#89731C2218yes—
64#89731C2218yes—
65#89720C2218yescomplemented
66#89720C2218yescomplemented
67#89448C2218yescomplemented
68#89433C2218yescomplemented
69C2×#2823—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C22×C22⋊D7—42no—
79C22×C22⋊D7—42no—
80C22×C22⋊D7—42no—
81C22×C22⋊D7C2314yes—
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C2×C7×C4⋊C4—24no—
90C2×C7×C4⋊C4—42no—
91C2×C7×C4⋊C4—42no—
92C2×C7×C4⋊C4C2314yes—
93C2×C7×C4⋊C4C2314yes—
94C2×C7×C4⋊C4C2314yes—
95C2×C7×C22⋊C4—24no—
96C2×C7×C22⋊C4—42no—
97C2×C7×C22⋊C4—42no—
98C2×C7×C22⋊C4C2314yes—
99C2×C7×C22⋊C4C2314yes—
100C2×C7×C22⋊C4C2314yes—
101C2×C22⋊Dic7—24no—
102C2×C22⋊Dic7—24no—
103C2×C22⋊Dic7—42no—
104C2×C22⋊Dic7C2314yes—
105C2×C22⋊Dic7C2314yes—
106C2×C22⋊Dic7C2314yes—
107C2×(C2×D7)⋊C4—24no—
108C2×(C2×D7)⋊C4—24no—
109C2×(C2×D7)⋊C4—24no—
110C2×(C2×D7)⋊C4—42no—
111C2×(C2×D7)⋊C4—42no—
112C2×(C2×D7)⋊C4—42no—
113C2×(C2×D7)⋊C4C2314yes—
114C2×(C2×D7)⋊C4C2314yes—
115C2×(C2×D7)⋊C4C2314yes—
116C2×(C2×D7)⋊C4C2314yes—
117C2×(C2×D7)⋊C4C2314yes—
118C2×(C2×D7)⋊C4C2314yes—
119C2×C4⋊Dic7—24no—
120C2×C4⋊Dic7—24no—
121C2×C4⋊Dic7—42no—
122C2×C4⋊Dic7—42no—
123C2×C4⋊Dic7C2314yes—
124C2×C4⋊Dic7C2314yes—
125C2×C4⋊Dic7C2314yes—
126C2×C4⋊Dic7C2314yes—
127C2×Dic7⋊C4—24no—
128C2×Dic7⋊C4—24no—
129C2×Dic7⋊C4—24no—
130C2×Dic7⋊C4—42no—
131C2×Dic7⋊C4—42no—
132C2×Dic7⋊C4—42no—
133C2×Dic7⋊C4—42no—
134C2×Dic7⋊C4—42no—
135C2×Dic7⋊C4C2314yes—
136C2×Dic7⋊C4C2314yes—
137C2×Dic7⋊C4C2314yes—
138C2×Dic7⋊C4C2314yes—
139C2×Dic7⋊C4C2314yes—
140C2×Dic7⋊C4C2314yes—
141C2×Dic7⋊C4C2314yes—
142C2×Dic7⋊C4C2314yes—
143C2×C4×Dic7D418yescomplemented
144C2×C4×Dic7C2314yes—
145#6461—232no—
146#6442—232no—
147C7×#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C22×#126—71no—
154C22×#126—71no—
155#2823—716no—
156C2×#398—71no—
157C2×#398—71no—
158C2×#398—71no—
159C2×#396—71no—
160C2×#396—71no—
161C2×#396—71no—
162C2×#396—71no—
163C2×#396—71no—
164C2×#396D711yescharacteristic, complemented
165C2×#394—71no—
166C2×#394—71no—
167C2×#394—71no—
168C2×#384—71no—
169C24×C7—22no—
170C24×C7—22no—
171C24×C7—22no—
172C24×C7—22no—
173C24×C7—22no—
174C24×C7—22no—
175C24×C7—22no—
176C24×C7C2412yes—
177C24×C7C2411yescharacteristic
178C23×D7—22no—
179C23×D7—22no—
180C23×D7—22no—
181C23×D7—22no—
182C23×D7—22no—
183C23×D7—22no—
184C23×D7—22no—
185C23×D7C2412yes—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
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×C7C2×D414yes—
204C22×C4×C7C2412yes—
205C22×C4×C7C2412yes—
206C22×C4×C7C2412yes—
207C22×C4×C7C2412yes—
208C22×C4×C7C2412yes—
209C22×C4×C7C2412yes—
210C2×C22⋊D7—44no—
211C2×C22⋊D7—44no—
212C2×C22⋊D7—44no—
213C2×C22⋊D7—416no—
214C22×Dic7—22no—
215C22×Dic7—22no—
216C22×Dic7—22no—
217C22×Dic7—22no—
218C22×Dic7—22no—
219C22×Dic7—22no—
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×Dic7C2×D414yes—
234C22×Dic7C2×D414yes—
235C22×Dic7C2412yes—
236C22×Dic7C2412yes—
237C22×Dic7C2412yes—
238C22×Dic7C2412yes—
239C22×Dic7C2412yes—
240C22×Dic7C2412yes—
241C22×Dic7C2412yes—
242C7×C4⋊C4—28no—
243C7×C4⋊C4—44no—
244C7×C4⋊C4—44no—
245C7×C22⋊C4—28no—
246C7×C22⋊C4—44no—
247C7×C22⋊C4—44no—
248C22⋊Dic7—28no—
249C22⋊Dic7—28no—
250C22⋊Dic7—44no—
251(C2×D7)⋊C4—28no—
252(C2×D7)⋊C4—28no—
253(C2×D7)⋊C4—28no—
254(C2×D7)⋊C4—44no—
255(C2×D7)⋊C4—44no—
256(C2×D7)⋊C4—44no—
257C4⋊Dic7—28no—
258C4⋊Dic7—28no—
259C4⋊Dic7—44no—
260C4⋊Dic7—44no—
261Dic7⋊C4—28no—
262Dic7⋊C4—28no—
263Dic7⋊C4—28no—
264Dic7⋊C4—44no—
265Dic7⋊C4—44no—
266Dic7⋊C4—44no—
267Dic7⋊C4—44no—
268Dic7⋊C4—44no—
269C4×Dic7C2×D4116yescomplemented
270C23×D4—71no—
271C2×#126—78no—
272C2×#126—78no—
273C2×#126—148no—
274C2×#126—148no—
275C22×C4⋊C4—71no—
276C22×C4⋊C4—71no—
277C22×C4⋊C4—71no—
278C22×C4⋊C4—71no—
279C22×C4⋊C4—71no—
280C22×C4⋊C4—71no—
281C22×C4⋊C4—71no—
282C22×C4⋊C4—71no—
283C22×C4⋊C4—71no—
284C22×C4⋊C4—71no—
285C22×C4⋊C4—71no—
286C22×C4⋊C4—71no—
287C22×C4⋊C4C2×D711yescharacteristic
288C22×C4⋊C4C2×D711yescharacteristic
289C22×C4⋊C4C2×D711yescharacteristic
290C22×C22⋊C4—71no—
291C22×C22⋊C4—71no—
292C22×C22⋊C4—71no—
293C22×C22⋊C4—71no—
294C22×C22⋊C4—71no—
295C22×C22⋊C4—71no—
296C22×C22⋊C4—71no—
297C22×C22⋊C4—71no—
298C22×C22⋊C4—71no—
299C22×C22⋊C4C2×D711yescharacteristic
300C22×C22⋊C4C2×D711yescharacteristic
301C22×C22⋊C4C2×D711yescharacteristic
302C22×C42—71no—
303#398—78no—
304#398—78no—
305#398—78no—
306#396—78no—
307#396—78no—
308#396—78no—
309#396—78no—
310#396—78no—
311#396C2×D718yescomplemented
312#394—78no—
313#394—78no—
314#394—78no—
315#384—78no—
316C2×#95—71no—
317C2×#95—71no—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95C2×D711yescharacteristic
322C23×C7—22no—
323C23×C7—22no—
324C23×C7—22no—
325C23×C7—22no—
326C23×C7—22no—
327C23×C7—22no—
328C23×C7—22no—
329C23×C7—44no—
330C23×C7—44no—
331C23×C7—44no—
332C23×C7—44no—
333C23×C7—44no—
334C23×C7—44no—
335C23×C7—44no—
336C23×C7C22×D412yes—
337C23×C7H(5,𝔽2)12yes—
338C23×C7H(5,𝔽2)12yes—
339C23×C7H(5,𝔽2)12yes—
340C23×C72−1+412yes—
341C23×C72−1+412yes—
342C23×C72−1+412yes—
343C23×C7C2511yescharacteristic
344C22×D7—22no—
345C22×D7—22no—
346C22×D7—22no—
347C22×D7—22no—
348C22×D7—22no—
349C22×D7—22no—
350C22×D7—22no—
351C22×D7—44no—
352C22×D7—44no—
353C22×D7—44no—
354C22×D7—44no—
355C22×D7—44no—
356C22×D7—44no—
357C22×D7—44no—
358C2×C4×C7—28no—
359C2×C4×C7—22no—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—44no—
377C2×C4×C7—44no—
378C2×C4×C7—44no—
379C2×C4×C7—44no—
380C2×C4×C7—44no—
381C2×C4×C7C22×D414yes—
382C22⋊D7—416no—
383C2×Dic7—28no—
384C2×Dic7—28no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—44no—
405C2×Dic7—44no—
406C2×Dic7—44no—
407C2×Dic7—44no—
408C2×Dic7—44no—
409C2×Dic7C22×D414yes—
410C2×Dic7C22×D414yes—
411C25—71no—
412C25C22×D711yescharacteristic
413C22×D4—74no—
414C22×D4—282no—
415C22×D4—282no—
416C22×D4—282no—
417C23×C4—71no—
418C23×C4—71no—
419C23×C4—71no—
420C23×C4—71no—
421C23×C4—71no—
422C23×C4—71no—
423C23×C4—71no—
424C23×C4C22×D711yescharacteristic
425C23×C4C22×D711yescharacteristic
426C23×C4C22×D711yescharacteristic
427C23×C4C22×D711yescharacteristic
428C23×C4C22×D711yescharacteristic
429C23×C4C22×D711yescharacteristic
430#126—1432no—
431#126—1432no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—42no—
434C2×C4⋊C4—42no—
435C2×C4⋊C4—74no—
436C2×C4⋊C4—74no—
437C2×C4⋊C4—74no—
438C2×C4⋊C4—74no—
439C2×C4⋊C4—74no—
440C2×C4⋊C4—74no—
441C2×C4⋊C4—74no—
442C2×C4⋊C4—74no—
443C2×C4⋊C4—74no—
444C2×C4⋊C4—74no—
445C2×C4⋊C4—74no—
446C2×C4⋊C4—74no—
447C2×C4⋊C4—144no—
448C2×C4⋊C4—144no—
449C2×C4⋊C4—144no—
450C2×C4⋊C4—144no—
451C2×C4⋊C4—144no—
452C2×C4⋊C4—282no—
453C2×C4⋊C4—282no—
454C2×C4⋊C4—282no—
455C2×C4⋊C4—282no—
456C2×C4⋊C4—282no—
457C2×C4⋊C4—282no—
458C2×C4⋊C4—282no—
459C2×C4⋊C4C22×D714yes—
460C2×C4⋊C4C22×D714yes—
461C2×C4⋊C4C22×D714yes—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—42no—
464C2×C22⋊C4—42no—
465C2×C22⋊C4—74no—
466C2×C22⋊C4—74no—
467C2×C22⋊C4—74no—
468C2×C22⋊C4—74no—
469C2×C22⋊C4—74no—
470C2×C22⋊C4—74no—
471C2×C22⋊C4—74no—
472C2×C22⋊C4—74no—
473C2×C22⋊C4—74no—
474C2×C22⋊C4—144no—
475C2×C22⋊C4—144no—
476C2×C22⋊C4—144no—
477C2×C22⋊C4—144no—
478C2×C22⋊C4—144no—
479C2×C22⋊C4—282no—
480C2×C22⋊C4—282no—
481C2×C22⋊C4—282no—
482C2×C22⋊C4—282no—
483C2×C22⋊C4C22×D714yes—
484C2×C22⋊C4C22×D714yes—
485C2×C22⋊C4C22×D714yes—
486C2×C42—78no—
487C2×C42—74no—
488#95—74no—
489#95—74no—
490#95—74no—
491#95—74no—
492#95—74no—
493#95C22×D714yes—
494C22×C7—42no—
495C22×C7—42no—
496C22×C7—42no—
497C22×C7—42no—
498C22×C7—42no—
499C22×C7—42no—
500C22×C7—42no—
501C22×C7—88no—
502C22×C7#53714yes—
503C22×C7#53714yes—
504C22×C7#53714yes—
505C22×C7#56014yes—
506C22×C7#56314yes—
507C22×C7#56314yes—
508C22×C7#56314yes—
509C22×C7C23×D411yescharacteristic
510C22×C7C2×H(5,𝔽2)11yescharacteristic
511C22×C7C2×H(5,𝔽2)11yescharacteristic
512C22×C7C2×H(5,𝔽2)11yescharacteristic
513C22×C7C2×2−1+411yescharacteristic
514C22×C7C2×2−1+411yescharacteristic
515C22×C7C2×2−1+411yescharacteristic
516C2×D7—42no—
517C2×D7—42no—
518C2×D7—42no—
519C2×D7—42no—
520C2×D7—42no—
521C2×D7—42no—
522C2×D7—42no—
523C2×D7—88no—
524C4×C7—24no—
525C4×C7—42no—
526C4×C7—42no—
527C4×C7—42no—
528C4×C7—42no—
529C4×C7—42no—
530Dic7—24no—
531Dic7—24no—
532Dic7—42no—
533Dic7—42no—
534Dic7—42no—
535Dic7—42no—
536Dic7—42no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—72no—
545C24—142no—
546C24—142no—
547C24—142no—
548C24—142no—
549C24—142no—
550C24—142no—
551C24—142no—
552C24C23×D712yes—
553C24C23×D711yescharacteristic
554C2×D4—284no—
555C2×D4—284no—
556C2×D4—284no—
557C2×D4—2816no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—74no—
576C22×C4—74no—
577C22×C4—72no—
578C22×C4—72no—
579C22×C4—72no—
580C22×C4—72no—
581C22×C4—72no—
582C22×C4—72no—
583C22×C4—72no—
584C22×C4—142no—
585C22×C4—142no—
586C22×C4—142no—
587C22×C4—142no—
588C22×C4—142no—
589C22×C4—142no—
590C22×C4—142no—
591C22×C4—142no—
592C22×C4—142no—
593C22×C4—142no—
594C22×C4—142no—
595C22×C4—142no—
596C22×C4—142no—
597C22×C4—142no—
598C22×C4—142no—
599C22×C4—142no—
600C22×C4—142no—
601C22×C4—142no—
602C22×C4—142no—
603C22×C4D4×D714yes—
604C22×C4C23×D712yes—
605C22×C4C23×D712yes—
606C22×C4C23×D712yes—
607C22×C4C23×D712yes—
608C22×C4C23×D712yes—
609C22×C4C23×D712yes—
610C4⋊C4—28no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C4⋊C4—148no—
614C4⋊C4—148no—
615C4⋊C4—148no—
616C4⋊C4—148no—
617C4⋊C4—148no—
618C4⋊C4—284no—
619C4⋊C4—284no—
620C4⋊C4—284no—
621C4⋊C4—284no—
622C4⋊C4—284no—
623C4⋊C4—284no—
624C4⋊C4—284no—
625C22⋊C4—28no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—148no—
629C22⋊C4—148no—
630C22⋊C4—148no—
631C22⋊C4—148no—
632C22⋊C4—148no—
633C22⋊C4—284no—
634C22⋊C4—284no—
635C22⋊C4—284no—
636C22⋊C4—284no—
637C42—716no—
638C2×C7—82no—
639C2×C7#282318yescomplemented
640C2×C7C2×#53711yescharacteristic
641C2×C7C2×#53711yescharacteristic
642C2×C7C2×#53711yescharacteristic
643C2×C7C2×#56011yescharacteristic
644C2×C7C2×#56311yescharacteristic
645C2×C7C2×#56311yescharacteristic
646C2×C7C2×#56311yescharacteristic
647D7—82no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—142no—
663C23—142no—
664C23—142no—
665C23—142no—
666C23—142no—
667C23—142no—
668C23—142no—
669C23—284no—
670C23—284no—
671C23—284no—
672C23—284no—
673C23—284no—
674C23—284no—
675C23—284no—
676C23C2×D4×D712yes—
677C23#654812yes—
678C23#654812yes—
679C23#655112yes—
680C23#655312yes—
681C23#655412yes—
682C23#655412yes—
683C23C24×D711yescharacteristic
684D4—2816no—
685C2×C4—28no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—74no—
709C2×C4—74no—
710C2×C4—148no—
711C2×C4—148no—
712C2×C4—142no—
713C2×C4—142no—
714C2×C4—142no—
715C2×C4—142no—
716C2×C4—142no—
717C2×C4—142no—
718C2×C4—142no—
719C2×C4—142no—
720C2×C4—142no—
721C2×C4—142no—
722C2×C4—142no—
723C2×C4—142no—
724C2×C4—142no—
725C2×C4—142no—
726C2×C4—142no—
727C2×C4—142no—
728C2×C4—142no—
729C2×C4—142no—
730C2×C4—142no—
731C2×C4—284no—
732C2×C4—284no—
733C2×C4—284no—
734C2×C4—284no—
735C2×C4—284no—
736C2×C4C2×D4×D714yes—
737C7C2×#282311yescharacteristic, complemented, Sylow
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—88no—
746C22—282no—
747C22—282no—
748C22—282no—
749C22—282no—
750C22—282no—
751C22—282no—
752C22—282no—
753C22—568no—
754C22#9028814yes—
755C22#9029914yes—
756C22#9031114yes—
757C22#9032014yes—
758C22#9033714yes—
759C22#9033714yes—
760C22#9040314yes—
761C22C22×D4×D711yescharacteristic
762C22C2×#654811yescharacteristic
763C22C2×#654811yescharacteristic
764C22C2×#655111yescharacteristic
765C22C2×#655311yescharacteristic
766C22C2×#655411yescharacteristic
767C22C2×#655411yescharacteristic
768C4—24no—
769C4—42no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—144no—
775C4—144no—
776C4—282no—
777C4—282no—
778C4—282no—
779C4—282no—
780C4—282no—
781C2—82no—
782C2—562no—
783C2#1173489518yesdirect product factor
784C2C2×#9028811yescharacteristic
785C2C2×#9029911yescharacteristic
786C2C2×#9031111yescharacteristic
787C2C2×#9033711yescharacteristic
788C2C2×#9033711yescharacteristic
789C2C2×#9032011yescharacteristic
790C2C2×#9040311yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#396C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×#396D7
hypocenterC7C2×#2823
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#6461C2semidirect
2. C22×#6442C2semidirect
3. C2×C7×#396C2semidirect
4. C2×#89766C2semidirect
5. C2×#89766C2semidirect
6. C2×#89752C2semidirect
7. C2×#89756C2semidirect
8. C2×#89748C2semidirect
11. C2×#89720C2semidirect
12. C2×#89720C2semidirect
14. #11734895C2direct (N × H)
15. C2×#89448C2semidirect
16. C2×#89433C2semidirect
47. C2×#6461C22semidirect
49. C2×#6442C22semidirect
50. C7×#396C22semidirect
57. #89766C22semidirect
58. #89766C22semidirect
59. #89756C22semidirect
60. #89752C22semidirect
61. #89748C22semidirect
65. #89720C22semidirect
66. #89720C22semidirect
67. #89448C22semidirect
68. #89433C22semidirect
143. C2×C4×Dic7D4semidirect
164. C2×#396D7semidirect
269. C4×Dic7C2×D4semidirect
311. #396C2×D7semidirect
639. C2×C7#2823semidirect
737. C7C2×#2823semidirect
783. C2#11734895direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64612
C22×#64422
C2×C7×#3962
C2×#897662
C2×#897522
C2×#897562
C2×#897482
C2×#897312
C2×#897202
C2×#897332
#117348952
C2×#894482
C2×#894332
C2×#28237