Finite Group Databasebeta

← C2×#11734938 #13522928

Subgroups — C2×#11734938 #13522928

Order 1792.

2726 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×#397C211yesmaximal, characteristic, complemented
4C2×#89748C211yesmaximal, characteristic, complemented
5C2×#89720C211yesmaximal, characteristic, complemented
6C2×#89729C211yesmaximal, characteristic
7C2×#89729C211yesmaximal, characteristic
8C2×#89729C211yesmaximal, characteristic
9C2×#89717C211yesmaximal, characteristic, complemented
10#11734938C2116yesmaximal, direct product factor
11C2×#89448C211yesmaximal, characteristic, complemented
12C2×#89446C211yesmaximal, characteristic, complemented
13C2×#89419C211yesmaximal, characteristic, complemented
14C2×#89441C211yesmaximal, characteristic, complemented
15C2×#89421C211yesmaximal, characteristic, complemented
16C2×#89421C211yesmaximal, characteristic, complemented
17C23×C22⋊D7C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
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×C4⋊Dic7C2211yescharacteristic
32C22×C4⋊Dic7C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
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×#6461—28no—
47C2×#6461C2218yescomplemented
48C2×#6442—28no—
49C2×#6442C2218yescomplemented
50C7×#397C2218yescomplemented
51C2×C7×#95C2211yescharacteristic
52C2×C7×#95C2211yescharacteristic
53C2×C7×#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57#89748C2218yescomplemented
58#89729C2218yes—
59#89729C2218yes—
60#89729C2218yes—
61#89720C2218yescomplemented
62#89717C2218yescomplemented
63#89448C2218yescomplemented
64#89446C2218yescomplemented
65#89441C2218yescomplemented
66#89421C2218yescomplemented
67#89421C2218yescomplemented
68#89419C2218yescomplemented
69C2×#2512—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—24no—
79C22×C22⋊D7—24no—
80C22×C22⋊D7—24no—
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⋊C4C2314yes—
91C2×C7×C22⋊C4—24no—
92C2×C7×C22⋊C4—42no—
93C2×C7×C22⋊C4—42no—
94C2×C7×C22⋊C4C2314yes—
95C2×C7×C22⋊C4C2314yes—
96C2×C7×C22⋊C4C2314yes—
97C2×C22⋊Dic7—24no—
98C2×C22⋊Dic7—24no—
99C2×C22⋊Dic7—24no—
100C2×C22⋊Dic7C2314yes—
101C2×C22⋊Dic7C2314yes—
102C2×C22⋊Dic7C2314yes—
103C2×(C2×D7)⋊C4—24no—
104C2×(C2×D7)⋊C4—24no—
105C2×(C2×D7)⋊C4—24no—
106C2×(C2×D7)⋊C4—24no—
107C2×(C2×D7)⋊C4—42no—
108C2×(C2×D7)⋊C4—42no—
109C2×(C2×D7)⋊C4C2314yes—
110C2×(C2×D7)⋊C4C2314yes—
111C2×(C2×D7)⋊C4C2314yes—
112C2×(C2×D7)⋊C4C2314yes—
113C2×(C2×D7)⋊C4C2314yes—
114C2×(C2×D7)⋊C4C2314yes—
115C2×C4⋊Dic7—24no—
116C2×C4⋊Dic7—24no—
117C2×C4⋊Dic7C2314yes—
118C2×C4⋊Dic7C2314yes—
119C2×Dic7⋊C4—24no—
120C2×Dic7⋊C4—24no—
121C2×Dic7⋊C4—24no—
122C2×Dic7⋊C4—24no—
123C2×Dic7⋊C4—24no—
124C2×Dic7⋊C4—42no—
125C2×Dic7⋊C4—42no—
126C2×Dic7⋊C4D418yescomplemented
127C2×Dic7⋊C4C2314yes—
128C2×Dic7⋊C4C2314yes—
129C2×Dic7⋊C4C2314yes—
130C2×Dic7⋊C4C2314yes—
131C2×Dic7⋊C4C2314yes—
132C2×Dic7⋊C4C2314yes—
133C2×Dic7⋊C4C2314yes—
134C2×Dic7⋊C4C2314yes—
135C2×C4×Dic7—24no—
136C2×C4×Dic7—24no—
137C2×C4×Dic7—24no—
138C2×C4×Dic7—24no—
139C2×C4×Dic7—24no—
140C2×C4×Dic7C2314yes—
141C2×C4×Dic7C2314yes—
142C2×C4×Dic7C2314yes—
143C2×C4×Dic7C2314yes—
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#2512—716no—
156C2×#397—71no—
157C2×#397D711yescharacteristic, complemented
158C2×#396—71no—
159C2×#396—71no—
160C2×#390—71no—
161C2×#390—71no—
162C2×#390—71no—
163C2×#389—71no—
164C2×#388—71no—
165C2×#388—71no—
166C2×#384—71no—
167C2×C4×C4⋊C4—71no—
168C2×C4×C4⋊C4—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—28no—
211C2×C22⋊D7—28no—
212C2×C22⋊D7—28no—
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×Dic7C2×D414yes—
230C22×Dic7C2×D414yes—
231C22×Dic7#4114yes—
232C22×Dic7#4114yes—
233C22×Dic7#4114yes—
234C22×Dic7#4114yes—
235C22×Dic7C2412yes—
236C22×Dic7C2412yes—
237C22×Dic7C2412yes—
238C22×Dic7C2412yes—
239C22×Dic7C2412yes—
240C22×Dic7C2412yes—
241C22×Dic7C2412yes—
242C7×C4⋊C4—28no—
243C7×C22⋊C4—28no—
244C7×C22⋊C4—44no—
245C7×C22⋊C4—44no—
246C22⋊Dic7—28no—
247C22⋊Dic7—28no—
248C22⋊Dic7—28no—
249(C2×D7)⋊C4—28no—
250(C2×D7)⋊C4—28no—
251(C2×D7)⋊C4—28no—
252(C2×D7)⋊C4—28no—
253(C2×D7)⋊C4—44no—
254(C2×D7)⋊C4—44no—
255C4⋊Dic7—28no—
256C4⋊Dic7—28no—
257Dic7⋊C4—28no—
258Dic7⋊C4—28no—
259Dic7⋊C4—28no—
260Dic7⋊C4—28no—
261Dic7⋊C4—28no—
262Dic7⋊C4—44no—
263Dic7⋊C4—44no—
264Dic7⋊C4C2×D4116yescomplemented
265C4×Dic7—28no—
266C4×Dic7—28no—
267C4×Dic7—28no—
268C4×Dic7—28no—
269C4×Dic7—28no—
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⋊C4C2×D711yescharacteristic
286C22×C22⋊C4—71no—
287C22×C22⋊C4—71no—
288C22×C22⋊C4—71no—
289C22×C22⋊C4—71no—
290C22×C22⋊C4—71no—
291C22×C22⋊C4—71no—
292C22×C22⋊C4—71no—
293C22×C22⋊C4—71no—
294C22×C22⋊C4—71no—
295C22×C22⋊C4C2×D711yescharacteristic
296C22×C22⋊C4C2×D711yescharacteristic
297C22×C22⋊C4C2×D711yescharacteristic
298C22×C42—71no—
299C22×C42—71no—
300C22×C42—71no—
301C22×C42—71no—
302C22×C42—71no—
303#397—78no—
304#397C2×D718yescomplemented
305#396—78no—
306#396—78no—
307#390—78no—
308#390—78no—
309#390—78no—
310#389—78no—
311#388—78no—
312#388—78no—
313#384—78no—
314C4×C4⋊C4—78no—
315C4×C4⋊C4—78no—
316C2×#95—71no—
317C2×#95—71no—
318C2×#95—71no—
319C2×#95C2×D711yescharacteristic
320C2×#95C2×D711yescharacteristic
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×C7C2×#4112yes—
338C23×C7C2×#4112yes—
339C23×C7C2×#4112yes—
340C23×C7C2×#4112yes—
341C23×C7H(5,𝔽2)12yes—
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—28no—
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—44no—
402C2×Dic7—44no—
403C2×Dic7—44no—
404C2×Dic7#126116yescomplemented
405C2×Dic7C22×D414yes—
406C2×Dic7C22×D414yes—
407C2×Dic7C2×#4114yes—
408C2×Dic7C2×#4114yes—
409C2×Dic7C2×#4114yes—
410C2×Dic7C2×#4114yes—
411C25—71no—
412C25C22×D711yescharacteristic
413C22×D4—74no—
414C22×D4—144no—
415C22×D4—144no—
416C22×D4—144no—
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—78no—
434C2×C4⋊C4—74no—
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—144no—
445C2×C4⋊C4—144no—
446C2×C4⋊C4—144no—
447C2×C4⋊C4—144no—
448C2×C4⋊C4—144no—
449C2×C4⋊C4—144no—
450C2×C4⋊C4—144no—
451C2×C4⋊C4—282no—
452C2×C4⋊C4—282no—
453C2×C4⋊C4C22×D714yes—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—42no—
456C2×C22⋊C4—42no—
457C2×C22⋊C4—74no—
458C2×C22⋊C4—74no—
459C2×C22⋊C4—74no—
460C2×C22⋊C4—74no—
461C2×C22⋊C4—74no—
462C2×C22⋊C4—74no—
463C2×C22⋊C4—74no—
464C2×C22⋊C4—74no—
465C2×C22⋊C4—74no—
466C2×C22⋊C4—144no—
467C2×C22⋊C4—144no—
468C2×C22⋊C4—144no—
469C2×C22⋊C4—144no—
470C2×C22⋊C4—144no—
471C2×C22⋊C4—144no—
472C2×C22⋊C4—144no—
473C2×C22⋊C4—282no—
474C2×C22⋊C4—282no—
475C2×C22⋊C4C22×D714yes—
476C2×C22⋊C4C22×D714yes—
477C2×C22⋊C4C22×D714yes—
478C2×C42—74no—
479C2×C42—74no—
480C2×C42—74no—
481C2×C42—74no—
482C2×C42—74no—
483C2×C42—144no—
484C2×C42—144no—
485C2×C42—144no—
486C2×C42—144no—
487C2×C42—144no—
488#95—74no—
489#95—74no—
490#95—74no—
491#95C22×D714yes—
492#95C22×D714yes—
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×C7C2×#12614yes—
503C22×C7#53214yes—
504C22×C7#54214yes—
505C22×C7#54714yes—
506C22×C7#55014yes—
507C22×C7#55314yes—
508C22×C7#55614yes—
509C22×C7C23×D411yescharacteristic
510C22×C7C22×#4111yescharacteristic
511C22×C7C22×#4111yescharacteristic
512C22×C7C22×#4111yescharacteristic
513C22×C7C22×#4111yescharacteristic
514C22×C7C2×H(5,𝔽2)11yescharacteristic
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—24no—
533Dic7—42no—
534Dic7—42no—
535Dic7—42no—
536Dic7C2×#12618yescomplemented
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—148no—
555C2×D4—148no—
556C2×D4—148no—
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—74no—
578C22×C4—72no—
579C22×C4—74no—
580C22×C4—74no—
581C22×C4—74no—
582C22×C4—72no—
583C22×C4—72no—
584C22×C4—72no—
585C22×C4—72no—
586C22×C4—72no—
587C22×C4—72no—
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—716no—
612C4⋊C4—148no—
613C4⋊C4—148no—
614C4⋊C4—148no—
615C4⋊C4—148no—
616C4⋊C4—148no—
617C4⋊C4—148no—
618C4⋊C4—148no—
619C4⋊C4—284no—
620C4⋊C4—284no—
621C22⋊C4—28no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—148no—
625C22⋊C4—148no—
626C22⋊C4—148no—
627C22⋊C4—148no—
628C22⋊C4—148no—
629C22⋊C4—148no—
630C22⋊C4—148no—
631C22⋊C4—284no—
632C22⋊C4—284no—
633C42—148no—
634C42—148no—
635C42—148no—
636C42—148no—
637C42—148no—
638C2×C7—82no—
639C2×C7#251218yescomplemented
640C2×C7C22×#12611yescharacteristic
641C2×C7C2×#53211yescharacteristic
642C2×C7C2×#54211yescharacteristic
643C2×C7C2×#54711yescharacteristic
644C2×C7C2×#55011yescharacteristic
645C2×C7C2×#55311yescharacteristic
646C2×C7C2×#55611yescharacteristic
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—
678C23D7×#4112yes—
679C23D7×#4112yes—
680C23D7×#4112yes—
681C23D7×#4112yes—
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—716no—
709C2×C4—74no—
710C2×C4—74no—
711C2×C4—74no—
712C2×C4—74no—
713C2×C4—74no—
714C2×C4—74no—
715C2×C4—148no—
716C2×C4—148no—
717C2×C4—142no—
718C2×C4—142no—
719C2×C4—142no—
720C2×C4—142no—
721C2×C4—142no—
722C2×C4—148no—
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—142no—
732C2×C4—142no—
733C2×C4—284no—
734C2×C4—284no—
735C2×C4—284no—
736C2×C4C2×D4×D714yes—
737C7C2×#251211yescharacteristic, 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#9029014yes—
755C22#9034614yes—
756C22#9035214yes—
757C22#9035314yes—
758C22#9035914yes—
759C22#9039314yes—
760C22D7×#12614yes—
761C22C22×D4×D711yescharacteristic
762C22C2×#654811yescharacteristic
763C22C2×D7×#4111yescharacteristic
764C22C2×D7×#4111yescharacteristic
765C22C2×D7×#4111yescharacteristic
766C22C2×D7×#4111yescharacteristic
767C22C2×#655411yescharacteristic
768C4—24no—
769C4—42no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—78no—
775C4—144no—
776C4—144no—
777C4—144no—
778C4—282no—
779C4—282no—
780C4—282no—
781C2—82no—
782C2—562no—
783C2#1173493818yesdirect product factor
784C2C2×#9029011yescharacteristic
785C2C2×#9035311yescharacteristic
786C2C2×#9035211yescharacteristic
787C2C2×#9034611yescharacteristic
788C2C2×#9035911yescharacteristic
789C2C2×#9039311yescharacteristic
790C2C2×D7×#12611yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#397C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×#397D7
hypocenterC7C2×#2512
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C22×#6461C2semidirect
2. C22×#6442C2semidirect
3. C2×C7×#397C2semidirect
4. C2×#89748C2semidirect
5. C2×#89720C2semidirect
9. C2×#89717C2semidirect
10. #11734938C2direct (N × H)
11. C2×#89448C2semidirect
12. C2×#89446C2semidirect
13. C2×#89419C2semidirect
14. C2×#89441C2semidirect
15. C2×#89421C2semidirect
16. C2×#89421C2semidirect
47. C2×#6461C22semidirect
49. C2×#6442C22semidirect
50. C7×#397C22semidirect
57. #89748C22semidirect
61. #89720C22semidirect
62. #89717C22semidirect
63. #89448C22semidirect
64. #89446C22semidirect
65. #89441C22semidirect
66. #89421C22semidirect
67. #89421C22semidirect
68. #89419C22semidirect
126. C2×Dic7⋊C4D4semidirect
157. C2×#397D7semidirect
264. Dic7⋊C4C2×D4semidirect
304. #397C2×D7semidirect
404. C2×Dic7#126semidirect
536. Dic7C2×#126semidirect
639. C2×C7#2512semidirect
737. C7C2×#2512semidirect
783. C2#11734938direct (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×#3972
C2×#897482
C2×#897202
C2×#897292
C2×#897172
#117349382
C2×#894482
C2×#894462
C2×#894192
C2×#894412
C2×#894212
C2×#25127