Finite Group Databasebeta

← C2×#11734789 #13520530

Subgroups — C2×#11734789 #13520530

Order 1792.

3002 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6461C211yesmaximal, characteristic, complemented
2C22×#6448C211yesmaximal, characteristic, complemented
3C2×C7×#396C211yesmaximal, characteristic, complemented
4C2×#89766C211yesmaximal, characteristic, complemented
5C2×#89763C211yesmaximal, characteristic, complemented
6C2×#89751C211yesmaximal, characteristic, complemented
7C2×#89760C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
9C2×#89731C211yesmaximal, characteristic, complemented
10C2×#89732C211yesmaximal, characteristic
11C2×#89733C211yesmaximal, characteristic, complemented
12C2×#89729C211yesmaximal, characteristic, complemented
13C2×#89723C211yesmaximal, characteristic, complemented
14#11734789C2116yesmaximal, direct product factor
15C2×#89445C211yesmaximal, characteristic, complemented
16C2×#89442C211yesmaximal, characteristic, complemented
17C23×C22⋊D7C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×D28C2211yescharacteristic
20C23×Dic14C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×(C2×D7)⋊C4C2211yescharacteristic
30C22×(C2×D7)⋊C4C2211yescharacteristic
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×C4⋊Dic7C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C22×C4×Dic7C2211yescharacteristic
45C22×C4×Dic7C2211yescharacteristic
46C2×#6461—28no—
47C2×#6461C2218yescomplemented
48C2×#6448—28no—
49C2×#6448C2218yescomplemented
50C7×#396C2218yescomplemented
51C2×C7×#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57#89766C2218yescomplemented
58#89763C2218yescomplemented
59#89760C2218yescomplemented
60#89751C2218yescomplemented
61C4⋊C4×Dic7C2218yescomplemented
62#89733C2218yescomplemented
63#89732C2218yes—
64#89731C2218yescomplemented
65#89729C2218yescomplemented
66#89723C2218yescomplemented
67#89445C2218yescomplemented
68#89442C2218yescomplemented
69C2×#2662—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C24×D7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C22×C22⋊D7—24no—
80C22×C22⋊D7—24no—
81C22×C22⋊D7—42no—
82C22×C22⋊D7—42no—
83C22×C22⋊D7—42no—
84C22×C22⋊D7—42no—
85C22×C22⋊D7C2314yes—
86C22×C22⋊D7C2314yes—
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C22×D28—24no—
94C22×D28—42no—
95C22×D28—42no—
96C22×D28C2314yes—
97C22×Dic14—24no—
98C22×Dic14—42no—
99C22×Dic14—42no—
100C22×Dic14C2314yes—
101C2×C7×C4⋊C4—24no—
102C2×C7×C4⋊C4—24no—
103C2×C7×C4⋊C4—42no—
104C2×C7×C4⋊C4C2314yes—
105C2×C7×C4⋊C4C2314yes—
106C2×C7×C4⋊C4C2314yes—
107C2×C7×C22⋊C4—24no—
108C2×C7×C22⋊C4—24no—
109C2×C7×C22⋊C4—42no—
110C2×C7×C22⋊C4C2314yes—
111C2×C7×C22⋊C4C2314yes—
112C2×C7×C22⋊C4C2314yes—
113C2×C22⋊Dic7—24no—
114C2×C22⋊Dic7—42no—
115C2×C22⋊Dic7C2314yes—
116C2×C22⋊Dic7C2314yes—
117C2×(C2×D7)⋊C4—24no—
118C2×(C2×D7)⋊C4—24no—
119C2×(C2×D7)⋊C4—24no—
120C2×(C2×D7)⋊C4—24no—
121C2×(C2×D7)⋊C4—24no—
122C2×(C2×D7)⋊C4—24no—
123C2×(C2×D7)⋊C4—42no—
124C2×(C2×D7)⋊C4—42no—
125C2×(C2×D7)⋊C4—42no—
126C2×(C2×D7)⋊C4—42no—
127C2×(C2×D7)⋊C4C2314yes—
128C2×(C2×D7)⋊C4C2314yes—
129C2×(C2×D7)⋊C4C2314yes—
130C2×(C2×D7)⋊C4C2314yes—
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×C4⋊Dic7—24no—
138C2×C4⋊Dic7—24no—
139C2×C4⋊Dic7C2314yes—
140C2×C4⋊Dic7C2314yes—
141C2×Dic7⋊C4—24no—
142C2×Dic7⋊C4—42no—
143C2×Dic7⋊C4C2314yes—
144C2×Dic7⋊C4C2314yes—
145C2×C4×Dic7—42no—
146C2×C4×Dic7—42no—
147C2×C4×Dic7D418yescomplemented
148C2×C4×Dic7C2314yes—
149C2×C4×Dic7C2314yes—
150C2×C4×Dic7C2314yes—
151#6461—232no—
152#6448—232no—
153C7×#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×#126—71no—
160C22×#124—71no—
161#2662—716no—
162C2×#396—71no—
163C2×#396D711yescharacteristic, complemented
164C2×#395—71no—
165C2×#394—71no—
166C2×#394—71no—
167C2×#394—71no—
168C2×#393—71no—
169C2×#392—71no—
170C2×#390—71no—
171C2×#390—71no—
172C2×#388—71no—
173C2×#388—71no—
174C2×C4×C4⋊C4—71no—
175C24×C7—22no—
176C24×C7—22no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7—22no—
180C24×C7—22no—
181C24×C7—22no—
182C24×C7C2412yes—
183C24×C7C2411yescharacteristic
184C23×D7—22no—
185C23×D7—22no—
186C23×D7—22no—
187C23×D7—22no—
188C23×D7—22no—
189C23×D7—22no—
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×D7C2412yes—
199C23×D7C2412yes—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
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×C7C2×D414yes—
217C22×C4×C7#4114yes—
218C22×C4×C7C2412yes—
219C22×C4×C7C2412yes—
220C22×C4×C7C2412yes—
221C22×C4×C7C2412yes—
222C22×C4×C7C2412yes—
223C22×C4×C7C2412yes—
224C2×C22⋊D7—28no—
225C2×C22⋊D7—28no—
226C2×C22⋊D7—44no—
227C2×C22⋊D7—44no—
228C2×C22⋊D7—44no—
229C2×C22⋊D7—44no—
230C2×C22⋊D7—416no—
231C2×C22⋊D7—416no—
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×Dic7—22no—
241C22×Dic7—22no—
242C22×Dic7—22no—
243C22×Dic7—22no—
244C22×Dic7—22no—
245C22×Dic7—22no—
246C22×Dic7—22no—
247C22×Dic7C2×D414yes—
248C22×Dic7C2×D414yes—
249C22×Dic7#4114yes—
250C22×Dic7C2412yes—
251C22×Dic7C2412yes—
252C22×Dic7C2412yes—
253C22×Dic7C2412yes—
254C22×Dic7C2412yes—
255C22×Dic7C2412yes—
256C2×D28—28no—
257C2×D28—44no—
258C2×D28—44no—
259C2×D28—416no—
260C2×Dic14—28no—
261C2×Dic14—44no—
262C2×Dic14—44no—
263C2×Dic14—416no—
264C7×C4⋊C4—28no—
265C7×C4⋊C4—28no—
266C7×C4⋊C4—44no—
267C7×C22⋊C4—28no—
268C7×C22⋊C4—28no—
269C7×C22⋊C4—44no—
270C22⋊Dic7—28no—
271C22⋊Dic7—44no—
272(C2×D7)⋊C4—28no—
273(C2×D7)⋊C4—28no—
274(C2×D7)⋊C4—28no—
275(C2×D7)⋊C4—28no—
276(C2×D7)⋊C4—28no—
277(C2×D7)⋊C4—28no—
278(C2×D7)⋊C4—44no—
279(C2×D7)⋊C4—44no—
280(C2×D7)⋊C4—44no—
281(C2×D7)⋊C4—44no—
282C4⋊Dic7—28no—
283C4⋊Dic7—28no—
284Dic7⋊C4—28no—
285Dic7⋊C4—44no—
286C4×Dic7—44no—
287C4×Dic7—44no—
288C4×Dic7C2×D4116yescomplemented
289C23×Q8—71no—
290C23×D4—71no—
291C23×D4—71no—
292C23×D4—71no—
293C2×#126—78no—
294C2×#126—148no—
295C2×#124—78no—
296C2×#124—148no—
297C22×C4⋊C4—71no—
298C22×C4⋊C4—71no—
299C22×C4⋊C4—71no—
300C22×C4⋊C4—71no—
301C22×C4⋊C4C2×D711yescharacteristic
302C22×C4⋊C4C2×D711yescharacteristic
303C22×C4⋊C4C2×D711yescharacteristic
304C22×C22⋊C4—71no—
305C22×C22⋊C4—71no—
306C22×C22⋊C4—71no—
307C22×C22⋊C4—71no—
308C22×C22⋊C4—71no—
309C22×C22⋊C4—71no—
310C22×C22⋊C4—71no—
311C22×C22⋊C4—71no—
312C22×C22⋊C4—71no—
313C22×C22⋊C4—71no—
314C22×C22⋊C4—71no—
315C22×C22⋊C4—71no—
316C22×C22⋊C4C2×D711yescharacteristic
317C22×C22⋊C4C2×D711yescharacteristic
318C22×C22⋊C4C2×D711yescharacteristic
319C22×C42—71no—
320C22×C42—71no—
321C22×C42—71no—
322#396—78no—
323#396C2×D718yescomplemented
324#395—78no—
325#394—78no—
326#394—78no—
327#394—78no—
328#393—78no—
329#392—78no—
330#390—78no—
331#390—78no—
332#388—78no—
333#388—78no—
334C4×C4⋊C4—78no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95C2×D711yescharacteristic
341C23×C7—22no—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—22no—
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—44no—
349C23×C7—44no—
350C23×C7—44no—
351C23×C7—44no—
352C23×C7—44no—
353C23×C7—44no—
354C23×C7—44no—
355C23×C7C22×D412yes—
356C23×C7C2×#4112yes—
357C23×C7C2×#4112yes—
358C23×C7H(5,𝔽2)12yes—
359C23×C7H(5,𝔽2)12yes—
360C23×C7H(5,𝔽2)12yes—
361C23×C72−1+412yes—
362C23×C7C2511yescharacteristic
363C22×D7—22no—
364C22×D7—22no—
365C22×D7—22no—
366C22×D7—22no—
367C22×D7—22no—
368C22×D7—22no—
369C22×D7—22no—
370C22×D7—22no—
371C22×D7—22no—
372C22×D7—22no—
373C22×D7—22no—
374C22×D7—22no—
375C22×D7—22no—
376C22×D7—22no—
377C22×D7—44no—
378C22×D7—44no—
379C22×D7—44no—
380C22×D7—44no—
381C22×D7—44no—
382C22×D7—44no—
383C22×D7—44no—
384C22×D7—44no—
385C22×D7—44no—
386C22×D7—44no—
387C22×D7—44no—
388C22×D7—44no—
389C22×D7—44no—
390C22×D7—44no—
391C2×C4×C7—28no—
392C2×C4×C7—28no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—44no—
410C2×C4×C7—44no—
411C2×C4×C7—44no—
412C2×C4×C7—44no—
413C2×C4×C7C22×D414yes—
414C2×C4×C7C2×#4114yes—
415C22⋊D7—416no—
416C22⋊D7—416no—
417C2×Dic7—28no—
418C2×Dic7—28no—
419C2×Dic7—28no—
420C2×Dic7—22no—
421C2×Dic7—22no—
422C2×Dic7—22no—
423C2×Dic7—22no—
424C2×Dic7—22no—
425C2×Dic7—22no—
426C2×Dic7—22no—
427C2×Dic7—22no—
428C2×Dic7—22no—
429C2×Dic7—22no—
430C2×Dic7—22no—
431C2×Dic7—22no—
432C2×Dic7—22no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—44no—
436C2×Dic7—44no—
437C2×Dic7—44no—
438C2×Dic7C22×D414yes—
439C2×Dic7C22×D414yes—
440C2×Dic7C2×#4114yes—
441D28—416no—
442Dic14—416no—
443C25—71no—
444C25—71no—
445C25C22×D711yescharacteristic
446C22×Q8—74no—
447C22×Q8—144no—
448C22×Q8—282no—
449C22×Q8—282no—
450C22×D4—74no—
451C22×D4—74no—
452C22×D4—74no—
453C22×D4—144no—
454C22×D4—144no—
455C22×D4—144no—
456C22×D4—282no—
457C22×D4—282no—
458C22×D4—282no—
459C22×D4—282no—
460C22×D4—282no—
461C22×D4—282no—
462C23×C4—71no—
463C23×C4—71no—
464C23×C4—71no—
465C23×C4—71no—
466C23×C4—71no—
467C23×C4—71no—
468C23×C4C22×D711yescharacteristic
469C23×C4C22×D711yescharacteristic
470C23×C4C22×D711yescharacteristic
471C23×C4C22×D711yescharacteristic
472C23×C4C22×D711yescharacteristic
473C23×C4C22×D711yescharacteristic
474#126—1432no—
475#124—1432no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—74no—
480C2×C4⋊C4—74no—
481C2×C4⋊C4—74no—
482C2×C4⋊C4—74no—
483C2×C4⋊C4—144no—
484C2×C4⋊C4—144no—
485C2×C4⋊C4—144no—
486C2×C4⋊C4—282no—
487C2×C4⋊C4C22×D714yes—
488C2×C4⋊C4C22×D714yes—
489C2×C4⋊C4C22×D714yes—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—74no—
494C2×C22⋊C4—74no—
495C2×C22⋊C4—74no—
496C2×C22⋊C4—74no—
497C2×C22⋊C4—74no—
498C2×C22⋊C4—74no—
499C2×C22⋊C4—74no—
500C2×C22⋊C4—74no—
501C2×C22⋊C4—74no—
502C2×C22⋊C4—74no—
503C2×C22⋊C4—74no—
504C2×C22⋊C4—74no—
505C2×C22⋊C4—144no—
506C2×C22⋊C4—144no—
507C2×C22⋊C4—144no—
508C2×C22⋊C4—144no—
509C2×C22⋊C4—144no—
510C2×C22⋊C4—144no—
511C2×C22⋊C4—144no—
512C2×C22⋊C4—282no—
513C2×C22⋊C4—282no—
514C2×C22⋊C4—282no—
515C2×C22⋊C4—282no—
516C2×C22⋊C4—282no—
517C2×C22⋊C4C22×D714yes—
518C2×C22⋊C4C22×D714yes—
519C2×C22⋊C4C22×D714yes—
520C2×C42—78no—
521C2×C42—74no—
522C2×C42—74no—
523C2×C42—74no—
524C2×C42—282no—
525C2×C42—282no—
526#95—74no—
527#95—74no—
528#95—74no—
529#95—74no—
530#95—74no—
531#95C22×D714yes—
532C22×C7—42no—
533C22×C7—42no—
534C22×C7—42no—
535C22×C7—42no—
536C22×C7—42no—
537C22×C7—42no—
538C22×C7—42no—
539C22×C7—88no—
540C22×C7#53214yes—
541C22×C7#53514yes—
542C22×C7#53714yes—
543C22×C7#53814yes—
544C22×C7#53814yes—
545C22×C7#54214yes—
546C22×C7#54214yes—
547C22×C7C23×D411yescharacteristic
548C22×C7C22×#4111yescharacteristic
549C22×C7C22×#4111yescharacteristic
550C22×C7C2×H(5,𝔽2)11yescharacteristic
551C22×C7C2×H(5,𝔽2)11yescharacteristic
552C22×C7C2×H(5,𝔽2)11yescharacteristic
553C22×C7C2×2−1+411yescharacteristic
554C2×D7—42no—
555C2×D7—42no—
556C2×D7—42no—
557C2×D7—42no—
558C2×D7—42no—
559C2×D7—42no—
560C2×D7—42no—
561C2×D7—42no—
562C2×D7—42no—
563C2×D7—42no—
564C2×D7—42no—
565C2×D7—42no—
566C2×D7—42no—
567C2×D7—42no—
568C2×D7—88no—
569C2×D7—88no—
570C4×C7—24no—
571C4×C7—24no—
572C4×C7—42no—
573C4×C7—42no—
574C4×C7—42no—
575C4×C7—42no—
576Dic7—24no—
577Dic7—24no—
578Dic7—24no—
579Dic7—42no—
580Dic7—42no—
581Dic7—42no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—72no—
590C24—72no—
591C24—142no—
592C24—142no—
593C24—142no—
594C24—142no—
595C24—142no—
596C24—142no—
597C24—142no—
598C24—142no—
599C24—142no—
600C24—142no—
601C24—142no—
602C24—142no—
603C24—142no—
604C24—142no—
605C24C23×D712yes—
606C24C23×D711yescharacteristic
607C2×Q8—148no—
608C2×Q8—284no—
609C2×Q8—284no—
610C2×Q8—2816no—
611C2×D4—148no—
612C2×D4—148no—
613C2×D4—148no—
614C2×D4—284no—
615C2×D4—284no—
616C2×D4—2816no—
617C2×D4—284no—
618C2×D4—284no—
619C2×D4—284no—
620C2×D4—284no—
621C2×D4—2816no—
622C2×D4—2816no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—74no—
640C22×C4—74no—
641C22×C4—74no—
642C22×C4—72no—
643C22×C4—72no—
644C22×C4—72no—
645C22×C4—72no—
646C22×C4—72no—
647C22×C4—72no—
648C22×C4—142no—
649C22×C4—142no—
650C22×C4—142no—
651C22×C4—142no—
652C22×C4—142no—
653C22×C4—142no—
654C22×C4—142no—
655C22×C4—142no—
656C22×C4—142no—
657C22×C4—142no—
658C22×C4—142no—
659C22×C4—142no—
660C22×C4—142no—
661C22×C4—142no—
662C22×C4—142no—
663C22×C4D4×D714yes—
664C22×C4#115914yes—
665C22×C4C23×D712yes—
666C22×C4C23×D712yes—
667C22×C4C23×D712yes—
668C22×C4C23×D712yes—
669C22×C4C23×D712yes—
670C22×C4C23×D712yes—
671C4⋊C4—28no—
672C4⋊C4—28no—
673C4⋊C4—44no—
674C4⋊C4—148no—
675C4⋊C4—148no—
676C4⋊C4—148no—
677C4⋊C4—284no—
678C22⋊C4—28no—
679C22⋊C4—28no—
680C22⋊C4—44no—
681C22⋊C4—148no—
682C22⋊C4—148no—
683C22⋊C4—148no—
684C22⋊C4—148no—
685C22⋊C4—148no—
686C22⋊C4—148no—
687C22⋊C4—148no—
688C22⋊C4—284no—
689C22⋊C4—284no—
690C22⋊C4—284no—
691C22⋊C4—284no—
692C22⋊C4—284no—
693C42—716no—
694C42—284no—
695C42—284no—
696C2×C7—82no—
697C2×C7#266218yescomplemented
698C2×C7C2×#53211yescharacteristic
699C2×C7C2×#53511yescharacteristic
700C2×C7C2×#53711yescharacteristic
701C2×C7C2×#53811yescharacteristic
702C2×C7C2×#53811yescharacteristic
703C2×C7C2×#54211yescharacteristic
704C2×C7C2×#54211yescharacteristic
705D7—82no—
706D7—82no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—142no—
722C23—142no—
723C23—142no—
724C23—142no—
725C23—142no—
726C23—142no—
727C23—142no—
728C23—142no—
729C23—142no—
730C23—142no—
731C23—142no—
732C23—142no—
733C23—142no—
734C23—142no—
735C23—284no—
736C23—284no—
737C23—284no—
738C23—284no—
739C23—284no—
740C23—284no—
741C23—284no—
742C23—284no—
743C23—284no—
744C23—284no—
745C23—284no—
746C23—284no—
747C23—284no—
748C23—284no—
749C23C2×D4×D712yes—
750C23C2×#115912yes—
751C23#654812yes—
752C23#655112yes—
753C23D7×#4112yes—
754C23#655312yes—
755C23#655312yes—
756C23C24×D711yescharacteristic
757Q8—2816no—
758D4—2816no—
759D4—2816no—
760D4—2816no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—74no—
784C2×C4—74no—
785C2×C4—74no—
786C2×C4—148no—
787C2×C4—148no—
788C2×C4—148no—
789C2×C4—142no—
790C2×C4—142no—
791C2×C4—142no—
792C2×C4—142no—
793C2×C4—142no—
794C2×C4—142no—
795C2×C4—142no—
796C2×C4—142no—
797C2×C4—142no—
798C2×C4—142no—
799C2×C4—142no—
800C2×C4—142no—
801C2×C4—142no—
802C2×C4—142no—
803C2×C4—142no—
804C2×C4—284no—
805C2×C4—284no—
806C2×C4—284no—
807C2×C4C2×D4×D714yes—
808C2×C4C2×#115914yes—
809C7C2×#266211yescharacteristic, complemented, Sylow
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—88no—
818C22—282no—
819C22—282no—
820C22—282no—
821C22—282no—
822C22—282no—
823C22—282no—
824C22—282no—
825C22—282no—
826C22—282no—
827C22—282no—
828C22—282no—
829C22—282no—
830C22—282no—
831C22—282no—
832C22—568no—
833C22—568no—
834C22#9028714yes—
835C22#9029814yes—
836C22#9030814yes—
837C22#9032014yes—
838C22#9033114yes—
839C22#9033414yes—
840C22#9039514yes—
841C22C22×D4×D711yescharacteristic
842C22C22×#115911yescharacteristic
843C22C2×#654811yescharacteristic
844C22C2×#655111yescharacteristic
845C22C2×D7×#4111yescharacteristic
846C22C2×#655311yescharacteristic
847C22C2×#655311yescharacteristic
848C4—24no—
849C4—24no—
850C4—42no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—144no—
855C4—144no—
856C4—144no—
857C4—282no—
858C4—282no—
859C4—282no—
860C2—82no—
861C2—562no—
862C2—562no—
863C2#1173478918yesdirect product factor
864C2C2×#9028711yescharacteristic
865C2C2×#9029811yescharacteristic
866C2C2×#9030811yescharacteristic
867C2C2×#9033411yescharacteristic
868C2C2×#9033111yescharacteristic
869C2C2×#9032011yescharacteristic
870C2C2×#9039511yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#396C2
socleC24×C7C24
prime radicalC2×#89732C2
hypercenterC2×#396D7
hypocenterC7C2×#2662
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×#6448C2semidirect
3. C2×C7×#396C2semidirect
4. C2×#89766C2semidirect
5. C2×#89763C2semidirect
6. C2×#89751C2semidirect
7. C2×#89760C2semidirect
8. C2×C4⋊C4×Dic7C2semidirect
9. C2×#89731C2semidirect
11. C2×#89733C2semidirect
12. C2×#89729C2semidirect
13. C2×#89723C2semidirect
14. #11734789C2direct (N × H)
15. C2×#89445C2semidirect
16. C2×#89442C2semidirect
47. C2×#6461C22semidirect
49. C2×#6448C22semidirect
50. C7×#396C22semidirect
57. #89766C22semidirect
58. #89763C22semidirect
59. #89760C22semidirect
60. #89751C22semidirect
61. C4⋊C4×Dic7C22semidirect
62. #89733C22semidirect
64. #89731C22semidirect
65. #89729C22semidirect
66. #89723C22semidirect
67. #89445C22semidirect
68. #89442C22semidirect
147. C2×C4×Dic7D4semidirect
163. C2×#396D7semidirect
288. C4×Dic7C2×D4semidirect
323. #396C2×D7semidirect
697. C2×C7#2662semidirect
809. C7C2×#2662semidirect
863. C2#11734789direct (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×#64482
C2×C7×#3962
C2×#897662
C2×#897632
C2×#897512
C2×#897602
C2×C4⋊C4×Dic72
C2×#897312
C2×#897322
C2×#897332
C2×#897292
C2×#897232
#117347892
C2×#894452
C2×#894422
C2×#26627