Finite Group Databasebeta

← C2×#11734761 #13523874

Subgroups — C2×#11734761 #13523874

Order 1792.

3158 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×#6449C211yesmaximal, characteristic, complemented
3C2×C7×#396C211yesmaximal, characteristic, complemented
4C2×#89763C211yesmaximal, characteristic, complemented
5C2×#89756C211yesmaximal, characteristic, complemented
6C2×#89760C211yesmaximal, characteristic, complemented
7C2×#89762C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
9C2×#89732C211yesmaximal, characteristic
10C2×#89729C211yesmaximal, characteristic, complemented
11C2×#89729C211yesmaximal, characteristic, complemented
12C2×#89730C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic7C211yesmaximal, characteristic, complemented
14#11734761C2116yesmaximal, direct product factor
15C2×#89442C211yesmaximal, characteristic, complemented
16C2×#89441C211yesmaximal, characteristic, complemented
17C23×C22⋊D7C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C24×Dic7C2211yescharacteristic
20C23×D28C2211yescharacteristic
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×(C2×D7)⋊C4C2211yescharacteristic
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×C4⋊Dic7C2211yescharacteristic
39C22×C4⋊Dic7C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×C4×Dic7C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C22×C4×Dic7C2211yescharacteristic
45C22×C4×Dic7C2211yescharacteristic
46C2×#6461—28no—
47C2×#6461C2218yescomplemented
48C2×#6449—28no—
49C2×#6449C2218yescomplemented
50C7×#396C2218yescomplemented
51C2×C7×#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57#89763C2218yescomplemented
58#89762C2218yescomplemented
59#89760C2218yescomplemented
60#89756C2218yescomplemented
61C4⋊C4×Dic7C2218yescomplemented
62#89732C2218yes—
63#89730C2218yescomplemented
64#89729C2218yescomplemented
65#89729C2218yescomplemented
66C22⋊C4×Dic7C2218yescomplemented
67#89442C2218yescomplemented
68#89441C2218yescomplemented
69C2×#2554—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—24no—
82C22×C22⋊D7—24no—
83C22×C22⋊D7—42no—
84C22×C22⋊D7—42no—
85C22×C22⋊D7C2314yes—
86C22×C22⋊D7C2314yes—
87C23×Dic7—24no—
88C23×Dic7—24no—
89C23×Dic7—42no—
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2314yes—
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2311yescharacteristic
96C23×Dic7C2311yescharacteristic
97C22×D28—24no—
98C22×D28—42no—
99C22×D28—42no—
100C22×D28C2314yes—
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⋊Dic7C2314yes—
115C2×(C2×D7)⋊C4—24no—
116C2×(C2×D7)⋊C4—24no—
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)⋊C4C2314yes—
126C2×(C2×D7)⋊C4C2314yes—
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×C4⋊Dic7—24no—
136C2×C4⋊Dic7D418yescomplemented
137C2×C4⋊Dic7C2314yes—
138C2×C4⋊Dic7C2314yes—
139C2×Dic7⋊C4—24no—
140C2×Dic7⋊C4—42no—
141C2×Dic7⋊C4C2314yes—
142C2×Dic7⋊C4C2314yes—
143C2×C4×Dic7—24no—
144C2×C4×Dic7—24no—
145C2×C4×Dic7—42no—
146C2×C4×Dic7—42no—
147C2×C4×Dic7C2314yes—
148C2×C4×Dic7C2314yes—
149C2×C4×Dic7C2314yes—
150C2×C4×Dic7C2314yes—
151#6461—232no—
152#6449—232no—
153C7×#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×#126—71no—
160C22×#123—71no—
161#2554—716no—
162C2×#398—71no—
163C2×#396D711yescharacteristic, complemented
164C2×#394—71no—
165C2×#392—71no—
166C2×#390—71no—
167C2×#390—71no—
168C2×#390—71no—
169C2×#388—71no—
170C2×#388—71no—
171C2×#388—71no—
172C2×#386—71no—
173C2×C4×C4⋊C4—71no—
174C2×C4×C22⋊C4—71no—
175C24×C7—22no—
176C24×C7—22no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7—22no—
180C24×C7—22no—
181C24×C7#4114yes—
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—28no—
227C2×C22⋊D7—28no—
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—28no—
244C22×Dic7—22no—
245C22×Dic7—22no—
246C22×Dic7—22no—
247C22×Dic7—28no—
248C22×Dic7—44no—
249C22×Dic7—416no—
250C22×Dic7C2×D414yes—
251C22×Dic7C2×D414yes—
252C22×Dic7#4114yes—
253C22×Dic7#4114yes—
254C22×Dic7C2412yes—
255C22×Dic7C2412yes—
256C22×Dic7C2412yes—
257C22×Dic7C2412yes—
258C22×Dic7C2412yes—
259C22×Dic7C2412yes—
260C2×D28—28no—
261C2×D28—44no—
262C2×D28—44no—
263C2×D28—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—
271(C2×D7)⋊C4—28no—
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—28no—
279(C2×D7)⋊C4—44no—
280(C2×D7)⋊C4—44no—
281C4⋊Dic7—28no—
282C4⋊Dic7C2×D4116yescomplemented
283Dic7⋊C4—28no—
284Dic7⋊C4—44no—
285C4×Dic7—28no—
286C4×Dic7—28no—
287C4×Dic7—44no—
288C4×Dic7—44no—
289C23×D4—71no—
290C23×D4—71no—
291C23×D4—71no—
292C24×C4—71no—
293C2×#126—78no—
294C2×#126—148no—
295C2×#123—78no—
296C2×#123—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⋊C4C2×D711yescharacteristic
316C22×C22⋊C4C2×D711yescharacteristic
317C22×C22⋊C4C2×D711yescharacteristic
318C22×C42—71no—
319C22×C42—71no—
320C22×C42—71no—
321C22×C42—71no—
322#398—78no—
323#396C2×D718yescomplemented
324#394—78no—
325#392—78no—
326#390—78no—
327#390—78no—
328#390—78no—
329#388—78no—
330#388—78no—
331#388—78no—
332#386—78no—
333C4×C4⋊C4—78no—
334C4×C22⋊C4—78no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95C2×D711yescharacteristic
341C23×C7—28no—
342C23×C7—28no—
343C23×C7—28no—
344C23×C7—22no—
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7—44no—
351C23×C7—44no—
352C23×C7—44no—
353C23×C7—44no—
354C23×C7C22×D412yes—
355C23×C7C2×#4112yes—
356C23×C7C2×#4114yes—
357C23×C7C2×#4112yes—
358C23×C7C2×#4112yes—
359C23×C7C2×#4112yes—
360C23×C7H(5,𝔽2)12yes—
361C23×C7H(5,𝔽2)12yes—
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—28no—
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—416no—
436C2×Dic7—44no—
437C2×Dic7—44no—
438C2×Dic7C22×D414yes—
439C2×Dic7C22×D414yes—
440C2×Dic7C2×#4114yes—
441C2×Dic7C2×#4114yes—
442D28—416no—
443C25—71no—
444C25—71no—
445C25C22×D711yescharacteristic
446C22×D4—74no—
447C22×D4—74no—
448C22×D4—74no—
449C22×D4—144no—
450C22×D4—144no—
451C22×D4—144no—
452C22×D4—144no—
453C22×D4—144no—
454C22×D4—282no—
455C22×D4—282no—
456C22×D4—282no—
457C22×D4—282no—
458C23×C4—71no—
459C23×C4—71no—
460C23×C4—71no—
461C23×C4—71no—
462C23×C4—71no—
463C23×C4—71no—
464C23×C4—74no—
465C23×C4—144no—
466C23×C4—144no—
467C23×C4—282no—
468C23×C4C22×D711yescharacteristic
469C23×C4C22×D711yescharacteristic
470C23×C4C22×D711yescharacteristic
471C23×C4C22×D711yescharacteristic
472C23×C4C22×D711yescharacteristic
473C23×C4C22×D711yescharacteristic
474#126—1432no—
475#123—1432no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—78no—
480C2×C4⋊C4—74no—
481C2×C4⋊C4—74no—
482C2×C4⋊C4—74no—
483C2×C4⋊C4—74no—
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—144no—
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—144no—
513C2×C22⋊C4—282no—
514C2×C22⋊C4—282no—
515C2×C22⋊C4C22×D714yes—
516C2×C22⋊C4C22×D714yes—
517C2×C22⋊C4C22×D714yes—
518C2×C42—74no—
519C2×C42—74no—
520C2×C42—74no—
521C2×C42—74no—
522C2×C42—144no—
523C2×C42—144no—
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—24no—
533C22×C7—24no—
534C22×C7—24no—
535C22×C7—42no—
536C22×C7—42no—
537C22×C7—42no—
538C22×C7—42no—
539C22×C7—416no—
540C22×C7#52914yes—
541C22×C7#53214yes—
542C22×C7#53814yes—
543C22×C7#54614yes—
544C22×C7#55014yes—
545C22×C7#55114yes—
546C22×C7#55314yes—
547C22×C7C23×D411yescharacteristic
548C22×C7C22×#4111yescharacteristic
549C22×C7C22×#4111yescharacteristic
550C22×C7C22×#4111yescharacteristic
551C22×C7C22×#4111yescharacteristic
552C22×C7C2×H(5,𝔽2)11yescharacteristic
553C22×C7C2×H(5,𝔽2)11yescharacteristic
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—24no—
580Dic7—42no—
581Dic7—42no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—72no—
589C24—72no—
590C24—142no—
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#116114yes—
605C24C23×D712yes—
606C24C23×D711yescharacteristic
607C2×D4—148no—
608C2×D4—148no—
609C2×D4—148no—
610C2×D4—148no—
611C2×D4—148no—
612C2×D4—284no—
613C2×D4—284no—
614C2×D4—2816no—
615C2×D4—284no—
616C2×D4—284no—
617C2×D4—2816no—
618C2×D4—2816no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
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—74no—
636C22×C4—74no—
637C22×C4—74no—
638C22×C4—74no—
639C22×C4—72no—
640C22×C4—72no—
641C22×C4—72no—
642C22×C4—72no—
643C22×C4—72no—
644C22×C4—72no—
645C22×C4—148no—
646C22×C4—142no—
647C22×C4—142no—
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—148no—
658C22×C4—142no—
659C22×C4—142no—
660C22×C4—142no—
661C22×C4—284no—
662C22×C4—2816no—
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—716no—
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—148no—
689C22⋊C4—148no—
690C22⋊C4—284no—
691C22⋊C4—284no—
692C42—148no—
693C42—148no—
694C42—284no—
695C42—284no—
696C2×C7—44no—
697C2×C7#255418yescomplemented
698C2×C7C2×#52911yescharacteristic
699C2×C7C2×#53211yescharacteristic
700C2×C7C2×#53811yescharacteristic
701C2×C7C2×#54611yescharacteristic
702C2×C7C2×#55011yescharacteristic
703C2×C7C2×#55111yescharacteristic
704C2×C7C2×#55311yescharacteristic
705D7—82no—
706D7—82no—
707C23—28no—
708C23—28no—
709C23—28no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—142no—
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—284no—
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—
748C23C2×D4×D712yes—
749C23C2×#115912yes—
750C23#654812yes—
751C23C2×#116114yes—
752C23C2×#116112yes—
753C23D7×#4112yes—
754C23D7×#4112yes—
755C23#655312yes—
756C23C24×D711yescharacteristic
757D4—2816no—
758D4—2816no—
759D4—2816no—
760C2×C4—28no—
761C2×C4—28no—
762C2×C4—22no—
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—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—74no—
783C2×C4—74no—
784C2×C4—74no—
785C2×C4—74no—
786C2×C4—148no—
787C2×C4—148no—
788C2×C4—148no—
789C2×C4—148no—
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—2816no—
805C2×C4—284no—
806C2×C4—284no—
807C2×C4C2×D4×D714yes—
808C2×C4C2×#115914yes—
809C7C2×#255411yescharacteristic, complemented, Sylow
810C22—24no—
811C22—24no—
812C22—24no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—416no—
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#9029014yes—
836C22#9030814yes—
837C22#9031514yes—
838C22#9032114yes—
839C22#9032814yes—
840C22#9040014yes—
841C22C22×D4×D711yescharacteristic
842C22C22×#115911yescharacteristic
843C22C2×#654811yescharacteristic
844C22C22×#116111yescharacteristic
845C22C2×D7×#4111yescharacteristic
846C22C2×D7×#4111yescharacteristic
847C22C2×#655311yescharacteristic
848C4—24no—
849C4—24no—
850C4—42no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—144no—
855C4—144no—
856C4—144no—
857C4—144no—
858C4—282no—
859C4—282no—
860C2—44no—
861C2—562no—
862C2—562no—
863C2#1173476118yesdirect product factor
864C2C2×#9028711yescharacteristic
865C2C2×#9029011yescharacteristic
866C2C2×#9030811yescharacteristic
867C2C2×#9031511yescharacteristic
868C2C2×#9032111yescharacteristic
869C2C2×#9032811yescharacteristic
870C2C2×#9040011yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#396C2
socleC24×C7C24
prime radicalC2×#89732C2
hypercenterC2×#396D7
hypocenterC7C2×#2554
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×#6449C2semidirect
3. C2×C7×#396C2semidirect
4. C2×#89763C2semidirect
5. C2×#89756C2semidirect
6. C2×#89760C2semidirect
7. C2×#89762C2semidirect
8. C2×C4⋊C4×Dic7C2semidirect
10. C2×#89729C2semidirect
11. C2×#89729C2semidirect
12. C2×#89730C2semidirect
13. C2×C22⋊C4×Dic7C2semidirect
14. #11734761C2direct (N × H)
15. C2×#89442C2semidirect
16. C2×#89441C2semidirect
47. C2×#6461C22semidirect
49. C2×#6449C22semidirect
50. C7×#396C22semidirect
57. #89763C22semidirect
58. #89762C22semidirect
59. #89760C22semidirect
60. #89756C22semidirect
61. C4⋊C4×Dic7C22semidirect
63. #89730C22semidirect
64. #89729C22semidirect
65. #89729C22semidirect
66. C22⋊C4×Dic7C22semidirect
67. #89442C22semidirect
68. #89441C22semidirect
136. C2×C4⋊Dic7D4semidirect
163. C2×#396D7semidirect
282. C4⋊Dic7C2×D4semidirect
323. #396C2×D7semidirect
697. C2×C7#2554semidirect
809. C7C2×#2554semidirect
863. C2#11734761direct (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×#64492
C2×C7×#3962
C2×#897632
C2×#897562
C2×#897602
C2×#897622
C2×C4⋊C4×Dic72
C2×#897322
C2×#897292
C2×#897302
C2×C22⋊C4×Dic72
#117347612
C2×#894422
C2×#894412
C2×#25547